dlib C++ Library - layers_abstract.h (original) (raw)

// Copyright (C) 2015 Davis E. King (davis@dlib.net) // License: Boost Software License See LICENSE.txt for the full license. #undef DLIB_DNn_LAYERS_ABSTRACT_H_ #ifdef DLIB_DNn_LAYERS_ABSTRACT_H_

#include "../cuda/tensor_abstract.h" #include "core_abstract.h" #include "../cuda/operation_mode.h"

namespace dlib {

// ----------------------------------------------------------------------------------------

class **SUBNET** 
**{**
    /*!
        WHAT THIS OBJECT REPRESENTS
            This object represents a deep neural network.  In particular, it is
            the simplified interface through which layer objects interact with their
            subnetworks.  A layer's two important tasks are to (1) take outputs from its
            subnetwork and forward propagate them through itself and (2) to backwards
            propagate an error gradient through itself and onto its subnetwork.
            The idea of a subnetwork is illustrated in the following diagram:

              +---------------------------------------------------------+
              | loss <-- layer1 <-- layer2 <-- ... <-- layern <-- input |
              +---------------------------------------------------------+
                                  ^                            ^
                                  \__ subnetwork for layer1 __/

            Therefore, by "subnetwork" we mean the part of the network closer to the
            input.

            Note that there is no dlib::SUBNET type.  It is shown here purely to
            document the interface layer objects expect to see when they interact
            with a network.
    !*/

public:
    // You aren't allowed to copy subnetworks from inside a layer.
    **SUBNET**(const SUBNET&) = delete;
    SUBNET& **operator**=(const SUBNET&) = delete;

    const tensor& **get_output**(
    ) const;
    /*!
        ensures
            - returns the output of this subnetwork.  This is the data that the next
              layer in the network will take as input.
            - have_same_dimensions(#get_gradient_input(), get_output()) == true
    !*/

    tensor& **get_gradient_input**(
    );
    /*!
        ensures
            - returns the error gradient for this subnetwork.  That is, this is the
              error gradient that this network will use to update itself.  Therefore,
              when performing back propagation, layers that sit on top of this
              subnetwork write their back propagated error gradients into
              get_gradient_input().  Or to put it another way, during back propagation,
              layers take the contents of their get_gradient_input() and back propagate
              it through themselves and store the results into their subnetwork's
              get_gradient_input().
    !*/

    const NEXT_SUBNET& **subnet**(
    ) const;
    /*!
        ensures
            - returns the subnetwork of *this network.  With respect to the diagram
              above, if *this was layer1 then subnet() would return the network that
              begins with layer2.
    !*/

    NEXT_SUBNET& **subnet**(
    );
    /*!
        ensures
            - returns the subnetwork of *this network.  With respect to the diagram
              above, if *this was layer1 then subnet() would return the network that
              begins with layer2.
    !*/

    const INPUT_LAYER& **input_layer**(
    ) const;
    /*!
        ensures
            - returns the very first layer in *this network.  It's equivalent to calling
              subnet() recursively until you get to the first layer.  This means it will return
              the object that is an implementation of the EXAMPLE_INPUT_LAYER interface defined
              in input_abstract.h
    !*/

    INPUT_LAYER& **input_layer**(
    );
    /*!
        ensures
            - returns the very first layer in *this network.  It's equivalent to calling
              subnet() recursively until you get to the first layer.  This means it will return
              the object that is an implementation of the EXAMPLE_INPUT_LAYER interface defined
              in input_abstract.h
    !*/

    const layer_details_type& **layer_details**(
    ) const; 
    /*!
        ensures
            - returns the layer_details_type instance that defines the behavior of the
              layer at the top of this network.  I.e. returns the layer details that
              defines the behavior of the layer nearest to the network output rather
              than the input layer.  For computational layers, this is the object
              implementing the EXAMPLE_COMPUTATIONAL_LAYER_ interface that defines the
              layer's behavior.
    !*/

    unsigned int **sample_expansion_factor** (
    ) const;
    /*!
        ensures
            - When to_tensor() is invoked on this network's input layer it converts N
              input objects into M samples, all stored inside a resizable_tensor.  It
              is always the case that M is some integer multiple of N.
              sample_expansion_factor() returns the value of this multiplier.  To be
              very specific, it is always true that M==I*N where I is some integer.
              This integer I is what is returned by sample_expansion_factor().

              It should be noted that computational layers likely do not care about the
              sample expansion factor.  It is only really of concern inside a loss
              layer where you need to know its value so that tensor samples can be
              matched against truth objects.  Moreover, in most cases the sample
              expansion factor is 1.
    !*/

**}**;

// ----------------------------------------------------------------------------------------

class **EXAMPLE_COMPUTATIONAL_LAYER_**
**{**
    /*!
        WHAT THIS OBJECT REPRESENTS
            Each computational layer in a deep neural network can be thought of as a
            function, f(data,parameters), that takes in a data tensor, some parameters,
            and produces an output tensor.  You create an entire deep network by
            composing these functions.  Importantly, you are able to use a wide range
            of different functions to accommodate the task you are trying to
            accomplish.  Therefore, dlib includes a number of common layer types but if
            you want to define your own then you simply implement a class with the same
            interface as EXAMPLE_COMPUTATIONAL_LAYER_.

            Note that there is no dlib::EXAMPLE_COMPUTATIONAL_LAYER_ type.  It is shown
            here purely to document the interface that a layer object must implement.

            The central work of defining a layer is implementing the forward and backward
            methods.  When you do this you have four options:
                - Implement the forward() and backward() methods according to the
                  specification shown below.  Do not implement forward_inplace() and
                  backward_inplace().
                - Implement the forward() and backward() methods according to the
                  specification shown below, except exclude the computed_output
                  parameter from backward().  Doing this will allow dlib to make some
                  layers execute in-place and therefore run a little faster and use
                  less memory. Do not implement forward_inplace() and
                  backward_inplace().
                - Implement the forward_inplace() and backward_inplace() methods
                  according to the specification shown below.  Do not implement
                  forward() and backward().  These in-place methods allow some types of
                  layers to be implemented more efficiently.
                - Implement the forward_inplace() and backward_inplace() methods
                  according to the specification shown below, except exclude the
                  computed_output parameter from backward_inplace().  Doing this will
                  allow dlib to make some layers execute in-place and therefore run a
                  little faster and use less memory.  Do not implement forward() and
                  backward().


            It should also be noted that layers may define additional layer specific
            fields and the solvers can use these fields as they see fit.  For example,
            some layers define get_learning_rate_multiplier() and
            get_weight_decay_multiplier() methods.  The solvers that come with dlib
            look at these methods, if they exist, and adjust the learning rate or
            weight decay for that layer according to the multiplier.  Therefore, you
            can add these methods to your layer types if you want, or even define new
            fields and new solvers that use those fields in some way.  
    !*/

public:

    **EXAMPLE_COMPUTATIONAL_LAYER_**(
    );
    /*!
        ensures
            - Default constructs this object.  This function is not required to do
              anything in particular but it must exist, that is, it is required that
              layer objects be default constructable. 
    !*/

    **EXAMPLE_COMPUTATIONAL_LAYER_** (
        const EXAMPLE_COMPUTATIONAL_LAYER_& item
    );
    /*!
        ensures
            - EXAMPLE_COMPUTATIONAL_LAYER_ objects are copy constructable
    !*/

    **EXAMPLE_COMPUTATIONAL_LAYER_**(
        const some_other_layer_type& item
    );
    /*!
        ensures
            - Constructs this object from item.  This form of constructor is optional
              but it allows you to provide a conversion from one layer type to another.
              For example, the following code is valid only if my_layer2 can be
              constructed from my_layer1:
                relu<fc<my_layer1<fc<input<matrix<float>>>>>> my_dnn1;
                relu<fc<my_layer2<fc<input<matrix<float>>>>>> my_dnn2(my_dnn1);
              This kind of pattern is useful if you want to use one type of layer
              during training but a different type of layer during testing since it
              allows you to easily convert between related deep neural network types.  

              Additionally, if you provide a constructor to build a layer from another
              layer type you should also write your layer's deserialize() routine such
              that it can read that other layer's serialized data in addition to your
              own serialized data.  
    !*/

    template <typename SUBNET>
    void **setup** (
        const SUBNET& sub
    );
    /*!
        requires
            - SUBNET implements the SUBNET interface defined at the top of this file.
        ensures
            - performs any necessary initial memory allocations and/or sets parameters
              to their initial values prior to learning.  Therefore, calling setup
              destroys any previously learned parameters.  Also, typically setup()
              would look at the dimensions of the outputs of sub and configure the
              number of parameters in *this accordingly.
    !*/

    template <typename SUBNET>
    void **forward**(
        const SUBNET& sub, 
        resizable_tensor& data_output
    );
    /*!
        requires
            - SUBNET implements the SUBNET interface defined at the top of this file.
            - setup() has been called.
        ensures
            - Runs the output of the subnetwork through this layer and stores the
              results into #data_output.  In particular, forward() can use any of the
              outputs in sub (e.g. sub.get_output(), sub.subnet().get_output(), etc.)
              to compute whatever it wants.
    !*/

    template <typename SUBNET>
    void **backward**(
        const tensor& computed_output, // this parameter is optional
        const tensor& gradient_input, 
        SUBNET& sub, 
        tensor& params_grad
    );
    /*!
        requires
            - SUBNET implements the SUBNET interface defined at the top of this file.
            - setup() has been called.
            - computed_output is the tensor resulting from calling forward(sub,computed_output).  
              Moreover, this was the most recent call to forward().  This means that
              forward() is allowed to cache intermediate results so they can be used
              during the backward computation.
            - have_same_dimensions(gradient_input, computed_output) == true
            - have_same_dimensions(sub.get_gradient_input(), sub.get_output()) == true
            - have_same_dimensions(params_grad, get_layer_params()) == true
        ensures
            - This function outputs the gradients of this layer with respect to the
              input data from sub and also with respect to this layer's parameters.
              These gradients are stored into #sub and #params_grad, respectively. To be
              precise, the gradients are taken of a function f(sub,get_layer_params())
              which is defined thusly:   
                - Recalling that computed_output is a function of both sub and get_layer_params(), 
                  since it is the result of calling forward(sub,computed_output):
                  let f(sub,get_layer_params()) == dot(computed_output, gradient_input)
              Then we define the following gradient vectors: 
                - PARAMETER_GRADIENT == gradient of f(sub,get_layer_params()) with
                  respect to get_layer_params(). 
                - for all valid I:
                    - DATA_GRADIENT_I == gradient of f(sub,get_layer_params()) with
                      respect to layer<I>(sub).get_output() (recall that forward() can
                      draw inputs from the immediate sub layer, sub.subnet(), or
                      any earlier layer.  So you must consider the gradients with
                      respect to all inputs drawn from sub)
              Finally, backward() outputs these gradients by performing:
                - params_grad = PARAMETER_GRADIENT 
                - for all valid I:
                    - layer<I>(sub).get_gradient_input() += DATA_GRADIENT_I
    !*/

    void **forward_inplace**(
        const tensor& data_input, 
        tensor& data_output
    );
    /*!
        requires
            - have_same_dimensions(data_input,data_output) == true
            - setup() has been called.
        ensures
            - Runs the data_input tensor through this layer and stores the output into
              #data_output.
            - This function supports in-place operation, i.e. having
              is_same_object(data_input, data_output)==true
    !*/

    void **backward_inplace**(
        const tensor& computed_output, // this parameter is optional
        const tensor& gradient_input,
        tensor& data_grad,
        tensor& params_grad
    );
    /*!
        requires
            - setup() has been called.
            - computed_output is the tensor resulting from the most recent call to
              forward_inplace().  This means that forward_inplace() is allowed to cache
              intermediate results so they can be used during the backward computation.
            - have_same_dimensions(gradient_input, data_grad) == true
            - have_same_dimensions(gradient_input, computed_output) == true
            - have_same_dimensions(params_grad, get_layer_params()) == true
        ensures
            - This function supports in-place operation, i.e. having
              is_same_object(gradient_input, data_grad)==true
            - This function outputs the gradients of this layer with respect to the
              input data from a sublayer and also with respect to this layer's parameters.
              These gradients are stored into #data_grad and #params_grad, respectively. To be
              precise, the gradients are taken of a function f(data_input,get_layer_params())
              which is defined thusly:   
                - Recalling that computed_output is a function of both the input to
                  forward_inplace() and get_layer_params(), since it is the result of
                  calling forward_inplace(data_input,computed_output):
                  let f(data_input,get_layer_params()) == dot(computed_output, gradient_input)
              Then we define the following gradient vectors: 
                - PARAMETER_GRADIENT == gradient of f(data_input,get_layer_params()) with
                  respect to get_layer_params(). 
                - DATA_GRADIENT == gradient of f(data_input,get_layer_params()) with respect
                  to data_input. 
              Finally, backward_inplace() outputs these gradients by performing:
                - params_grad = PARAMETER_GRADIENT 
                - if (is_same_object(gradient_input, data_grad)) then
                    - data_grad = DATA_GRADIENT
                - else
                    - data_grad += DATA_GRADIENT
    !*/

    const tensor& **get_layer_params**(
    ) const; 
    /*!
        ensures
            - returns the parameters that define the behavior of forward().
    !*/

    tensor& **get_layer_params**(
    ); 
    /*!
        ensures
            - returns the parameters that define the behavior of forward().
    !*/


    dpoint **map_input_to_output**(dpoint p) const;
    dpoint **map_output_to_input**(dpoint p) const;
    /*!
        These two functions are optional.  If provided, they should map between
        (column,row) coordinates in input and output tensors of forward().  Providing
        these functions allows you to use global utility functions like
        input_tensor_to_output_tensor().
    !*/

    void **clean** (
    );
    /*!
        Implementing this function is optional.  If you don't need it then you don't
        have to provide a clean().  But if you do provide it then it must behave as
        follows:

        ensures
            - calling clean() causes this object to forget about everything except its
              parameters.  This is useful if your layer caches information between
              forward and backward passes and you want to clean out that cache
              information before saving the network to disk.  
    !*/

**}**;

std::ostream& **operator**<<(std::ostream& out, const EXAMPLE_COMPUTATIONAL_LAYER_& item);
/*!
    print a string describing this layer.
!*/

void **to_xml**(const EXAMPLE_COMPUTATIONAL_LAYER_& item, std::ostream& out);
/*!
    This function is optional, but required if you want to print your networks with
    net_to_xml().  Therefore, to_xml() prints a layer as XML.
!*/

void **serialize**(const EXAMPLE_COMPUTATIONAL_LAYER_& item, std::ostream& out);
void **deserialize**(EXAMPLE_COMPUTATIONAL_LAYER_& item, std::istream& in);
/*!
    provides serialization support  
!*/

// For each layer you define, always define an add_layer template so that layers can be
// easily composed.  Moreover, the convention is that the layer class ends with an _
// while the add_layer template has the same name but without the trailing _.
template <typename SUBNET>
using EXAMPLE_COMPUTATIONAL_LAYER = add_layer<EXAMPLE_COMPUTATIONAL_LAYER_, SUBNET>;

// ---------------------------------------------------------------------------------------- // ---------------------------------------------------------------------------------------- // ----------------------------------------------------------------------------------------

enum **fc_bias_mode**
**{**
    FC_HAS_BIAS = 0,
    FC_NO_BIAS = 1
**}**;

struct **num_fc_outputs**
**{**
    **num_fc_outputs**(unsigned long n) : num_outputs(n) **{** **}**
    unsigned long num_outputs;
**}**;

template <
    unsigned long num_outputs,
    fc_bias_mode bias_mode
    >
class **fc_**
**{**
    /*!
        REQUIREMENTS ON num_outputs
            num_outputs > 0

        WHAT THIS OBJECT REPRESENTS
            This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
            defined above.  In particular, it defines a fully connected layer that
            takes an input tensor and multiplies it by a weight matrix and outputs the
            results.

            The dimensions of the tensors output by this layer are as follows (letting
            IN be the input tensor and OUT the output tensor):
                - OUT.num_samples() == IN.num_samples()
                - OUT.k()  == get_num_outputs()
                - OUT.nr() == 1
                - OUT.nc() == 1
    !*/

public:

    **fc_**(
    );
    /*!
        ensures
            - #get_num_outputs() == num_outputs
            - #get_bias_mode() == bias_mode 
            - #get_learning_rate_multiplier()      == 1
            - #get_weight_decay_multiplier()       == 1
            - #get_bias_learning_rate_multiplier() == 1
            - #get_bias_weight_decay_multiplier()  == 0
    !*/

    **fc_**(
        num_fc_outputs o
    );
    /*!
        ensures
            - #get_num_outputs() == o.num_outputs 
            - #get_bias_mode() == bias_mode 
            - #get_learning_rate_multiplier()      == 1
            - #get_weight_decay_multiplier()       == 1
            - #get_bias_learning_rate_multiplier() == 1
            - #get_bias_weight_decay_multiplier()  == 0
    !*/

    unsigned long **get_num_outputs** (
    ) const; 
    /*!
        ensures
            - This layer outputs column vectors that contain get_num_outputs()
              elements. That is, the output tensor T from forward() will be such that:
                - T.num_samples() == however many samples were given to forward().
                - T.k() == get_num_outputs()
                - The rest of the dimensions of T will be 1.
    !*/

    void **set_num_outputs**(
        long num
    );
    /*!
        requires
            - num > 0
            - get_layer_params().size() == 0 || get_num_outputs() == num
              (i.e. You can't change the number of outputs in fc_ if the parameter
              tensor has already been allocated.)
        ensures
            - #get_num_outputs() == num
    !*/

    fc_bias_mode **get_bias_mode** (
    ) const;
    /*!
        ensures
            - returns the bias mode which determines if this layer includes bias terms.
              That is, if the bias mode is FC_HAS_BIAS then a different constant scalar
              is added to each of the outputs of this layer. 
    !*/

    double **get_learning_rate_multiplier**(
    ) const;  
    /*!
        ensures
            - returns a multiplier number.  The interpretation is that this object is
              requesting that the learning rate used to optimize its parameters be
              multiplied by get_learning_rate_multiplier().
    !*/

    double **get_weight_decay_multiplier**(
    ) const; 
    /*!
        ensures
            - returns a multiplier number.  The interpretation is that this object is
              requesting that the weight decay used to optimize its parameters be
              multiplied by get_weight_decay_multiplier().
    !*/

    void **set_learning_rate_multiplier**(
        double val
    );
    /*!
        requires
            - val >= 0
        ensures
            - #get_learning_rate_multiplier() == val
    !*/

    void **set_weight_decay_multiplier**(
        double val
    ); 
    /*!
        requires
            - val >= 0
        ensures
            - #get_weight_decay_multiplier() == val
    !*/

    double **get_bias_learning_rate_multiplier**(
    ) const; 
    /*!
        ensures
            - returns a multiplier number.  The interpretation is that this object is
              requesting that the learning rate used to optimize its bias parameters be
              multiplied by get_learning_rate_multiplier()*get_bias_learning_rate_multiplier().
    !*/

    double **get_bias_weight_decay_multiplier**(
    ) const; 
    /*!
        ensures
            - returns a multiplier number.  The interpretation is that this object is
              requesting that the weight decay used to optimize its bias parameters be
              multiplied by get_weight_decay_multiplier()*get_bias_weight_decay_multiplier().
    !*/

    void **set_bias_learning_rate_multiplier**(
        double val
    ); 
    /*!
        requires
            - val >= 0
        ensures
            - #get_bias_learning_rate_multiplier() == val
    !*/

    void **set_bias_weight_decay_multiplier**(
        double val
    ); 
    /*!
        requires
            - val >= 0
        ensures
            - #get_bias_weight_decay_multiplier() == val
    !*/

    void **disable_bias**(
    );
    /*!
        ensures
            - bias_is_disabled() returns true
    !*/

    bool **bias_is_disabled**(
    ) const;
    /*!
        ensures
            - returns true if bias learning is disabled for this layer.  This means the biases will
              not be learned during the training and they will not be used in the forward or backward
              methods either.
    !*/

    alias_tensor_const_instance **get_weights**(
    ) const;
    /*!
        ensures
            - returns an alias of get_layer_params(), containing the weights matrix of
              the fully connected layer.
            - #get_weights().num_samples() is the number of elements in input sample,
              i.e. sublayer's output's k * nc * nr.
            - #get_bias().k() == #get_num_outputs()
            - if get_bias_mode() == FC_HAS_BIAS:
                - #get_layer_params().size() == (#get_weights().size() + #get_biases().size())
            - else:
                - #get_layer_params().size() == #get_weights().size()
    !*/

    alias_tensor_instance **get_weights**(
    );
    /*!
        ensures
            - returns an alias of get_layer_params(), containing the weights matrix of
              the fully connected layer.
            - #get_weights().num_samples() is the number of elements in input sample,
              i.e. sublayer's output's k * nc * nr.
            - #get_bias().k() == #get_num_outputs()
            - if get_bias_mode() == FC_HAS_BIAS:
                - #get_layer_params().size() == (#get_weights().size() + #get_biases().size())
            - else:
                - #get_layer_params().size() == #get_weights().size()
    !*/

    alias_tensor_const_instance **get_biases**(
    ) const;
    /*!
        requires
            - #get_bias_mode() == FC_HAS_BIAS
        ensures
            - returns an alias of get_layer_params(), containing the bias vector of
              the fully connected layer.
            - #get_bias().num_samples() == 1
            - #get_bias().k() == #get_num_outputs()
            - #get_layer_params().size() == (#get_weights().size() + #get_biases().size())
    !*/

    alias_tensor_instance **get_biases**(
    );
    /*!
        requires
            - #get_bias_mode() == FC_HAS_BIAS
        ensures
            - returns an alias of get_layer_params(), containing the bias vector of
              the fully connected layer.
            - #get_bias().num_samples() == 1
            - #get_bias().k() == #get_num_outputs()
            - #get_layer_params().size() == (#get_weights().size() + #get_biases().size())
    !*/

    template <typename SUBNET> void **setup** (const SUBNET& sub);
    template <typename SUBNET> void **forward**(const SUBNET& sub, resizable_tensor& output);
    template <typename SUBNET> void **backward**(const tensor& gradient_input, SUBNET& sub, tensor& params_grad);
    const tensor& **get_layer_params**() const; 
    tensor& **get_layer_params**(); 
    /*!
        These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ interface.
    !*/

**}**;

template <
    unsigned long num_outputs,
    typename SUBNET
    >
using fc = add_layer<fc_<num_outputs,FC_HAS_BIAS>, SUBNET>;

template <
    unsigned long num_outputs,
    typename SUBNET
    >
using fc_no_bias = add_layer<fc_<num_outputs,FC_NO_BIAS>, SUBNET>;

// ----------------------------------------------------------------------------------------

// ----------------------------------------------------------------------------------------

enum **linear_bias_mode**
**{**
    LINEAR_HAS_BIAS,
    LINEAR_NO_BIAS
**}**;

template <
    unsigned long num_outputs,
    linear_bias_mode bias_mode
>
class **linear_**
**{**
    /*!
        REQUIREMENTS ON num_outputs
            num_outputs > 0

        WHAT THIS OBJECT REPRESENTS
            This is an implementation of a linear layer, which applies a linear
            transformation to the input data. For a layer with bias, the transformation
            is:
                output = input * weights + bias
            For a layer without bias, it's simply:
                output = input * weights

            The input tensor can have any number of sample, k (channel), and nr (row)
            dimensions, but the nc (column) dimension must match the number of input features.
            The output tensor will have the same dimensions as the input tensor, except for
            the nc dimension which will be equal to num_outputs.

            This layer is similar to the fc_ layer, but optimized for the case where the
            input and output tensors maintain the same dimensions, excluding the feature
            dimension (nc). This makes it useful for working with multi-dimensional data.
    !*/

public:
    **linear_**(
    );
    /*!
        ensures
            - #get_num_outputs() == num_outputs
            - #get_bias_mode() == bias_mode
            - #get_learning_rate_multiplier() == 1
    !*/

    double **get_learning_rate_multiplier**(
    ) const;
    /*!
        ensures
            - returns a multiplier that will be applied to the gradient of this layer during
              training. This value appears as a multiplicative factor in the update rule. So
              if get_learning_rate_multiplier() == 1 then the learning rate will be multiplied
              by 1 and thus not modified. However, if get_learning_rate_multiplier() == 0.1 then
              the learning rate will be multiplied by 0.1, making the layer update 10 times
              slower than it would otherwise be.
    !*/

    void **set_learning_rate_multiplier**(
        double val
    );
    /*!
        ensures
            - #get_learning_rate_multiplier() == val
    !*/

    unsigned long **get_num_inputs**(
    ) const;
    /*!
        ensures
            - Returns the number of input features this layer expects.
            - For an uninitialized layer (i.e., one that has not seen any data during setup
              or forward pass), this will be zero.
    !*/

    unsigned long **get_num_outputs**(
    ) const;
    /*!
        ensures
            - Returns the number of output features this layer produces.
              I.e., this value is num_outputs.
    !*/

    void **set_num_outputs**(
        long num
    );
    /*!
        requires
            - num > 0
        ensures
            - #get_num_outputs() == num
        throws
            - std::runtime_error if this function is called after the layer parameters
              have been allocated and the new number of outputs doesn't match the
              previously set number of outputs.
    !*/

    linear_bias_mode **get_bias_mode**(
    ) const;
    /*!
        ensures
            - Returns a value indicating whether this layer has a bias term.
              I.e. returns bias_mode.
    !*/

    template <typename SUBNET>
    void **setup**(
        const SUBNET& sub
    );
    /*!
        ensures
            - Performs the necessary setup work to process data through this layer.
            - Sets the input size based on the dimensions of the input tensor from sub.
            - Allocates the parameter tensor and initializes its values.
            - #get_num_inputs() == the number of columns in sub.get_output() (i.e., nc).
    !*/

    template <typename SUBNET>
    void **forward**(
        const SUBNET& sub,
        resizable_tensor& output
    );
    /*!
        requires
            - setup() has been called
            - sub.get_output().nc() == get_num_inputs()
        ensures
            - Applies the linear transformation to the input tensor from sub and stores
              the results in output.
            - #output.num_samples() == sub.get_output().num_samples()
            - #output.k()           == sub.get_output().k()
            - #output.nr()          == sub.get_output().nr()
            - #output.nc()          == get_num_outputs()
    !*/

    template <typename SUBNET>
    void **backward**(
        const tensor& gradient_input,
        SUBNET& sub,
        tensor& params_grad
    );
    /*!
        requires
            - setup() has been called
            - sub.get_output().nc() == get_num_inputs()
            - gradient_input has the same dimensions as the output of forward()
        ensures
            - Computes the gradients of this layer with respect to the parameters
              and the input tensor, and updates the corresponding gradient tensors.
            - Updates params_grad based on the gradients of the weights
              and biases (if present).
            - Updates sub's gradient_input based on the gradients of the
              inputs to this layer.
    !*/

    alias_tensor_instance **get_weights**(
    );
    /*!
        requires
            - setup() has been called
        ensures
            - Returns a reference to the weights matrix of this layer.
    !*/

    alias_tensor_const_instance **get_weights**(
    ) const;
    /*!
        requires
            - setup() has been called
        ensures
            - Returns a const reference to the weights matrix of this layer.
    !*/

    alias_tensor_instance **get_biases**(
    );
    /*!
        requires
            - bias_mode == LINEAR_HAS_BIAS
            - setup() has been called
        ensures
            - Returns a reference to the bias vector of this layer.
        throws
            - static_assert failure if bias_mode != LINEAR_HAS_BIAS
    !*/

    alias_tensor_const_instance **get_biases**(
    ) const;
    /*!
        requires
            - bias_mode == LINEAR_HAS_BIAS
            - setup() has been called
        ensures
            - Returns a const reference to the bias vector of this layer.
        throws
            - static_assert failure if bias_mode != LINEAR_HAS_BIAS
    !*/

    dpoint **map_input_to_output**(
        const dpoint& p
    ) const;
    /*!
        ensures
            - Returns p, since the linear layer maintains the same spatial dimensions.
    !*/

    dpoint **map_output_to_input**(
        const dpoint& p
    ) const;
    /*!
        ensures
            - Returns p, since the linear layer maintains the same spatial dimensions.
    !*/

    const tensor& **get_layer_params**(
    ) const;
    /*!
        ensures
            - Returns the parameters that define this layer, i.e., the weights and biases
              (if present) that are updated during training.
    !*/

    tensor& **get_layer_params**(
    );
    /*!
        ensures
            - Returns the parameters that define this layer, i.e., the weights and biases
              (if present) that are updated during training.
    !*/

    friend void **serialize**(const linear_& item, std::ostream& out);
    friend void **deserialize**(linear_& item, std::istream& in);
    /*!
        provides serialization support
    !*/
**}**;

template <
    unsigned long num_outputs,
    typename SUBNET
>
using linear = add_layer<linear_<num_outputs, LINEAR_HAS_BIAS>, SUBNET>;
/*!
    This is a layer that applies a linear transformation with bias to the input:
    output = input * weights + bias
!*/

template <
    unsigned long num_outputs,
    typename SUBNET
>
using linear_no_bias = add_layer<linear_<num_outputs, LINEAR_NO_BIAS>, SUBNET>;
/*!
    This is a layer that applies a linear transformation without bias to the input:
    output = input * weights
!*/

// ----------------------------------------------------------------------------------------

// ----------------------------------------------------------------------------------------

struct **num_con_outputs**
**{**
    **num_con_outputs**(unsigned long n) : num_outputs(n) **{** **}**
    unsigned long num_outputs;
**}**;

template <
    long _num_filters,
    long _nr,
    long _nc,
    int _stride_y,
    int _stride_x,
    int _padding_y = _stride_y!=1? 0 : _nr/2,
    int _padding_x = _stride_x!=1? 0 : _nc/2
    >
class **con_**
**{**
    /*!
        REQUIREMENTS ON TEMPLATE ARGUMENTS
            - _num_filters > 0
            - _nr >= 0
            - _nc >= 0
            - _stride_y > 0
            - _stride_x > 0
            - _padding_y >= 0
            - _padding_x >= 0
            - Also, we require that:
                - if (_nr == 0) then
                    - _padding_y == 0
                - else
                    - _padding_y < _nr
                - if (_nc == 0) then
                    - _padding_x == 0
                - else
                    - _padding_x < _nc

        WHAT THIS OBJECT REPRESENTS
            This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
            defined above.  In particular, it defines a convolution layer that takes an
            input tensor (nominally representing an image) and convolves it with a set
            of filters and then outputs the results. 

            The dimensions of the tensors output by this layer are as follows (letting
            IN be the input tensor and OUT the output tensor):
                - OUT.num_samples() == IN.num_samples()
                - OUT.k()  == num_filters()
                - OUT.nr() == 1+(IN.nr() + 2*padding_y() - nr())/stride_y()
                - OUT.nc() == 1+(IN.nc() + 2*padding_x() - nc())/stride_x()

            Note also that setting _nr or _nc to 0 has a special meaning of "set the
            filter size equal to the input image size".  Specifically, it means: 
                - if (_nr == 0) then
                    - nr() == IN.nr()
                    - OUT.nr() == 1
                - if (_nc == 0) then
                    - nc() == IN.nc()
                    - OUT.nc() == 1
    !*/

public:
    **con_**(
    );
    /*!
        ensures
            - #num_filters() == _num_filters
            - #nr() == _nr
            - #nc() == _nc
            - #stride_y() == _stride_y
            - #stride_x() == _stride_x
            - #padding_y() == _padding_y
            - #padding_x() == _padding_x
            - #get_learning_rate_multiplier()      == 1
            - #get_weight_decay_multiplier()       == 1
            - #get_bias_learning_rate_multiplier() == 1
            - #get_bias_weight_decay_multiplier()  == 0
    !*/

    **con_**(
        num_con_outputs o
    );
    /*!
        ensures
            - #num_filters() == o.num_outputs 
            - #nr() == _nr
            - #nc() == _nc
            - #stride_y() == _stride_y
            - #stride_x() == _stride_x
            - #padding_y() == _padding_y
            - #padding_x() == _padding_x
            - #get_learning_rate_multiplier()      == 1
            - #get_weight_decay_multiplier()       == 1
            - #get_bias_learning_rate_multiplier() == 1
            - #get_bias_weight_decay_multiplier()  == 0
    !*/

    long **num_filters**(
    ) const; 
    /*!
        ensures
            - returns the number of filters contained in this layer.  The k dimension
              of the output tensors produced by this layer will be equal to the number
              of filters.
    !*/

    void **set_num_filters**(
        long num
    );
    /*!
        requires
            - num > 0
            - get_layer_params().size() == 0 || num_filters() == num
              (i.e. You can't change the number of filters in con_ if the parameter
              tensor has already been allocated.)
        ensures
            - #num_filters() == num
    !*/

    long **nr**(
    ) const; 
    /*!
        ensures
            - returns the number of rows in the filters in this layer.  Note that if
              nr()==0 then it means the size of the filter is not yet assigned, but
              once setup() is called nr() will be set to the input tensor's nr().
              Therefore, nr()==0 has the special interpretation of "be the same size as
              the input tensor".
    !*/

    long **nc**(
    ) const;
    /*!
        ensures
            - returns the number of columns in the filters in this layer.  Note that if
              nc()==0 then it means the size of the filter is not yet assigned, but
              once setup() is called nc() will be set to the input tensor's nc().
              Therefore, nc()==0 has the special interpretation of "be the same size as
              the input tensor".
    !*/

    long **stride_y**(
    ) const; 
    /*!
        ensures
            - returns the vertical stride used when convolving the filters over an
              image.  That is, each filter will be moved stride_y() pixels down at a
              time when it moves over the image.
    !*/

    long **stride_x**(
    ) const;
    /*!
        ensures
            - returns the horizontal stride used when convolving the filters over an
              image.  That is, each filter will be moved stride_x() pixels right at a
              time when it moves over the image.
    !*/

    long **padding_y**(
    ) const; 
    /*!
        ensures
            - returns the number of pixels of zero padding added to the top and bottom
              sides of the image.
    !*/

    long **padding_x**(
    ) const; 
    /*!
        ensures
            - returns the number of pixels of zero padding added to the left and right 
              sides of the image.
    !*/

    double **get_learning_rate_multiplier**(
    ) const;  
    /*!
        ensures
            - returns a multiplier number.  The interpretation is that this object is
              requesting that the learning rate used to optimize its parameters be
              multiplied by get_learning_rate_multiplier().
    !*/

    double **get_weight_decay_multiplier**(
    ) const; 
    /*!
        ensures
            - returns a multiplier number.  The interpretation is that this object is
              requesting that the weight decay used to optimize its parameters be
              multiplied by get_weight_decay_multiplier().
    !*/

    void **set_learning_rate_multiplier**(
        double val
    );
    /*!
        requires
            - val >= 0
        ensures
            - #get_learning_rate_multiplier() == val
    !*/

    void **set_weight_decay_multiplier**(
        double val
    ); 
    /*!
        requires
            - val >= 0
        ensures
            - #get_weight_decay_multiplier() == val
    !*/

    double **get_bias_learning_rate_multiplier**(
    ) const; 
    /*!
        ensures
            - returns a multiplier number.  The interpretation is that this object is
              requesting that the learning rate used to optimize its bias parameters be
              multiplied by get_learning_rate_multiplier()*get_bias_learning_rate_multiplier().
    !*/

    double **get_bias_weight_decay_multiplier**(
    ) const; 
    /*!
        ensures
            - returns a multiplier number.  The interpretation is that this object is
              requesting that the weight decay used to optimize its bias parameters be
              multiplied by get_weight_decay_multiplier()*get_bias_weight_decay_multiplier().
    !*/

    void **set_bias_learning_rate_multiplier**(
        double val
    ); 
    /*!
        requires
            - val >= 0
        ensures
            - #get_bias_learning_rate_multiplier() == val
    !*/

    void **set_bias_weight_decay_multiplier**(
        double val
    ); 
    /*!
        requires
            - val >= 0
        ensures
            - #get_bias_weight_decay_multiplier() == val
    !*/

    void **disable_relu**(
    );
    /*!
        ensures
            - relu_is_disabled() returns true
    !*/

    void **enable_relu**(
    );
    /*!
        ensures
            - relu_is_disabled() returns false
    !*/

    bool **relu_is_disabled**(
    ) const;
    /*!
        ensures
            - returns true if relu is disabled for this layer. This means no activation function
              will be applied after the convolution when calling forward.
    !*/

    void **disable_bias**(
    );
    /*!
        ensures
            - bias_is_disabled() returns true
            - if bias was enabled and allocated, it resizes the layer parameters
              to accommodate the filter parameters only, and free the bias parameters.
    !*/

    void **enable_bias**(
    );
    /*!
        ensures
            - bias_is_disabled() returns false
            - if bias was disabled and not allocated, it resizes the layer parameters
              to accommodate the new zero-inizialized biases
    !*/

    bool **bias_is_disabled**(
    ) const;
    /*!
        ensures
            - returns true if bias learning is disabled for this layer.  This means the biases will
              not be learned during the training and they will not be used in the forward or backward
              methods either.
    !*/

    template <typename SUBNET> void **setup** (const SUBNET& sub);
    template <typename SUBNET> void **forward**(const SUBNET& sub, resizable_tensor& output);
    template <typename SUBNET> void **backward**(const tensor& gradient_input, SUBNET& sub, tensor& params_grad);
    dpoint **map_input_to_output**(dpoint p) const;
    dpoint **map_output_to_input**(dpoint p) const;
    const tensor& **get_layer_params**() const; 
    tensor& **get_layer_params**(); 
    /*!
        These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ interface.
    !*/

**}**;

template <
    long num_filters,
    long nr,
    long nc,
    int stride_y,
    int stride_x,
    typename SUBNET
    >
using con = add_layer<con_<num_filters,nr,nc,stride_y,stride_x>, SUBNET>;

// ----------------------------------------------------------------------------------------

template <
    long _num_filters,
    long _nr,
    long _nc,
    int _stride_y,
    int _stride_x,
    int _padding_y = _stride_y!=1? 0 : _nr/2,
    int _padding_x = _stride_x!=1? 0 : _nc/2
    >
class **cont_**
**{**
    /*!
        REQUIREMENTS ON TEMPLATE ARGUMENTS
            All of them must be > 0.
            Also, we require that:
                - 0 <= _padding_y && _padding_y < _nr
                - 0 <= _padding_x && _padding_x < _nc

        WHAT THIS OBJECT REPRESENTS
            This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
            defined above.  In particular, it defines a transposed convolution layer
            that takes an input tensor and transpose convolves (sometimes called
            "deconvolution") it with a set of filters and then outputs the results. 

            This is essentially a convolutional layer that allows fractional strides.
            Therefore, you can make output tensors that are larger than the input
            tensors using this layer type. 

            
            The dimensions of the tensors output by this layer are as follows (letting
            IN be the input tensor and OUT the output tensor):
                - OUT.num_samples() == IN.num_samples()
                - OUT.k()  == num_filters()
                - OUT.nr() == stride_y()*(IN.nr()-1) + nr() - 2*padding_y()
                - OUT.nc() == stride_x()*(IN.nc()-1) + nc() - 2*padding_x()
    !*/

public:
    **cont_**(
    );
    /*!
        ensures
            - #num_filters() == _num_filters
            - #nr() == _nr
            - #nc() == _nc
            - #stride_y() == _stride_y
            - #stride_x() == _stride_x
            - #padding_y() == _padding_y
            - #padding_x() == _padding_x
            - #get_learning_rate_multiplier()      == 1
            - #get_weight_decay_multiplier()       == 1
            - #get_bias_learning_rate_multiplier() == 1
            - #get_bias_weight_decay_multiplier()  == 0
    !*/

    **cont_**(
        num_con_outputs o
    );
    /*!
        ensures
            - #num_filters() == o.num_outputs 
            - #nr() == _nr
            - #nc() == _nc
            - #stride_y() == _stride_y
            - #stride_x() == _stride_x
            - #padding_y() == _padding_y
            - #padding_x() == _padding_x
            - #get_learning_rate_multiplier()      == 1
            - #get_weight_decay_multiplier()       == 1
            - #get_bias_learning_rate_multiplier() == 1
            - #get_bias_weight_decay_multiplier()  == 0
    !*/

    long **num_filters**(
    ) const; 
    /*!
        ensures
            - returns the number of filters contained in this layer.  The k dimension
              of the output tensors produced by this layer will be equal to the number
              of filters.
    !*/

    void **set_num_filters**(
        long num
    );
    /*!
        requires
            - num > 0
            - get_layer_params().size() == 0 || num_filters() == num
              (i.e. You can't change the number of filters in cont_ if the parameter
              tensor has already been allocated.)
        ensures
            - #num_filters() == num
    !*/

    long **nr**(
    ) const; 
    /*!
        ensures
            - returns the number of rows in the filters in this layer.
    !*/

    long **nc**(
    ) const;
    /*!
        ensures
            - returns the number of columns in the filters in this layer.
    !*/

    long **stride_y**(
    ) const; 
    /*!
        ensures
            - returns the vertical stride used when convolving the filters over an
              image.  That is, each filter will be moved 1.0/stride_y() pixels down at
              a time when it moves over the image.
    !*/

    long **stride_x**(
    ) const;
    /*!
        ensures
            - returns the horizontal stride used when convolving the filters over an
              image.  That is, each filter will be moved 1.0/stride_x() pixels right at
              a time when it moves over the image.
    !*/

    long **padding_y**(
    ) const; 
    /*!
        ensures
            - returns the number of pixels of zero padding added to the top and bottom
              sides of the image.
    !*/

    long **padding_x**(
    ) const; 
    /*!
        ensures
            - returns the number of pixels of zero padding added to the left and right 
              sides of the image.
    !*/

    double **get_learning_rate_multiplier**(
    ) const;  
    /*!
        ensures
            - returns a multiplier number.  The interpretation is that this object is
              requesting that the learning rate used to optimize its parameters be
              multiplied by get_learning_rate_multiplier().
    !*/

    double **get_weight_decay_multiplier**(
    ) const; 
    /*!
        ensures
            - returns a multiplier number.  The interpretation is that this object is
              requesting that the weight decay used to optimize its parameters be
              multiplied by get_weight_decay_multiplier().
    !*/

    void **set_learning_rate_multiplier**(
        double val
    );
    /*!
        requires
            - val >= 0
        ensures
            - #get_learning_rate_multiplier() == val
    !*/

    void **set_weight_decay_multiplier**(
        double val
    ); 
    /*!
        requires
            - val >= 0
        ensures
            - #get_weight_decay_multiplier() == val
    !*/

    double **get_bias_learning_rate_multiplier**(
    ) const; 
    /*!
        ensures
            - returns a multiplier number.  The interpretation is that this object is
              requesting that the learning rate used to optimize its bias parameters be
              multiplied by get_learning_rate_multiplier()*get_bias_learning_rate_multiplier().
    !*/

    double **get_bias_weight_decay_multiplier**(
    ) const; 
    /*!
        ensures
            - returns a multiplier number.  The interpretation is that this object is
              requesting that the weight decay used to optimize its bias parameters be
              multiplied by get_weight_decay_multiplier()*get_bias_weight_decay_multiplier().
    !*/

    void **set_bias_learning_rate_multiplier**(
        double val
    ); 
    /*!
        requires
            - val >= 0
        ensures
            - #get_bias_learning_rate_multiplier() == val
    !*/

    void **set_bias_weight_decay_multiplier**(
        double val
    ); 
    /*!
        requires
            - val >= 0
        ensures
            - #get_bias_weight_decay_multiplier() == val
    !*/

    void **disable_bias**(
    );
    /*!
        ensures
            - bias_is_disabled() returns true
    !*/

    bool **bias_is_disabled**(
    ) const;
    /*!
        ensures
            - returns true if bias learning is disabled for this layer.  This means the biases will
              not be learned during the training and they will not be used in the forward or backward
              methods either.
    !*/

    template <typename SUBNET> void **setup** (const SUBNET& sub);
    template <typename SUBNET> void **forward**(const SUBNET& sub, resizable_tensor& output);
    template <typename SUBNET> void **backward**(const tensor& gradient_input, SUBNET& sub, tensor& params_grad);
    dpoint **map_input_to_output**(dpoint p) const;
    dpoint **map_output_to_input**(dpoint p) const;
    const tensor& **get_layer_params**() const; 
    tensor& **get_layer_params**(); 
    /*!
        These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ interface.
    !*/

**}**;

template <
    long num_filters,
    long nr,
    long nc,
    int stride_y,
    int stride_x,
    typename SUBNET
    >
using cont = add_layer<cont_<num_filters,nr,nc,stride_y,stride_x>, SUBNET>;

// ----------------------------------------------------------------------------------------

template <
    int scale_y, 
    int scale_x 
    >
class **upsample_**
**{**
    /*!
        REQUIREMENTS ON TEMPLATE ARGUMENTS
            All of them must be >= 1.

        WHAT THIS OBJECT REPRESENTS
            This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
            defined above.  In particular, it allows you to upsample a layer using
            bilinear interpolation.  To be very specific, it upsamples each of the
            channels in an input tensor.  Therefore, if IN is the input tensor to this
            layer and OUT the output tensor, then we will have:
                - OUT.num_samples() == IN.num_samples()
                - OUT.k()  == IN.k() 
                - OUT.nr() == IN.nr()*scale_y
                - OUT.nc() == IN.nc()*scale_x
                - for all valid i,k:  image_plane(OUT,i,k) is a copy of
                  image_plane(IN,i,k) that has been bilinearly interpolated to fit into
                  the shape of image_plane(OUT,i,k).
    !*/
public:

    **upsample_**(
    );
    /*!
        ensures
            - This object has no state, so the constructor does nothing, aside from
              providing default constructability.
    !*/

    template <typename SUBNET> void **setup** (const SUBNET& sub);
    template <typename SUBNET> void **forward**(const SUBNET& sub, resizable_tensor& output);
    template <typename SUBNET> void **backward**(const tensor& gradient_input, SUBNET& sub, tensor& params_grad);
    dpoint **map_input_to_output**(dpoint p) const;
    dpoint **map_output_to_input**(dpoint p) const;
    const tensor& **get_layer_params**() const; 
    tensor& **get_layer_params**(); 
    /*!
        These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ interface.
    !*/
**}**;

template <
    int scale,
    typename SUBNET
    >
using upsample = add_layer<upsample_<scale,scale>, SUBNET>;

// ----------------------------------------------------------------------------------------

template <
    long NR_, 
    long NC_
    >
class **resize_to_**
**{**
    /*!
        REQUIREMENTS ON THE INPUT ARGUMENTS
            - NR_ >= 1
            - NC_ >= 1

        WHAT THIS OBJECT REPRESENTS
            This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
            defined above.  In particular, it allows you to resize a layer using
            bilinear interpolation.  To be very specific, it resizes each of the
            channels in an input tensor.  Therefore, if IN is the input tensor to this
            layer and OUT the output tensor, then we will have:
                - OUT.num_samples() == IN.num_samples()
                - OUT.k()  == IN.k() 
                - OUT.nr() == NR_
                - OUT.nc() == NC_
                - for all valid i,k:  image_plane(OUT,i,k) is a copy of
                  image_plane(IN,i,k) that has been bilinearly interpolated to fit into
                  the shape of image_plane(OUT,i,k).
    !*/
public:

    **resize_to_**(
    );
    /*!
        ensures
            - This object has no state, so the constructor does nothing, aside from
              providing default constructability.
    !*/

    template <typename SUBNET> void **setup** (const SUBNET& sub);
    template <typename SUBNET> void **forward**(const SUBNET& sub, resizable_tensor& output);
    template <typename SUBNET> void **backward**(const tensor& gradient_input, SUBNET& sub, tensor& params_grad);
    dpoint **map_input_to_output**(dpoint p) const;
    dpoint **map_output_to_input**(dpoint p) const;
    const tensor& **get_layer_params**() const; 
    tensor& **get_layer_params**(); 
    /*!
        These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ interface.
    !*/
**}**;

template <
    long NR,
    long NC,
    typename SUBNET
    >
using resize_to = add_layer<resize_to_<NR,NC>, SUBNET>;

// ----------------------------------------------------------------------------------------

template <long k_ = -1, long nr_ = -1, long nc_ = -1>
class **reshape_to_**
**{**
    /*!
        REQUIREMENTS ON TEMPLATE ARGUMENTS
            - k_, nr_, and nc_ must be either -1 or greater than 0.

        WHAT THIS OBJECT REPRESENTS
            This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
            defined above. It defines a layer that reshapes or resizes an input tensor
            into a different shape. The layer operates in two modes:

            1. Pure Reshape Mode: When the total number of elements in the input tensor
               equals the total number of elements in the output tensor, this layer
               performs a simple reshaping operation without changing the values.

            2. Spatial Rescaling Mode: When the channel dimension (k) remains constant
               but the total number of elements changes, this layer performs bilinear
               interpolation to resize the spatial dimensions while preserving the
               channel information.

            The dimensions of the output tensor are determined by the template parameters:
                - If k_ is -1, the output tensor will have the same number of channels as the input.
                - If nr_ is -1, the output tensor will have the same number of rows as the input.
                - If nc_ is -1, the output tensor will have the same number of columns as the input.

            Setting a value of -1 for any dimension means "keep the original dimension from the input."

            Note that this layer will throw an exception if you attempt to change both the
            channel count (k) and the total number of elements. Either:
            - Keep the total number of elements the same (Pure Reshape Mode), or
            - Keep the channel count the same and only change spatial dimensions (Spatial Rescaling Mode)
    !*/

public:
    explicit **reshape_to_**();
    /*!
        ensures
            - #get_output_k() == k_
            - #get_output_nr() == nr_
            - #get_output_nc() == nc_
    !*/

    long **get_output_k**() const;
    /*!
        ensures
            - Returns the number of channels in the output tensor. If this value is -1,
              then the output will have the same number of channels as the input.
    !*/

    long **get_output_nr**() const;
    /*!
        ensures
            - Returns the number of rows in the output tensor. If this value is -1,
              then the output will have the same number of rows as the input.
    !*/

    long **get_output_nc**() const;
    /*!
        ensures
            - Returns the number of columns in the output tensor. If this value is -1,
              then the output will have the same number of columns as the input.
    !*/

    void **set_output_k**(long k);
    /*!
        requires
            - k == -1 || k > 0
        ensures
            - #get_output_k() == k
    !*/

    void **set_output_nr**(long nr);
    /*!
        requires
            - nr == -1 || nr > 0
        ensures
            - #get_output_nr() == nr
    !*/

    void **set_output_nc**(long nc);
    /*!
        requires
            - nc == -1 || nc > 0
        ensures
            - #get_output_nc() == nc
    !*/

    template <typename SUBNET> void **setup**(const SUBNET& sub);
    /*!
        requires
            - SUBNET implements the SUBNET interface defined at the top of this file.
        ensures
            - Configures this layer to operate on the output of sub.
            - If the total number of elements in the input tensor doesn't match the total
              number of elements in the output tensor and the channel dimension is different,
              an exception will be thrown.
    !*/

    template <typename SUBNET> void **forward**(const SUBNET& sub, resizable_tensor& output);
    /*!
        requires
            - SUBNET implements the SUBNET interface defined at the top of this file.
            - setup() has been called.
        ensures
            - Reshapes or resizes the output of sub and stores it in #output.
            - If is_spatial_rescale() == false, then performs a pure reshape operation.
            - If is_spatial_rescale() == true, then performs bilinear interpolation to resize
              the spatial dimensions while preserving the channel information.
            - #output.num_samples() == sub.get_output().num_samples()
            - #output.k() == get_output_k() if get_output_k() != -1, otherwise sub.get_output().k()
            - #output.nr() == get_output_nr() if get_output_nr() != -1, otherwise sub.get_output().nr()
            - #output.nc() == get_output_nc() if get_output_nc() != -1, otherwise sub.get_output().nc()
    !*/

    template <typename SUBNET> void **backward**(
        const tensor& gradient_input,
        SUBNET& sub,
        tensor& params_grad
    );
    /*!
        requires
            - SUBNET implements the SUBNET interface defined at the top of this file.
            - setup() has been called.
            - gradient_input has the same dimensions as the output of forward().
        ensures
            - Computes the gradients of this layer with respect to the input tensor and
              parameters, and stores them in sub.get_gradient_input() and params_grad,
              respectively.
            - This function supports both pure reshaping and spatial rescaling operations.
    !*/

    dpoint **map_input_to_output**(dpoint p) const;
    /*!
        ensures
            - Maps a point in the input tensor's coordinate system to the corresponding point
              in the output tensor. This is useful for tracking how spatial locations change
              through the network, especially during spatial rescaling.
    !*/

    dpoint **map_output_to_input**(dpoint p) const;
    /*!
        ensures
            - Maps a point in the output tensor's coordinate system to the corresponding point
              in the input tensor. This is the inverse of map_input_to_output().
    !*/

    const tensor& **get_layer_params**() const;
    /*!
        ensures
            - Returns the layer's parameters. This layer has no parameters,
              so this always returns an empty tensor.
    !*/

    tensor& **get_layer_params**();
    /*!
        ensures
            - Returns the layer's parameters. This layer has no parameters,
              so this always returns an empty tensor.
    !*/
**}**;

template <long k, long nr, long nc, typename SUBNET>
using reshape_to = add_layer<reshape_to_<k, nr, nc>, SUBNET>;

template <long k, long nr, long nc, typename SUBNET>
using flatten = add_layer<reshape_to_<k * nr, * nc, 1, 1>, SUBNET>;

// ----------------------------------------------------------------------------------------

class **dropout_**
**{**
    /*!
        WHAT THIS OBJECT REPRESENTS
            This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
            defined above.  In particular, it defines a dropout layer.  Therefore, it
            passes its inputs through the stochastic function f(x) which outputs either
            0 or x.  The probability of 0 being output is given by the drop_rate
            argument to this object's constructor.

            Note that, after you finish training a network with dropout, it is a good
            idea to replace each dropout_ layer with a multiply_ layer because the
            multiply_ layer is faster and deterministic. 
    !*/

public:

    explicit **dropout_**(
        float drop_rate = 0.5
    );
    /*!
        requires
            - 0 <= drop_rate <= 1
        ensures
            - #get_drop_rate() == drop_rate
    !*/

    float **get_drop_rate** (
    ) const; 
    /*!
        ensures
            - returns the probability that an individual input value to this layer will
              be replaced with 0.
    !*/

    template <typename SUBNET> void **setup** (const SUBNET& sub);
    void **forward_inplace**(const tensor& input, tensor& output);
    void **backward_inplace**(const tensor& gradient_input, tensor& data_grad, tensor& params_grad);
    dpoint **map_input_to_output**(dpoint p) const;
    dpoint **map_output_to_input**(dpoint p) const;
    const tensor& **get_layer_params**() const; 
    tensor& **get_layer_params**(); 
    /*!
        These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ interface.
    !*/
**}**;

template <typename SUBNET>
using dropout = add_layer<dropout_, SUBNET>;

// ----------------------------------------------------------------------------------------

template <int DROP_RATE_PERCENT>
class **dropout_rate_** : public dropout_
**{**
    /*!
        WHAT THIS OBJECT REPRESENTS
            This object represents a customizable dropout layer that inherits from
            the dropout_ class. It allows specifying the dropout rate at compile-time,
            which is particularly useful for deep networks with many layers where it
            might be cumbersome to explicitly modify the dropout rate for each layer
            individually.

            The main advantage of this layer is that it offers the possibility to specify
            the dropout rate at the moment of network construction, providing more
            flexibility and clarity in the network architecture definition.

        TEMPLATE PARAMETERS
            - DROP_RATE_PERCENT: A int value between 0 and 100 that specifies the dropout rate.
              This value is set at compile-time and cannot be changed during runtime.
    !*/

public:
    explicit **dropout_rate_**();
    /*!
        ensures
            - Constructs a dropout layer with a dropout rate of DROP_RATE.
            - Calls the base class constructor dropout_(DROP_RATE).
    !*/
**}**;

template <int DROP_RATE, typename SUBNET>
using dropout_rate = add_layer<dropout_rate_<DROP_RATE>, SUBNET>;
template <typename SUBNET>
using dropout_10 = add_layer<dropout_rate_<10>, SUBNET>;

// ----------------------------------------------------------------------------------------

class **multiply_**
**{**
    /*!
        WHAT THIS OBJECT REPRESENTS
            This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
            defined above.  In particular, it defines a basic layer that just
            multiplies its input tensor with a constant value and returns the result.
            It therefore has no learnable parameters.
    !*/

public:
    explicit **multiply_**(
        float val = 0.5
    ); 
    /*!
        ensures
            - #get_multiply_value() == val
    !*/

    **multiply_** (
        const dropout_& item
    ); 
    /*!
        ensures
            - #get_multiply_value() == 1-item.get_drop_rate()
              (i.e. We construct the multiply_ layer so that it is essentially a
              deterministic version of the given dropout_ layer)
    !*/

    float **get_multiply_value** (
    ) const;
    /*!
        ensures
            - this layer simply multiplies its input tensor by get_multiply_value() and
              produces the result as output.
    !*/

    template <typename SUBNET> void **setup** (const SUBNET& sub);
    void **forward_inplace**(const tensor& input, tensor& output);
    void **backward_inplace**(const tensor& gradient_input, tensor& data_grad, tensor& params_grad);
    dpoint **map_input_to_output**(dpoint p) const;
    dpoint **map_output_to_input**(dpoint p) const;
    const tensor& **get_layer_params**() const; 
    tensor& **get_layer_params**(); 
    /*!
        These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ interface.
    !*/
**}**;

template <typename SUBNET>
using multiply = add_layer<multiply_, SUBNET>;

// ----------------------------------------------------------------------------------------

const double DEFAULT_LAYER_NORM_EPS = 1e-5;

class **layer_norm_**
**{**
    /*!
        WHAT THIS OBJECT REPRESENTS
            This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
            defined above.  In particular, it defines a batch normalization layer that
            implements the method described in the paper:
                Layer Normalization by Jimmy Lei Ba, Jamie Ryan Kiros, Geoffrey E. Hinton

            In particular, this layer produces output tensors with the same
            dimensionality as the input tensors, except that the mean and variances of
            the elements in each sample have been standardized to 0 and 1 respectively.
            This is different from batch normalization, since this layer learns one scaling
            factor and one bias for each sample in the batch, independently.  As a result,
            this layer is batch-size independent.
    !*/
public:
    **layer_norm_**(
    );
    /*!
        ensures
            - #get_learning_rate_multiplier()       == 1
            - #get_weight_decay_multiplier()        == 0
            - #get_bias_learning_rate_multiplier()  == 1
            - #get_bias_weight_decay_multiplier()   == 1
            - #get_eps() == DEFAULT_LAYER_NORM_EPS
    !*/

    explicit **layer_norm_**(
        double eps_ = DEFAULT_LAYER_NORM_EPS
    )
    /*!
        requires
            - eps > 0
        ensures
            - #get_learning_rate_multiplier()      == 1
            - #get_weight_decay_multiplier()       == 0
            - #get_bias_learning_rate_multiplier() == 1
            - #get_bias_weight_decay_multiplier()  == 1
            - #get_eps() == eps
    !*/

    double **get_eps**(
    ) const;
    /*!
        ensures
            - When doing layer normalization, we are dividing by the standard
              deviation.  This epsilon value returned by this function is added to the
              variance to prevent the division from dividing by zero.
    !*/

    double **get_learning_rate_multiplier**(
    ) const;
    /*!
        ensures
            - returns a multiplier number.  The interpretation is that this object is
              requesting that the learning rate used to optimize its parameters be
              multiplied by get_learning_rate_multiplier().
    !*/

    double **get_weight_decay_multiplier**(
    ) const;
    /*!
        ensures
            - returns a multiplier number.  The interpretation is that this object is
              requesting that the weight decay used to optimize its parameters be
              multiplied by get_weight_decay_multiplier().
    !*/

    void **set_learning_rate_multiplier**(
        double val
    );
    /*!
        requires
            - val >= 0
        ensures
            - #get_learning_rate_multiplier() == val
    !*/

    void **set_weight_decay_multiplier**(
        double val
    );
    /*!
        requires
            - val >= 0
        ensures
            - #get_weight_decay_multiplier() == val
    !*/

    double **get_bias_learning_rate_multiplier**(
    ) const;
    /*!
        ensures
            - returns a multiplier number.  The interpretation is that this object is
              requesting that the learning rate used to optimize its bias parameters be
              multiplied by get_learning_rate_multiplier()*get_bias_learning_rate_multiplier().
    !*/

    double **get_bias_weight_decay_multiplier**(
    ) const;
    /*!
        ensures
            - returns a multiplier number.  The interpretation is that this object is
              requesting that the weight decay used to optimize its bias parameters be
              multiplied by get_weight_decay_multiplier()*get_bias_weight_decay_multiplier().
    !*/

    void **set_bias_learning_rate_multiplier**(
        double val
    );
    /*!
        requires
            - val >= 0
        ensures
            - #get_bias_learning_rate_multiplier() == val
    !*/

    void **set_bias_weight_decay_multiplier**(
        double val
    );
    /*!
        requires
            - val >= 0
        ensures
            - #get_bias_weight_decay_multiplier() == val
    !*/

    template <typename SUBNET> void **setup** (const SUBNET& sub);
    template <typename SUBNET> void **forward**(const SUBNET& sub, resizable_tensor& output);
    template <typename SUBNET> void **backward**(const tensor& gradient_input, SUBNET& sub, tensor& params_grad);
    dpoint **map_input_to_output**(dpoint p) const;
    dpoint **map_output_to_input**(dpoint p) const;
    const tensor& **get_layer_params**() const;
    tensor& **get_layer_params**();
    /*!
        These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ interface.
    !*/
**}**;

// ----------------------------------------------------------------------------------------

const float DEFAULT_RMS_NORM_EPS = 1e-5f;

class **rms_norm_**
**{**
    /*!
        WHAT THIS OBJECT REPRESENTS
            This object implements the EXAMPLE_COMPUTATIONAL_LAYER_ interface
            defined above, specifically defining a root mean square (RMS) normalization layer.

            RMS normalization is a technique that normalizes the input tensor based on the
            root mean square (RMS) of its elements. Unlike traditional layer normalization,
            which both centers and scales the data, RMS normalization only scales by the RMS
            value. This makes it computationally more efficient, as it avoids the need to
            compute the mean and subtract it from each element.

            This layer produces output tensors with the same dimensionality as the input tensors.
            Specifically, for an input tensor with shape [num_samples, k, nr, nc], the RMS
            normalization is applied across the [nr, nc] dimensions independently for each
            element in the [k] dimension and for each sample in the [num_samples] dimension.
            The scaling factor (RMS) and the learnable scaling parameter (gamma) are both of
            size [k].

            The key characteristics of this layer are:
            - The RMS of the elements in each sample is standardized to 1.
            - It does not center the data (i.e., it does not subtract the mean).
            - A learnable scaling factor (gamma) is applied after normalization, allowing the
            model to adapt the scaling dynamically.

            This layer is particularly effective in various natural language processing tasks,
            where it has been shown to provide performance similar to or better than traditional
            layer normalization, with reduced computational overhead.
    !*/

public:
    **rms_norm_**(
    );
    /*!
        ensures
            - #get_learning_rate_multiplier() == 1
            - #get_weight_decay_multiplier()  == 0
            - #get_bias_learning_rate_multiplier()  == 1
            - #get_bias_weight_decay_multiplier()   == 1            
            - #get_eps() == DEFAULT_RMS_NORM_EPS
    !*/

    explicit **rms_norm_**(
        float eps_ = DEFAULT_RMS_NORM_EPS
    );
    /*!
        requires
            - eps > 0
        ensures
            - #get_learning_rate_multiplier() == 1
            - #get_weight_decay_multiplier()  == 0
            - #get_bias_learning_rate_multiplier()  == 1
            - #get_bias_weight_decay_multiplier()   == 1            
            - #get_eps() == eps_
    !*/

    float **get_eps**(
    ) const;
    /*!
        ensures
            - When doing RMS normalization, we are dividing by the root mean square.
            This epsilon value returned by this function is added to the
            mean square to prevent division by zero.
    !*/

    void **set_eps**(
        float val
    );
    /*!
        requires
            - val > 0
        ensures
            - #get_eps() == val
    !*/    

    double **get_learning_rate_multiplier**(
    ) const;
    /*!
        ensures
            - returns a multiplier number. The interpretation is that this object is
            requesting that the learning rate used to optimize its parameters be
            multiplied by get_learning_rate_multiplier().
    !*/

    double **get_weight_decay_multiplier**(
    ) const;
    /*!
        ensures
            - returns a multiplier number. The interpretation is that this object is
            requesting that the weight decay used to optimize its parameters be
            multiplied by get_weight_decay_multiplier().
    !*/

    void **set_learning_rate_multiplier**(
        double val
    );
    /*!
        requires
            - val >= 0
        ensures
            - #get_learning_rate_multiplier() == val
    !*/

    void **set_weight_decay_multiplier**(
        double val
    );
    /*!
        requires
            - val >= 0
        ensures
            - #get_weight_decay_multiplier() == val
    !*/

    double **get_bias_learning_rate_multiplier**(
    ) const;
    /*!
        ensures
            - returns a multiplier number.  The interpretation is that this object is
            requesting that the learning rate used to optimize its bias parameters be
            multiplied by get_learning_rate_multiplier()*get_bias_learning_rate_multiplier().
    !*/

    double **get_bias_weight_decay_multiplier**(
    ) const;
    /*!
        ensures
            - returns a multiplier number.  The interpretation is that this object is
            requesting that the weight decay used to optimize its bias parameters be
            multiplied by get_weight_decay_multiplier()*get_bias_weight_decay_multiplier().
    !*/

    void **set_bias_learning_rate_multiplier**(
        double val
    );
    /*!
        requires
            - val >= 0
        ensures
            - #get_bias_learning_rate_multiplier() == val
    !*/

    void **set_bias_weight_decay_multiplier**(
        double val
    );
    /*!
        requires
            - val >= 0
        ensures
            - #get_bias_weight_decay_multiplier() == val
    !*/

    template <typename SUBNET> void **setup** (const SUBNET& sub);
    template <typename SUBNET> void **forward**(const SUBNET& sub, resizable_tensor& output);
    template <typename SUBNET> void **backward**(const tensor& gradient_input, SUBNET& sub, tensor& params_grad);
    dpoint **map_input_to_output**(dpoint p) const;
    dpoint **map_output_to_input**(dpoint p) const;
    const tensor& **get_layer_params**() const;
    tensor& **get_layer_params**();
    /*!
        These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ interface.
    !*/
**}**;

template <typename SUBNET>
using rms_norm = add_layer<rms_norm_, SUBNET>;

// ----------------------------------------------------------------------------------------

enum **layer_mode**
**{**
    CONV_MODE = 0, // convolutional mode
    FC_MODE = 1    // fully connected mode
**}**;

const double DEFAULT_BATCH_NORM_EPS = 0.0001;

template <
    layer_mode mode
    >
class **bn_**
**{**
    /*!
        WHAT THIS OBJECT REPRESENTS
            This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
            defined above.  In particular, it defines a batch normalization layer that
            implements the method described in the paper: 
                Batch Normalization: Accelerating Deep Network Training by Reducing
                Internal Covariate Shift by Sergey Ioffe and Christian Szegedy
            
            In particular, this layer produces output tensors with the same
            dimensionality as the input tensors, except that the mean and variances of
            the elements have been standardized to 0 and 1 respectively. 

            It should also be noted that when tensors with a num_samples() dimension of
            1 are passed to this layer it doesn't perform batch normalization.
            Instead, it runs in "inference mode" where the learned linear normalizing
            transformation is used to transform the tensor. 

            Finally, after you finish training a batch normalized network, it is a good
            idea to replace each bn_ layer with an affine_ layer because the affine_
            layer is faster and will never surprise you by performing batch
            normalization on tensors that have a num_samples() dimension > 1.  This allows
            you to run large mini-batches of samples through your final network without
            batch normalization executing at all. 
    !*/

public:
    **bn_**(
    );
    /*!
        ensures
            - #get_mode() == mode
            - #get_running_stats_window_size()      == 100
            - #get_learning_rate_multiplier()       == 1
            - #get_weight_decay_multiplier()        == 0
            - #get_bias_learning_rate_multiplier()  == 1
            - #get_bias_weight_decay_multiplier()   == 1
            - #get_eps() == tt::DEFAULT_BATCH_NORM_EPS
    !*/

    explicit **bn_**(
        unsigned long window_size,
        double eps = tt::DEFAULT_BATCH_NORM_EPS
    );
    /*!
        requires
            - eps > 0
            - window_size > 0
        ensures
            - #get_mode() == mode 
            - #get_running_stats_window_size()     == window_size
            - #get_learning_rate_multiplier()      == 1
            - #get_weight_decay_multiplier()       == 0
            - #get_bias_learning_rate_multiplier() == 1
            - #get_bias_weight_decay_multiplier()  == 1
            - #get_eps() == eps
    !*/

    layer_mode **get_mode**(
    ) const; 
    /*!
        ensures
            - returns the mode of this layer, either CONV_MODE or FC_MODE.
              If the mode is FC_MODE then the normalization is applied across the
              samples in a tensor (i.e. k()*nr()*nc() different things will be
              normalized).  Otherwise, normalization is applied across everything
              except for the k() dimension, resulting in there being only k()
              normalization equations that are applied spatially over the tensor.

              Therefore, if you are putting batch normalization after a fully connected
              layer you should use FC_MODE.  Otherwise, if you are putting batch
              normalization after a convolutional layer you should use CONV_MODE.
    !*/

    double **get_eps**(
    ) const; 
    /*!
        ensures
            - When doing batch normalization, we are dividing by the standard
              deviation.  This epsilon value returned by this function is added to the
              variance to prevent the division from dividing by zero.
    !*/

    unsigned long **get_running_stats_window_size** (
    ) const; 
    /*!
        ensures
            - Just as recommended in the batch normalization paper, this object keeps a
              running average of the mean and standard deviations of the features.
              These averages are used during "inference mode" so you can run a single
              object through a batch normalized network.  They are also what is used to
              initialize an affine_ layer that is constructed from a bn_ layer.  This
              function returns the effective number of recent samples used to compute
              the running average.
    !*/

    void **set_running_stats_window_size** (
        unsigned long new_window_size
    );
    /*!
        requires
            - new_window_size > 0
        ensures
            - #get_running_stats_window_size() == new_window_size
    !*/

    double **get_learning_rate_multiplier**(
    ) const;  
    /*!
        ensures
            - returns a multiplier number.  The interpretation is that this object is
              requesting that the learning rate used to optimize its parameters be
              multiplied by get_learning_rate_multiplier().
    !*/

    double **get_weight_decay_multiplier**(
    ) const; 
    /*!
        ensures
            - returns a multiplier number.  The interpretation is that this object is
              requesting that the weight decay used to optimize its parameters be
              multiplied by get_weight_decay_multiplier().
    !*/

    void **set_learning_rate_multiplier**(
        double val
    );
    /*!
        requires
            - val >= 0
        ensures
            - #get_learning_rate_multiplier() == val
    !*/

    void **set_weight_decay_multiplier**(
        double val
    ); 
    /*!
        requires
            - val >= 0
        ensures
            - #get_weight_decay_multiplier() == val
    !*/

    double **get_bias_learning_rate_multiplier**(
    ) const; 
    /*!
        ensures
            - returns a multiplier number.  The interpretation is that this object is
              requesting that the learning rate used to optimize its bias parameters be
              multiplied by get_learning_rate_multiplier()*get_bias_learning_rate_multiplier().
    !*/

    double **get_bias_weight_decay_multiplier**(
    ) const; 
    /*!
        ensures
            - returns a multiplier number.  The interpretation is that this object is
              requesting that the weight decay used to optimize its bias parameters be
              multiplied by get_weight_decay_multiplier()*get_bias_weight_decay_multiplier().
    !*/

    void **set_bias_learning_rate_multiplier**(
        double val
    ); 
    /*!
        requires
            - val >= 0
        ensures
            - #get_bias_learning_rate_multiplier() == val
    !*/

    void **set_bias_weight_decay_multiplier**(
        double val
    ); 
    /*!
        requires
            - val >= 0
        ensures
            - #get_bias_weight_decay_multiplier() == val
    !*/

    template <typename SUBNET> void **setup** (const SUBNET& sub);
    template <typename SUBNET> void **forward**(const SUBNET& sub, resizable_tensor& output);
    template <typename SUBNET> void **backward**(const tensor& gradient_input, SUBNET& sub, tensor& params_grad);
    dpoint **map_input_to_output**(dpoint p) const;
    dpoint **map_output_to_input**(dpoint p) const;
    const tensor& **get_layer_params**() const; 
    tensor& **get_layer_params**(); 
    /*!
        These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ interface.
    !*/
**}**;

template <typename SUBNET>
using bn_con = add_layer<bn_<CONV_MODE>, SUBNET>;
template <typename SUBNET>
using bn_fc = add_layer<bn_<FC_MODE>, SUBNET>;

// ----------------------------------------------------------------------------------------

class **affine_**
**{**
    /*!
        WHAT THIS OBJECT REPRESENTS
            This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
            defined above.  In particular, it applies a simple pointwise linear
            transformation to an input tensor.  You can think of it as having two
            parameter tensors, gamma and beta.  If the input tensor is called INPUT
            then the output of this layer is:
                gamma*INPUT+beta
            where all operations are performed element wise and each sample in the
            INPUT tensor is processed separately.

            Moreover, this object has two modes that affect the dimensionalities of
            gamma and beta and how they are applied to compute gamma*INPUT+beta.  If
            get_mode()==FC_MODE then gamma and beta each have the same dimensionality
            as the input tensor, except their num_samples() dimensions are 1.  If
            get_mode()==CONV_MODE then gamma and beta have all their dimensions set
            to 1 except for k(), which is equal to INPUT.k().

            In either case, the computation of gamma*INPUT+beta is performed pointwise
            over all the elements of INPUT using either:
                OUTPUT(n,k,r,c) == gamma(1,k,r,c)*INPUT(n,k,r,c)+beta(1,k,r,c)
            or
                OUTPUT(n,k,r,c) == gamma(1,k,1,1)*INPUT(n,k,r,c)+beta(1,k,1,1)
            as appropriate.


            Finally, note that the parameters of this layer are not learnable and
            therefore not modified during network updates.  Instead, the layer will
            perform the identity transformation unless it is initialized with a bn_
            layer, in which case it will perform whatever transformation the bn_ layer
            has learned.
    !*/

public:

    **affine_**(
    );
    /*!
        ensures
            - #get_mode() == FC_MODE 
    !*/

    **affine_**(
        layer_mode mode
    );
    /*!
        ensures
            - #get_mode() == mode
    !*/

    template <
        layer_mode mode
        >
    **affine_**(
        const bn_<mode>& layer
    );
    /*!
        ensures
            - Constructs affine_ so that it performs the same transformation as the
              supplied batch normalization layer.  You would want to do this after you
              finish training a network with bn_ layers because the affine_ layer will
              execute faster.  
            - #get_mode() == layer.get_mode()
    !*/

    layer_mode **get_mode**(
    ) const; 
    /*!
        ensures
            - returns the mode of this layer, either CONV_MODE or FC_MODE.  
    !*/

    void **disable**(
    );
    /*!
        ensures
            - #get_layer_params().size() == 0.
            - when forward_inplace and backward_inplace are called, they return immediately doing nothing.
              Causing this layer to trivially perform the an identity transform.
    !*/

    alias_tensor_instance **get_gamma**();
    /*!
        ensures
            - returns the gamma parameter that defines the behavior of forward().
    !*/

    alias_tensor_const_instance **get_gamma**() const;
    /*!
        ensures
            - returns the gamma parameter that defines the behavior of forward().
    !*/

    alias_tensor_instance **get_beta**();
    /*!
        ensures
            - returns the beta parameter that defines the behavior of forward().
    !*/

    alias_tensor_const_instance **get_beta**() const;
    /*!
        ensures
            - returns the beta parameter that defines the behavior of forward().
    !*/

    template <typename SUBNET> void **setup** (const SUBNET& sub);
    void **forward_inplace**(const tensor& input, tensor& output);
    void **backward_inplace**(const tensor& computed_output, const tensor& gradient_input, tensor& data_grad, tensor& params_grad);
    dpoint **map_input_to_output**(dpoint p) const;
    dpoint **map_output_to_input**(dpoint p) const;
    const tensor& **get_layer_params**() const; 
    tensor& **get_layer_params**(); 
    /*!
        These functions are implemented as described in the
        EXAMPLE_COMPUTATIONAL_LAYER_ interface.  Also note that get_layer_params()
        always returns an empty tensor since there are no learnable parameters in this
        object.
    !*/

**}**;

template <typename SUBNET>
using affine = add_layer<affine_, SUBNET>;

// ----------------------------------------------------------------------------------------

template <
    long _nr,
    long _nc,
    int _stride_y,
    int _stride_x,
    int _padding_y = _stride_y!=1? 0 : _nr/2,
    int _padding_x = _stride_x!=1? 0 : _nc/2
    >
class **max_pool_**
**{**
    /*!
        REQUIREMENTS ON TEMPLATE ARGUMENTS
            - _nr >= 0
            - _nc >= 0
            - _stride_y > 0
            - _stride_x > 0
            - _padding_y >= 0
            - _padding_x >= 0
            - if (_nr != 0) then
                - _padding_y < _nr
            - else
                - _padding_y == 0
            - if (_nc != 0) then
                - _padding_x < _nr
            - else
                - _padding_x == 0

        WHAT THIS OBJECT REPRESENTS
            This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
            defined above.  In particular, it defines a max pooling layer that takes an
            input tensor and downsamples it.  It does this by sliding a window over the
            images in an input tensor and outputting, for each channel, the maximum
            element within the window.  

            If _nr == 0 then it means the filter size covers all the rows in the input
            tensor, similarly for the _nc parameter.  To be precise, if we call the
            input tensor IN and the output tensor OUT, then OUT is defined as follows:
                - let FILT_NR == (nr()==0) ? IN.nr() : nr()
                - let FILT_NC == (nc()==0) ? IN.nc() : nc()
                - OUT.num_samples() == IN.num_samples()
                - OUT.k()  == IN.k()
                - OUT.nr() == 1+(IN.nr() + 2*padding_y() - FILT_NR)/stride_y()
                - OUT.nc() == 1+(IN.nc() + 2*padding_x() - FILT_NC)/stride_x()
                - for all valid s, k, r, and c:
                    - image_plane(OUT,s,k)(r,c) == max(subm_clipped(image_plane(IN,s,k),
                                                              centered_rect(x*stride_x() + FILT_NC/2 - padding_x(),
                                                                            y*stride_y() + FILT_NR/2 - padding_y(),
                                                                            FILT_NC,
                                                                            FILT_NR)))
    !*/

public:

    **max_pool_** (
    );
    /*!
        ensures
            - #nr() == _nr
            - #nc() == _nc
            - #stride_y() == _stride_y
            - #stride_x() == _stride_x
            - #padding_y() == _padding_y
            - #padding_x() == _padding_x
    !*/

    long **nr**(
    ) const; 
    /*!
        ensures
            - returns the number of rows in the pooling window or 0 if the window size
              is "the entire input tensor".
    !*/

    long **nc**(
    ) const;
    /*!
        ensures
            - returns the number of rows in the pooling window or 0 if the window size
              is "the entire input tensor".
    !*/

    long **stride_y**(
    ) const; 
    /*!
        ensures
            - returns the vertical stride used when scanning the max pooling window
              over an image.  That is, each window will be moved stride_y() pixels down
              at a time when it moves over the image.
    !*/

    long **stride_x**(
    ) const;
    /*!
        ensures
            - returns the horizontal stride used when scanning the max pooling window
              over an image.  That is, each window will be moved stride_x() pixels down
              at a time when it moves over the image.
    !*/

    long **padding_y**(
    ) const; 
    /*!
        ensures
            - returns the number of pixels of zero padding added to the top and bottom
              sides of the image.
    !*/

    long **padding_x**(
    ) const; 
    /*!
        ensures
            - returns the number of pixels of zero padding added to the left and right 
              sides of the image.
    !*/

    template <typename SUBNET> void **setup** (const SUBNET& sub);
    template <typename SUBNET> void **forward**(const SUBNET& sub, resizable_tensor& output);
    template <typename SUBNET> void **backward**(const tensor& computed_output, const tensor& gradient_input, SUBNET& sub, tensor& params_grad);
    dpoint **map_input_to_output**(dpoint p) const;
    dpoint **map_output_to_input**(dpoint p) const;
    const tensor& **get_layer_params**() const; 
    tensor& **get_layer_params**(); 
    /*!
        These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ 
        interface.  Note that this layer doesn't have any parameters, so the tensor
        returned by get_layer_params() is always empty.
    !*/
**}**;

template <
    long nr,
    long nc,
    int stride_y,
    int stride_x,
    typename SUBNET
    >
using max_pool = add_layer<max_pool_<nr,nc,stride_y,stride_x>, SUBNET>;

template <
    typename SUBNET
    >
using max_pool_everything = add_layer<max_pool_<0,0,1,1>, SUBNET>;

// ----------------------------------------------------------------------------------------

template <
    long _nr,
    long _nc,
    int _stride_y,
    int _stride_x,
    int _padding_y = _stride_y!=1? 0 : _nr/2,
    int _padding_x = _stride_x!=1? 0 : _nc/2
    >
class **avg_pool_**
**{**
    /*!
        REQUIREMENTS ON TEMPLATE ARGUMENTS
            - _nr >= 0
            - _nc >= 0
            - _stride_y > 0
            - _stride_x > 0
            - _padding_y >= 0
            - _padding_x >= 0
            - if (_nr != 0) then
                - _padding_y < _nr
            - else
                - _padding_y == 0
            - if (_nc != 0) then
                - _padding_x < _nr
            - else
                - _padding_x == 0

        WHAT THIS OBJECT REPRESENTS
            This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
            defined above.  In particular, it defines an average pooling layer that
            takes an input tensor and downsamples it.  It does this by sliding a window
            over the images in an input tensor and outputting, for each channel, the
            average element within the window.  

            If _nr == 0 then it means the filter size covers all the rows in the input
            tensor, similarly for the _nc parameter.  To be precise, if we call the
            input tensor IN and the output tensor OUT, then OUT is defined as follows:
                - let FILT_NR == (nr()==0) ? IN.nr() : nr()
                - let FILT_NC == (nc()==0) ? IN.nc() : nc()
                - OUT.num_samples() == IN.num_samples()
                - OUT.k()  == IN.k()
                - OUT.nr() == 1+(IN.nr() + 2*padding_y() - FILT_NR)/stride_y()
                - OUT.nc() == 1+(IN.nc() + 2*padding_x() - FILT_NC)/stride_x()
                - for all valid s, k, r, and c:
                    - image_plane(OUT,s,k)(r,c) == mean(subm_clipped(image_plane(IN,s,k),
                                                              centered_rect(x*stride_x() + FILT_NC/2 - padding_x(),
                                                                            y*stride_y() + FILT_NR/2 - padding_y(),
                                                                            FILT_NC,
                                                                            FILT_NR)))
    !*/

public:

    **avg_pool_** (
    );
    /*!
        ensures
            - #nr() == _nr
            - #nc() == _nc
            - #stride_y() == _stride_y
            - #stride_x() == _stride_x
            - #padding_y() == _padding_y
            - #padding_x() == _padding_x
    !*/

    long **nr**(
    ) const; 
    /*!
        ensures
            - returns the number of rows in the pooling window or 0 if the window size
              is "the entire input tensor".
    !*/

    long **nc**(
    ) const;
    /*!
        ensures
            - returns the number of rows in the pooling window or 0 if the window size
              is "the entire input tensor".
    !*/

    long **stride_y**(
    ) const; 
    /*!
        ensures
            - returns the vertical stride used when scanning the pooling window
              over an image.  That is, each window will be moved stride_y() pixels down
              at a time when it moves over the image.
    !*/

    long **stride_x**(
    ) const;
    /*!
        ensures
            - returns the horizontal stride used when scanning the pooling window
              over an image.  That is, each window will be moved stride_x() pixels down
              at a time when it moves over the image.
    !*/

    long **padding_y**(
    ) const; 
    /*!
        ensures
            - returns the number of pixels of zero padding added to the top and bottom
              sides of the image.
    !*/

    long **padding_x**(
    ) const; 
    /*!
        ensures
            - returns the number of pixels of zero padding added to the left and right 
              sides of the image.
    !*/

    template <typename SUBNET> void **setup** (const SUBNET& sub);
    template <typename SUBNET> void **forward**(const SUBNET& sub, resizable_tensor& output);
    template <typename SUBNET> void **backward**(const tensor& computed_output, const tensor& gradient_input, SUBNET& sub, tensor& params_grad);
    dpoint **map_input_to_output**(dpoint p) const;
    dpoint **map_output_to_input**(dpoint p) const;
    const tensor& **get_layer_params**() const; 
    tensor& **get_layer_params**(); 
    /*!
        These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ 
        interface.  Note that this layer doesn't have any parameters, so the tensor
        returned by get_layer_params() is always empty.
    !*/

**}**;

template <
    long nr,
    long nc,
    int stride_y,
    int stride_x,
    typename SUBNET
    >
using avg_pool = add_layer<avg_pool_<nr,nc,stride_y,stride_x>, SUBNET>;

template <
    typename SUBNET
    >
using avg_pool_everything = add_layer<avg_pool_<0,0,1,1>, SUBNET>;

// ----------------------------------------------------------------------------------------

class **relu_**
**{**
    /*!
        WHAT THIS OBJECT REPRESENTS
            This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
            defined above.  In particular, it defines a rectified linear layer.
            Therefore, it passes its inputs through the function 
                f(x)=max(x,0) 
            where f() is applied pointwise across the input tensor.
    !*/

public:

    **relu_**(
    );

    void **disable**(
    );
    /*!
        ensures
            - #get_layer_params().size() == 0.
            - when forward_inplace and backward_inplace are called, they return immediately doing nothing.
              Causing this layer to trivially perform the an identity transform.
    !*/

    template <typename SUBNET> void **setup** (const SUBNET& sub);
    void **forward_inplace**(const tensor& input, tensor& output);
    void **backward_inplace**(const tensor& computed_output, const tensor& gradient_input, tensor& data_grad, tensor& params_grad);
    dpoint **map_input_to_output**(dpoint p) const;
    dpoint **map_output_to_input**(dpoint p) const;
    const tensor& **get_layer_params**() const; 
    tensor& **get_layer_params**(); 
    /*!
        These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ 
        interface.  Note that this layer doesn't have any parameters, so the tensor
        returned by get_layer_params() is always empty.
    !*/
**}**;

template <typename SUBNET>
using relu = add_layer<relu_, SUBNET>;

// ----------------------------------------------------------------------------------------

class **prelu_**
**{**
    /*!
        WHAT THIS OBJECT REPRESENTS
            This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
            defined above.  In particular, it defines a parametric rectified linear
            layer.  Therefore, it passes its inputs through the function 
                f(x) = x>0 ? x : p*x 
            where f() is applied pointwise across the input tensor and p is a scalar
            parameter learned by this layer.


            This is the layer type introduced in the paper:
                He, Kaiming, et al. "Delving deep into rectifiers: Surpassing
                human-level performance on imagenet classification." Proceedings of the
                IEEE International Conference on Computer Vision. 2015.
    !*/

public:

    explicit **prelu_**(
        float initial_param_value = 0.25
    );
    /*!
        ensures
            - The p parameter will be initialized with initial_param_value.
            - #get_initial_param_value() == initial_param_value.
    !*/

    float **get_initial_param_value** (
    ) const;
    /*!
        ensures
            - returns the initial value of the prelu parameter. 
    !*/

    template <typename SUBNET> void **setup** (const SUBNET& sub);
    void **forward_inplace**(const tensor& input, tensor& output);
    void **backward_inplace**(const tensor& computed_output, const tensor& gradient_input, tensor& data_grad, tensor& params_grad);
    dpoint **map_input_to_output**(dpoint p) const;
    dpoint **map_output_to_input**(dpoint p) const;
    const tensor& **get_layer_params**() const; 
    tensor& **get_layer_params**(); 
    /*!
        These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ interface.
    !*/
**}**;

template <typename SUBNET>
using prelu = add_layer<prelu_, SUBNET>;

// ----------------------------------------------------------------------------------------

class **leaky_relu_**
**{**
    /*!
        WHAT THIS OBJECT REPRESENTS
            This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
            defined above.  In particular, it defines a leaky rectified linear
            layer.  Therefore, it passes its inputs through the function
                f(x) = x>0 ? x : alpha*x
            where f() is applied pointwise across the input tensor and alpha is a
            non-learned scalar.

            This is the layer type introduced in the paper:
                A. L. Maas, A. Y. Hannun, and A. Y. Ng. "Rectifier nonlinearities improve
                neural network acoustic models". In ICML, 2013.
    !*/

public:
    explicit **leaky_relu_**(
        float alpha = 0.01f
    );
    /*!
        ensures
            - the alpha parameter will be initialized with the alpha value
    !*/

    float **get_alpha**(
    ) const;
    /*!
        ensures
            - returns the alpha parameter of the leaky_relu
    !*/

    template <typename SUBNET> void **setup**(const SUBNET& sub);
    void **forward_inplace**(const tensor& input, tensor& output);
    void **backward_inplace**(const tensor& computed_output, const tensor& gradient_input, tensor& data_grad, tensor& params_grad);
    dpoint **map_input_to_output**(dpoint p) const;
    dpoint **map_output_to_input**(dpoint p) const;
    const tensor& **get_layer_params**() const;
    tensor& **get_layer_params**();
    /*!
        These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_
        interface.  Note that this layer doesn't have any parameters, so the tensor
        returned by get_layer_params() is always empty.
    !*/
**}**;

template <typename SUBNET>
using leaky_relu = add_layer<prelu_, SUBNET>;

// ----------------------------------------------------------------------------------------

class **sig_**
**{**
    /*!
        WHAT THIS OBJECT REPRESENTS
            This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
            defined above.  In particular, it defines a sigmoid layer.  Therefore, it
            passes its inputs through the function 
                f(x)=1/(1+exp(-x)) 
            where f() is applied pointwise across the input tensor.
    !*/

public:

    **sig_**(
    );

    template <typename SUBNET> void **setup** (const SUBNET& sub);
    void **forward_inplace**(const tensor& input, tensor& output);
    void **backward_inplace**(const tensor& computed_output, const tensor& gradient_input, tensor& data_grad, tensor& params_grad);
    dpoint **map_input_to_output**(dpoint p) const;
    dpoint **map_output_to_input**(dpoint p) const;
    const tensor& **get_layer_params**() const; 
    tensor& **get_layer_params**(); 
    /*!
        These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ 
        interface.  Note that this layer doesn't have any parameters, so the tensor
        returned by get_layer_params() is always empty.
    !*/
**}**;

template <typename SUBNET>
using sig = add_layer<sig_, SUBNET>;

// ----------------------------------------------------------------------------------------

class **mish_**
**{**
    /*!
        WHAT THIS OBJECT REPRESENTS
            This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
            defined above.  In particular, it defines a mish layer.  Therefore, it
            passes its inputs through the function
                f(x)= x*tanh(log(1+exp(x)))
            where f() is applied pointwise across the input tensor.

            This is the layer type introduced in the paper:
            Diganta Misra. "Mish: A Self Regularized Non-Monotonic Activation Function"
    !*/

public:

    **mish_**(
    );

    template <typename SUBNET> void **setup** (const SUBNET& sub);
    template <typename SUBNET> void **forward**(const SUBNET& sub, resizable_tensor& data_output);
    template <typename SUBNET> void **backward**(const tensor& gradient_input, SUBNET& sub, tensor&);
    dpoint **map_input_to_output**(dpoint p) const;
    dpoint **map_output_to_input**(dpoint p) const;
    const tensor& **get_layer_params**() const;
    tensor& **get_layer_params**();
    /*!
        These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_
        interface.  Note that this layer doesn't have any parameters, so the tensor
        returned by get_layer_params() is always empty.
    !*/
**}**;

template <typename SUBNET>
using mish = add_layer<mish_, SUBNET>;

// ----------------------------------------------------------------------------------------

class **htan_**
**{**
    /*!
        WHAT THIS OBJECT REPRESENTS
            This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
            defined above.  In particular, it defines a hyperbolic tangent layer.
            Therefore, it passes its inputs through the function 
                f(x)=std::tanh(x)
            where f() is applied pointwise across the input tensor.
    !*/

public:

    **htan_**(
    );

    template <typename SUBNET> void **setup** (const SUBNET& sub);
    void **forward_inplace**(const tensor& input, tensor& output);
    void **backward_inplace**(const tensor& computed_output, const tensor& gradient_input, tensor& data_grad, tensor& params_grad);
    dpoint **map_input_to_output**(dpoint p) const;
    dpoint **map_output_to_input**(dpoint p) const;
    const tensor& **get_layer_params**() const; 
    tensor& **get_layer_params**(); 
    /*!
        These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ 
        interface.  Note that this layer doesn't have any parameters, so the tensor
        returned by get_layer_params() is always empty.
    !*/
**}**;

template <typename SUBNET>
using htan = add_layer<htan_, SUBNET>;

// ----------------------------------------------------------------------------------------

class **clipped_relu_**
**{**
    /*!
        WHAT THIS OBJECT REPRESENTS
            This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
            defined above.  In particular, it defines a clipped version of the relu layer.
            Therefore, it passes its inputs through the function
                f(x) = min(max(x, 0), ceiling)
            where f() is applied pointwise across the input tensor and ceiling is a
            non-learned scalar.
    !*/

public:

    **clipped_relu_**(
        const float ceiling = 6.0f
    );
    /*!
        ensures
            - the ceiling parameter will be initialized with the ceiling value
    !*/

    float **get_ceiling**() const;
    /*!
        ensures
            - returns the celiling parameter of the clipped_relu
    !*/

    template <typename SUBNET> void **setup** (const SUBNET& sub);
    void **forward_inplace**(const tensor& input, tensor& output);
    void **backward_inplace**(const tensor& computed_output, const tensor& gradient_input, tensor& data_grad, tensor& params_grad);
    dpoint **map_input_to_output**(dpoint p) const;
    dpoint **map_output_to_input**(dpoint p) const;
    const tensor& **get_layer_params**() const;
    tensor& **get_layer_params**();
    /*!
        These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_
        interface.  Note that this layer doesn't have any parameters, so the tensor
        returned by get_layer_params() is always empty.
    !*/
**}**;

template <typename SUBNET>
using clipped_relu = add_layer<clipped_relu_, SUBNET>;

// ----------------------------------------------------------------------------------------

class **elu_**
**{**
    /*!
        WHAT THIS OBJECT REPRESENTS
            This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
            defined above.  In particular, it defines an exponential linear unit.
            Therefore, it passes its inputs through the function
                f(x) = x>0 ? x : alpha*(exp(x)-1)
            where f() is applied pointwise across the input tensor and alpha is a
            non-learned scalar.

            This is the layer type introduced in the paper:
            Djork-Arné Clevert, Thomas Unterthiner, Sepp Hochreiter.
            "Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)".
    !*/

public:

    **elu_**(
        const float alpha = 1.0f
    );
    /*!
        ensures
            - the alpha parameter will be initialized with the alpha value
    !*/

    float **get_alpha**() const;
    /*!
        ensures
            - returns the alpha parameter of the elu
    !*/
    template <typename SUBNET> void **setup** (const SUBNET& sub);
    void **forward_inplace**(const tensor& input, tensor& output);
    void **backward_inplace**(const tensor& computed_output, const tensor& gradient_input, tensor& data_grad, tensor& params_grad);
    dpoint **map_input_to_output**(dpoint p) const;
    dpoint **map_output_to_input**(dpoint p) const;
    const tensor& **get_layer_params**() const;
    tensor& **get_layer_params**();
    /*!
        These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_
        interface.  Note that this layer doesn't have any parameters, so the tensor
        returned by get_layer_params() is always empty.
    !*/
**}**;

template <typename SUBNET>
using elu = add_layer<elu_, SUBNET>;

// ----------------------------------------------------------------------------------------

class **gelu_**
**{**
    /*!
        WHAT THIS OBJECT REPRESENTS
            This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
            defined above.  In particular, it defines a gelu layer.  Therefore, it
            passes its inputs through the function
                    f(x)= x/2 * (1 + erf(x/sqrt(2))
            where f() is applied pointwise across the input tensor.

            This is the layer type introduced in the paper:
            Dan Hendrycks, Kevin Gimpel. "Gaussian Error Linear Units (GELUs)".
    !*/

public:

    **gelu_**(
    );

    template <typename SUBNET> void **setup** (const SUBNET& sub);
    template <typename SUBNET> void **forward**(const SUBNET& sub, resizable_tensor& data_output);
    template <typename SUBNET> void **backward**(const tensor& gradient_input, SUBNET& sub, tensor&);
    dpoint **map_input_to_output**(dpoint p) const;
    dpoint **map_output_to_input**(dpoint p) const;
    const tensor& **get_layer_params**() const;
    tensor& **get_layer_params**();
    /*!
        These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_
        interface.  Note that this layer doesn't have any parameters, so the tensor
        returned by get_layer_params() is always empty.
    !*/
**}**;

template <typename SUBNET>
using gelu = add_layer<gelu_, SUBNET>;

// ----------------------------------------------------------------------------------------

class **smelu_**
**{**
    /*!
        WHAT THIS OBJECT REPRESENTS
            This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
            defined above.  In particular, it defines a smooth rectified linear
            layer.  Therefore, it passes its inputs through the function f(x):
                - if (x > beta) 1
                - if (x < -beta) 0
                - else std::pow(x + beta, 2) / (4 * beta)
            where f() is applied pointwise across the input tensor and beta is a
            non-learned scalar.

            This is the layer type introduced in the paper:
            "Smooth activations and reproducibility in deep networks" by
            Gil I. Shamir, Dong Lin, Lorenzo Coviello (https://arxiv.org/abs/2010.09931)
    !*/

public:
    explicit **smelu_**(
        float beta = 1
    );
    /*!
        ensures
            - the beta parameter will be initialized with the beta value
    !*/

    float **get_beta**(
    ) const;
    /*!
        ensures
            - returns the beta parameter of the smelu
    !*/

    template <typename SUBNET> void **setup**(const SUBNET& sub);
    void **forward_inplace**(const tensor& input, tensor& output);
    void **backward_inplace**(const tensor& computed_output, const tensor& gradient_input, tensor& data_grad, tensor& params_grad);
    dpoint **map_input_to_output**(dpoint p) const;
    dpoint **map_output_to_input**(dpoint p) const;
    const tensor& **get_layer_params**() const;
    tensor& **get_layer_params**();
    /*!
        These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_
        interface.  Note that this layer doesn't have any parameters, so the tensor
        returned by get_layer_params() is always empty.
    !*/
**}**;

template <typename SUBNET>
using smelu = add_layer<prelu_, SUBNET>;

// ----------------------------------------------------------------------------------------

class **silu_**
**{**
    /*!
        WHAT THIS OBJECT REPRESENTS
            This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
            defined above.  In particular, it defines a silu layer.  Therefore, it
            passes its inputs through the function
                    f(x)= x * sigmoid(x) = x / (1 + exp(-x))
            where f() is applied pointwise across the input tensor.

            This is the layer type introduced in the paper:
            Dan Hendrycks, Kevin Gimpel. "Gaussian Error Linear Units (GELUs)".
    !*/

public:

    **silu_**(
    );

    template <typename SUBNET> void **setup** (const SUBNET& sub);
    template <typename SUBNET> void **forward**(const SUBNET& sub, resizable_tensor& data_output);
    template <typename SUBNET> void **backward**(const tensor& gradient_input, SUBNET& sub, tensor&);
    dpoint **map_input_to_output**(dpoint p) const;
    dpoint **map_output_to_input**(dpoint p) const;
    const tensor& **get_layer_params**() const;
    tensor& **get_layer_params**();
    /*!
        These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_
        interface.  Note that this layer doesn't have any parameters, so the tensor
        returned by get_layer_params() is always empty.
    !*/
**}**;

template <typename SUBNET>
using silu = add_layer<silu_, SUBNET>;

// ----------------------------------------------------------------------------------------

template <operation_mode s_mode_>
class **softmax_**
**{**
    /*!
        WHAT THIS OBJECT REPRESENTS
            This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
            defined above. It defines a softmax layer with two modes of operation:
            channel-wise and plane-wise.

            The softmax function s(x) is defined as:
                s(x) == exp(x)/sum(exp(x))
            where x is a vector.

            1. Channel-wise mode (s_mode_ == CHANNEL_WISE):
            This mode treats the input tensor as a collection of multi-channel images
            and applies s() to each spatial location in each image. The tensor::k()
            channel elements at each position are input to s() and then replaced by
            the outputs of s().

            2. Plane-wise mode (s_mode_ == PLANE_WISE):
            This mode applies the softmax function across entire planes (nr x nc) of
            the input tensor, useful for operations in Large Language Models (LLMs)
            and other applications requiring 2D tensor processing.

            In both modes, the sum of the outputs of s() will always be equal to 1 for
            each application of the function.

        TEMPLATE PARAMETERS
            - s_mode_: Determines the mode of operation (CHANNEL_WISE or PLANE_WISE)
    !*/

public:
    **softmax_**();

    template <typename SUBNET> void **setup**(const SUBNET& sub);
    void **forward_inplace**(const tensor& input, tensor& output);
    void **backward_inplace**(
        const tensor& computed_output,
        const tensor& gradient_input,
        tensor& data_grad,
        tensor& params_grad
    );
    const tensor& **get_layer_params**() const;
    tensor& **get_layer_params**();
    /*!
        These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_
        interface. Note that this layer doesn't have any parameters, so the tensor
        returned by get_layer_params() is always empty.
    !*/

    friend void **serialize**(const softmax_& item, std::ostream& out);
    friend void **deserialize**(softmax_& item, std::istream& in);
    friend std::ostream& **operator**<<(std::ostream& out, const softmax_& item);
    friend void **to_xml**(const softmax_& item, std::ostream& out);
**}**;

template <typename SUBNET>
using softmax = add_layer<softmax_<operation_mode::CHANNEL_WISE>, SUBNET>;

template <typename SUBNET>
using softmaxm = add_layer<softmax_<operation_mode::PLANE_WISE>, SUBNET>;

// ----------------------------------------------------------------------------------------

class **softmax_all_**
**{**
    /*!
        WHAT THIS OBJECT REPRESENTS
            This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
            defined above.  In particular, it defines a softmax layer.  To be precise,
            we define the softmax function s(x) as:
                s(x) == exp(x)/sum(exp(x)) 
            where x is a vector.  Then this layer treats its input tensor as a
            collection of tensor::num_samples() vectors and applies s() to each vector
            in the tensor.  Therefore, there are logically tensor::num_samples()
            invocations of s().
    !*/

public:

    **softmax_all_**(
    );

    template <typename SUBNET> void **setup** (const SUBNET& sub);
    void **forward_inplace**(const tensor& input, tensor& output);
    void **backward_inplace**(const tensor& computed_output, const tensor& gradient_input, tensor& data_grad, tensor& params_grad);
    const tensor& **get_layer_params**() const; 
    tensor& **get_layer_params**(); 
    /*!
        These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ 
        interface.  Note that this layer doesn't have any parameters, so the tensor
        returned by get_layer_params() is always empty.
    !*/
**}**;

template <typename SUBNET>
using softmax_all = add_layer<softmax_all_, SUBNET>;

// ----------------------------------------------------------------------------------------

template <
    template<typename> class **tag**
    >
class **add_prev_**
**{**
    /*!
        WHAT THIS OBJECT REPRESENTS
            This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
            defined above.  This layer simply adds the output of two previous layers.
            In particular, it adds the tensor from its immediate predecessor layer,
            sub.get_output(), with the tensor from a deeper layer,
            layer<tag>(sub).get_output().

            Therefore, you supply a tag via add_prev_'s template argument that tells it
            what layer to add to the output of the previous layer.  The result of this
            addition is output by add_prev_.  Finally, the addition happens pointwise
            according to 4D tensor arithmetic.  If the dimensions don't match then
            missing elements are presumed to be equal to 0.  Moreover, each dimension
            of the output tensor is equal to the maximum dimension of either of the
            inputs.  That is, if the tensors A and B are being added to produce C then:
                - C.num_samples() == max(A.num_samples(), B.num_samples())
                - C.k()  == max(A.k(), B.k())
                - C.nr() == max(A.nr(), B.nr())
                - C.nc() == max(A.nc(), B.nc())
    !*/

public:
    **add_prev_**(
    ); 

    template <typename SUBNET> void **setup** (const SUBNET& sub);
    template <typename SUBNET> void **forward**(const SUBNET& sub, resizable_tensor& output);
    template <typename SUBNET> void **backward**(const tensor& gradient_input, SUBNET& sub, tensor& params_grad);
    dpoint **map_input_to_output**(dpoint p) const;
    dpoint **map_output_to_input**(dpoint p) const;
    const tensor& **get_layer_params**() const; 
    tensor& **get_layer_params**(); 
    /*!
        These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ interface.
    !*/
**}**;


template <
    template<typename> class **tag**,
    typename SUBNET
    >
using add_prev = add_layer<add_prev_<tag>, SUBNET>;

// Here we add some convenient aliases for using add_prev_ with the tag layers. 
template <typename SUBNET> using add_prev1  = add_prev<tag1, SUBNET>;
template <typename SUBNET> using add_prev2  = add_prev<tag2, SUBNET>;
template <typename SUBNET> using add_prev3  = add_prev<tag3, SUBNET>;
template <typename SUBNET> using add_prev4  = add_prev<tag4, SUBNET>;
template <typename SUBNET> using add_prev5  = add_prev<tag5, SUBNET>;
template <typename SUBNET> using add_prev6  = add_prev<tag6, SUBNET>;
template <typename SUBNET> using add_prev7  = add_prev<tag7, SUBNET>;
template <typename SUBNET> using add_prev8  = add_prev<tag8, SUBNET>;
template <typename SUBNET> using add_prev9  = add_prev<tag9, SUBNET>;
template <typename SUBNET> using add_prev10 = add_prev<tag10, SUBNET>;
using add_prev1_  = add_prev_<tag1>;
using add_prev2_  = add_prev_<tag2>;
using add_prev3_  = add_prev_<tag3>;
using add_prev4_  = add_prev_<tag4>;
using add_prev5_  = add_prev_<tag5>;
using add_prev6_  = add_prev_<tag6>;
using add_prev7_  = add_prev_<tag7>;
using add_prev8_  = add_prev_<tag8>;
using add_prev9_  = add_prev_<tag9>;
using add_prev10_ = add_prev_<tag10>;

// ----------------------------------------------------------------------------------------

template <
    template<typename> class **tag**
    >
class **mult_prev_**
**{**
    /*!
        WHAT THIS OBJECT REPRESENTS
            This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
            defined above.  This layer simply multiplies the output of two previous
            layers.  In particular, it multiplies the tensor from its immediate
            predecessor layer, sub.get_output(), with the tensor from a deeper layer,
            layer<tag>(sub).get_output().

            Therefore, you supply a tag via mult_prev_'s template argument that tells
            it what layer to multiply with the output of the previous layer.  The
            result of this multiplication is output by mult_prev_.  Finally, the
            multiplication happens pointwise according to 4D tensor arithmetic.  If the
            dimensions don't match then missing elements are presumed to be equal to 0.
            Moreover, each dimension of the output tensor is equal to the maximum
            dimension of either of the inputs.  That is, if the tensors A and B are
            being multiplied to produce C then:
                - C.num_samples() == max(A.num_samples(), B.num_samples())
                - C.k()  == max(A.k(), B.k())
                - C.nr() == max(A.nr(), B.nr())
                - C.nc() == max(A.nc(), B.nc())
    !*/

public:
    **mult_prev_**(
    ); 

    template <typename SUBNET> void **setup** (const SUBNET& sub);
    template <typename SUBNET> void **forward**(const SUBNET& sub, resizable_tensor& output);
    template <typename SUBNET> void **backward**(const tensor& gradient_input, SUBNET& sub, tensor& params_grad);
    dpoint **map_input_to_output**(dpoint p) const;
    dpoint **map_output_to_input**(dpoint p) const;
    const tensor& **get_layer_params**() const; 
    tensor& **get_layer_params**(); 
    /*!
        These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ interface.
    !*/
**}**;


template <
    template<typename> class **tag**,
    typename SUBNET
    >
using mult_prev = add_layer<mult_prev_<tag>, SUBNET>;

// Here we add some convenient aliases for using mult_prev_ with the tag layers. 
template <typename SUBNET> using mult_prev1  = mult_prev<tag1, SUBNET>;
template <typename SUBNET> using mult_prev2  = mult_prev<tag2, SUBNET>;
template <typename SUBNET> using mult_prev3  = mult_prev<tag3, SUBNET>;
template <typename SUBNET> using mult_prev4  = mult_prev<tag4, SUBNET>;
template <typename SUBNET> using mult_prev5  = mult_prev<tag5, SUBNET>;
template <typename SUBNET> using mult_prev6  = mult_prev<tag6, SUBNET>;
template <typename SUBNET> using mult_prev7  = mult_prev<tag7, SUBNET>;
template <typename SUBNET> using mult_prev8  = mult_prev<tag8, SUBNET>;
template <typename SUBNET> using mult_prev9  = mult_prev<tag9, SUBNET>;
template <typename SUBNET> using mult_prev10 = mult_prev<tag10, SUBNET>;
using mult_prev1_  = mult_prev_<tag1>;
using mult_prev2_  = mult_prev_<tag2>;
using mult_prev3_  = mult_prev_<tag3>;
using mult_prev4_  = mult_prev_<tag4>;
using mult_prev5_  = mult_prev_<tag5>;
using mult_prev6_  = mult_prev_<tag6>;
using mult_prev7_  = mult_prev_<tag7>;
using mult_prev8_  = mult_prev_<tag8>;
using mult_prev9_  = mult_prev_<tag9>;
using mult_prev10_ = mult_prev_<tag10>;

// ----------------------------------------------------------------------------------------

template <
    template<typename> class **tag**
    >
class **multm_prev_**
**{**
    /*!
        WHAT THIS OBJECT REPRESENTS
            This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
            defined above. This layer performs matrix multiplication on the output
            of two previous layers. It multiplies the tensor from its immediate
            predecessor layer, sub.get_output(), with the tensor from a deeper layer,
            layer<tag>(sub).get_output().

            The tag template argument specifies which layer to multiply with the
            output of the previous layer. The result of this multiplication is
            output by multm_prev_. The multiplication is performed using a modified
            version of gemm() to account for the 2D matrix dimension in the nr()xnc()
            planes of Dlib's 4D tensors.

            This layer is similar to mult_prev_, but it considers the full matrix
            in the nr()xnc() planes of the tensor, rather than just the upper
            num_samples()xk() plane. This makes it suitable for implementing
            mechanisms like attention, especially when the k() channel plane is
            used to model multiple heads for parallel matrix processing.

            The output tensor dimensions are determined as follows:
                - output.num_samples() == t1.num_samples()
                - output.k() == t1.k()
                - output.nr() == t1.nr()
                - output.nc() == t2.nc()
            where t1 is sub.get_output() and t2 is layer<tag>(sub).get_output().
    !*/

public:
    **multm_prev_**(
    ); 

    template <typename SUBNET> void **setup** (const SUBNET& sub);
    template <typename SUBNET> void **forward**(const SUBNET& sub, resizable_tensor& output);
    template <typename SUBNET> void **backward**(const tensor& gradient_input, SUBNET& sub, tensor& params_grad);
    dpoint **map_input_to_output**(dpoint p) const;
    dpoint **map_output_to_input**(dpoint p) const;        
    const tensor& **get_layer_params**() const; 
    tensor& **get_layer_params**(); 
    /*!
        These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ interface.
    !*/
**}**;

template <
    template<typename> class **tag**,
    typename SUBNET
    >
using multm_prev = add_layer<multm_prev_<tag>, SUBNET>;

// Here we add some convenient aliases for using multm_prev_ with the tag layers. 
template <typename SUBNET> using multm_prev1  = multm_prev<tag1, SUBNET>;
template <typename SUBNET> using multm_prev2  = multm_prev<tag2, SUBNET>;
template <typename SUBNET> using multm_prev3  = multm_prev<tag3, SUBNET>;
template <typename SUBNET> using multm_prev4  = multm_prev<tag4, SUBNET>;
template <typename SUBNET> using multm_prev5  = multm_prev<tag5, SUBNET>;
template <typename SUBNET> using multm_prev6  = multm_prev<tag6, SUBNET>;
template <typename SUBNET> using multm_prev7  = multm_prev<tag7, SUBNET>;
template <typename SUBNET> using multm_prev8  = multm_prev<tag8, SUBNET>;
template <typename SUBNET> using multm_prev9  = multm_prev<tag9, SUBNET>;
template <typename SUBNET> using multm_prev10 = multm_prev<tag10, SUBNET>;
using multm_prev1_  = multm_prev_<tag1>;
using multm_prev2_  = multm_prev_<tag2>;
using multm_prev3_  = multm_prev_<tag3>;
using multm_prev4_  = multm_prev_<tag4>;
using multm_prev5_  = multm_prev_<tag5>;
using multm_prev6_  = multm_prev_<tag6>;
using multm_prev7_  = multm_prev_<tag7>;
using multm_prev8_  = multm_prev_<tag8>;
using multm_prev9_  = multm_prev_<tag9>;
using multm_prev10_ = multm_prev_<tag10>;

// ----------------------------------------------------------------------------------------

template <
    template<typename> class **tag**
    >
class **resize_prev_to_tagged_**
**{**
    /*!
        WHAT THIS OBJECT REPRESENTS
            This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
            defined above.  This layer resizes the output channels of the previous layer
            to have the same number of rows and columns as the output of the tagged layer.

            This layer uses bilinear interpolation. If the sizes match already, then it
            simply copies the data.

            Therefore, you supply a tag via resize_prev_to_tagged's template argument that
            tells it what layer to use for the target size.

            If tensor PREV is resized to size of tensor TAGGED, then a tensor OUT is
            produced such that:
                - OUT.num_samples() == PREV.num_samples()
                - OUT.k()  == PREV.k()
                - OUT.nr() == TAGGED.nr()
                - OUT.nc() == TAGGED.nc()
    !*/

public:
    **resize_prev_to_tagged_**(
    ); 

    template <typename SUBNET> void **setup**(const SUBNET& sub);
    template <typename SUBNET> void **forward**(const SUBNET& sub, resizable_tensor& output);
    template <typename SUBNET> void **backward**(const tensor& gradient_input, SUBNET& sub, tensor& params_grad);
    dpoint **map_input_to_output**(dpoint p) const;
    dpoint **map_output_to_input**(dpoint p) const;
    const tensor& **get_layer_params**() const; 
    tensor& **get_layer_params**(); 
    /*!
        These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ interface.
    !*/
**}**;


template <
    template<typename> class **tag**,
    typename SUBNET
    >
using resize_prev_to_tagged = add_layer<resize_prev_to_tagged_<tag>, SUBNET>;

// ----------------------------------------------------------------------------------------

template <
    template<typename> class **tag**
    >
class **scale_**
**{**
    /*!
        WHAT THIS OBJECT REPRESENTS
            This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
            defined above.  This layer scales the output channels of the tagged layer
            by multiplying it with the output of the previous layer.  To be specific:
                - Let INPUT  == layer<tag>(sub).get_output()
                - Let SCALES == sub.get_output()
                - This layer takes INPUT and SCALES as input.
                - The output of this layer has the same dimensions as INPUT.
                - This layer requires:
                    - SCALES.num_samples() == INPUT.num_samples()
                    - SCALES.k()  == INPUT.k()
                    - SCALES.nr() == 1
                    - SCALES.nc() == 1
                - The output tensor is produced by pointwise multiplying SCALES with
                  INPUT at each spatial location.  Therefore, if OUT is the output of
                  this layer then we would have:
                    OUT(n,k,r,c) == INPUT(n,k,r,c)*SCALES(n,k)
    !*/

public:
    **scale_**(
    ); 

    template <typename SUBNET> void **setup** (const SUBNET& sub);
    template <typename SUBNET> void **forward**(const SUBNET& sub, resizable_tensor& output);
    template <typename SUBNET> void **backward**(const tensor& gradient_input, SUBNET& sub, tensor& params_grad);
    const tensor& **get_layer_params**() const; 
    tensor& **get_layer_params**(); 
    /*!
        These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ interface.
    !*/
**}**;


template <
    template<typename> class **tag**,
    typename SUBNET
    >
using scale = add_layer<scale_<tag>, SUBNET>;

// Here we add some convenient aliases for using scale_ with the tag layers. 
template <typename SUBNET> using scale1  = scale<tag1, SUBNET>;
template <typename SUBNET> using scale2  = scale<tag2, SUBNET>;
template <typename SUBNET> using scale3  = scale<tag3, SUBNET>;
template <typename SUBNET> using scale4  = scale<tag4, SUBNET>;
template <typename SUBNET> using scale5  = scale<tag5, SUBNET>;
template <typename SUBNET> using scale6  = scale<tag6, SUBNET>;
template <typename SUBNET> using scale7  = scale<tag7, SUBNET>;
template <typename SUBNET> using scale8  = scale<tag8, SUBNET>;
template <typename SUBNET> using scale9  = scale<tag9, SUBNET>;
template <typename SUBNET> using scale10 = scale<tag10, SUBNET>;
using scale1_  = scale_<tag1>;
using scale2_  = scale_<tag2>;
using scale3_  = scale_<tag3>;
using scale4_  = scale_<tag4>;
using scale5_  = scale_<tag5>;
using scale6_  = scale_<tag6>;
using scale7_  = scale_<tag7>;
using scale8_  = scale_<tag8>;
using scale9_  = scale_<tag9>;
using scale10_ = scale_<tag10>;

// ----------------------------------------------------------------------------------------

template <
    template<typename> class **tag**
    >
class **scale_prev_**
**{**
    /*!
        WHAT THIS OBJECT REPRESENTS
            This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
            defined above.  This layer scales the output channels of the tagged layer
            by multiplying it with the output of the previous layer.  It is excatly the
            same as the scale_ layer, but with the inputs swapped, which is useful since
            it allows mapping between inputs and outputs of this layer.  To be specific:
                - Let INPUT == sub.get_output()
                - Let SCALES == layer<tag>(sub).get_output()
                - This layer takes INPUT and SCALES as input.
                - The output of this layer has the same dimensions as INPUT.
                - This layer requires:
                    - SCALES.num_samples() == INPUT.num_samples()
                    - SCALES.k()  == INPUT.k()
                    - SCALES.nr() == 1
                    - SCALES.nc() == 1
                - The output tensor is produced by pointwise multiplying SCALES with
                  INPUT at each spatial location.  Therefore, if OUT is the output of
                  this layer then we would have:
                    OUT(n,k,r,c) == INPUT(n,k,r,c)*SCALES(n,k)
    !*/

public:
    **scale_prev_**(
    );

    template <typename SUBNET> void **setup** (const SUBNET& sub);
    template <typename SUBNET> void **forward**(const SUBNET& sub, resizable_tensor& output);
    template <typename SUBNET> void **backward**(const tensor& gradient_input, SUBNET& sub, tensor& params_grad);
    dpoint **map_input_to_output**(dpoint p) const;
    dpoint **map_output_to_input**(dpoint p) const;
    const tensor& **get_layer_params**() const;
    tensor& **get_layer_params**();
    /*!
        These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ interface.
    !*/
**}**;


template <
    template<typename> class **tag**,
    typename SUBNET
    >
using scale_prev = add_layer<scale_prev_<tag>, SUBNET>;

// Here we add some convenient aliases for using scale_prev_ with the tag layers.
template <typename SUBNET> using scale_prev1  = scale_prev<tag1, SUBNET>;
template <typename SUBNET> using scale_prev2  = scale_prev<tag2, SUBNET>;
template <typename SUBNET> using scale_prev3  = scale_prev<tag3, SUBNET>;
template <typename SUBNET> using scale_prev4  = scale_prev<tag4, SUBNET>;
template <typename SUBNET> using scale_prev5  = scale_prev<tag5, SUBNET>;
template <typename SUBNET> using scale_prev6  = scale_prev<tag6, SUBNET>;
template <typename SUBNET> using scale_prev7  = scale_prev<tag7, SUBNET>;
template <typename SUBNET> using scale_prev8  = scale_prev<tag8, SUBNET>;
template <typename SUBNET> using scale_prev9  = scale_prev<tag9, SUBNET>;
template <typename SUBNET> using scale_prev10 = scale_prev<tag10, SUBNET>;
using scale_prev1_  = scale_prev_<tag1>;
using scale_prev2_  = scale_prev_<tag2>;
using scale_prev3_  = scale_prev_<tag3>;
using scale_prev4_  = scale_prev_<tag4>;
using scale_prev5_  = scale_prev_<tag5>;
using scale_prev6_  = scale_prev_<tag6>;
using scale_prev7_  = scale_prev_<tag7>;
using scale_prev8_  = scale_prev_<tag8>;
using scale_prev9_  = scale_prev_<tag9>;
using scale_prev10_ = scale_prev_<tag10>;

// ----------------------------------------------------------------------------------------

template<
    template<typename> class... **TAG_TYPES**
    >
class **concat_**
**{**
    /*!
        WHAT THIS OBJECT REPRESENTS
            This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
            defined above.  This layer simply concatenates the output of tagged layers.
            Importantly, each input layer must have the same dimensions (i.e.
            num_samples, nr, and nc) except for the k channel, which may vary.  This is
            because the concatenation happens along the k dimension.  That is, the
            output of this network is a tensor, OUT, that is the concatenation of the
            tensors:
                for each (tag in TAG_TYPES)
                    layer<tag>(subnet).get_output()
            Therefore, out.num_samples(), out.nr(), and out.nc() match the dimensions
            of the input tensors while OUT.k() is the sum of the input layer's k()
            dimensions.
    !*/

public:
    template <typename SUBNET> void **setup** (const SUBNET& sub);
    template <typename SUBNET> void **forward**(const SUBNET& sub, resizable_tensor& output);
    template <typename SUBNET> void **backward**(const tensor& gradient_input, SUBNET& sub, tensor& params_grad);
    dpoint **map_input_to_output**(dpoint p) const;
    dpoint **map_output_to_input**(dpoint p) const;
    const tensor& **get_layer_params**() const;
    tensor& **get_layer_params**();
    /*!
        These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ interface.
    !*/
**}**;


// concat layer definitions
template <template<typename> class **TAG1**,
          template<typename> class **TAG2**,
          typename SUBNET>
using concat2 = add_layer<concat_<TAG1, TAG2>, SUBNET>;

template <template<typename> class **TAG1**,
          template<typename> class **TAG2**,
          template<typename> class **TAG3**,
          typename SUBNET>
using concat3 = add_layer<concat_<TAG1, TAG2, TAG3>, SUBNET>;

template <template<typename> class **TAG1**,
          template<typename> class **TAG2**,
          template<typename> class **TAG3**,
          template<typename> class **TAG4**,
          typename SUBNET>
using concat4 = add_layer<concat_<TAG1, TAG2, TAG3, TAG4>, SUBNET>;

template <template<typename> class **TAG1**,
          template<typename> class **TAG2**,
          template<typename> class **TAG3**,
          template<typename> class **TAG4**,
          template<typename> class **TAG5**,
          typename SUBNET>
using concat5 = add_layer<concat_<TAG1, TAG2, TAG3, TAG4, TAG5>, SUBNET>;

// ----------------------------------------------------------------------------------------

/*!A inception layer definitions !*/

// Now define inception layer tag types.  These layer aliases allow creating
// the networks described in the paper: 
//   Szegedy, Christian, et al. "Going deeper with convolutions." Proceedings of
//   the IEEE Conference on Computer Vision and Pattern Recognition. 2015.
// See the dnn_inception_ex.cpp example for a complete example of their use.  Note also
// that we use tag ID numbers >= 1000 to avoid conflict with user's tag layers.
template <typename SUBNET> using itag0  = add_tag_layer< 1000 + 0, SUBNET>;
template <typename SUBNET> using itag1  = add_tag_layer< 1000 + 1, SUBNET>;
template <typename SUBNET> using itag2  = add_tag_layer< 1000 + 2, SUBNET>;
template <typename SUBNET> using itag3  = add_tag_layer< 1000 + 3, SUBNET>;
template <typename SUBNET> using itag4  = add_tag_layer< 1000 + 4, SUBNET>;
template <typename SUBNET> using itag5  = add_tag_layer< 1000 + 5, SUBNET>;
// skip to inception input
template <typename SUBNET> using iskip  = add_skip_layer< itag0, SUBNET>;

// here are some templates to be used for creating inception layer groups
template <template<typename>class **B1**,
          template<typename>class **B2**,
          typename SUBNET>
using inception2 = concat2<itag1, itag2, itag1<B1<iskip< itag2<B2< itag0<SUBNET>>>>>>>;

template <template<typename>class **B1**,
          template<typename>class **B2**,
          template<typename>class **B3**,
          typename SUBNET>
using inception3 = concat3<itag1, itag2, itag3, itag1<B1<iskip< itag2<B2<iskip< itag3<B3<  itag0<SUBNET>>>>>>>>>>;

template <template<typename>class **B1**,
          template<typename>class **B2**,
          template<typename>class **B3**,
          template<typename>class **B4**,
          typename SUBNET>
using inception4 = concat4<itag1, itag2, itag3, itag4,
            itag1<B1<iskip< itag2<B2<iskip< itag3<B3<iskip<  itag4<B4<  itag0<SUBNET>>>>>>>>>>>>>;

template <template<typename>class **B1**,
          template<typename>class **B2**,
          template<typename>class **B3**,
          template<typename>class **B4**,
          template<typename>class **B5**,
          typename SUBNET>
using inception5 = concat5<itag1, itag2, itag3, itag4, itag5,
            itag1<B1<iskip< itag2<B2<iskip< itag3<B3<iskip<  itag4<B4<iskip<  itag5<B5<  itag0<SUBNET>>>>>>>>>>>>>>>>;

// ----------------------------------------------------------------------------------------

const double DEFAULT_L2_NORM_EPS = 1e-5;

class **l2normalize_**
**{**
    /*!
        WHAT THIS OBJECT REPRESENTS
            This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
            defined above.  It takes tensors as input and L2 normalizes them.  In particular,
            it has the following properties:
                - The output tensors from this layer have the same dimensions as the
                  input tensors.
                - If you think of each input tensor as a set of tensor::num_samples()
                  vectors, then the output tensor contains the same vectors except they
                  have been length normalized so that their L2 norms are all 1.  I.e. 
                  for each vector v we will have ||v||==1.
    !*/

public:

    explicit **l2normalize_**(
        double eps = tt::DEFAULT_L2_NORM_EPS
    );
    /*!
        requires
            - eps > 0
        ensures
            - #get_eps() == eps
    !*/

    double **get_eps**(
    ) const; 
    /*!
        ensures
            - When we normalize a vector we divide it by its L2 norm.  However, the
              get_eps() value is added to the squared norm prior to division to avoid
              ever dividing by zero. 
    !*/

    template <typename SUBNET> void **setup** (const SUBNET& sub);
    void **forward_inplace**(const tensor& input, tensor& output);
    void **backward_inplace**(const tensor& computed_output, const tensor& gradient_input, tensor& data_grad, tensor& params_grad);
    const tensor& **get_layer_params**() const; 
    tensor& **get_layer_params**(); 
    /*!
        These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ interface.
    !*/
**}**;

// ----------------------------------------------------------------------------------------

template <
    long _offset,
    long _k,
    long _nr,
    long _nc
    >
class **extract_**
**{**
    /*!
        REQUIREMENTS ON TEMPLATE ARGUMENTS
            - 0 <= _offset
            - 0 < _k
            - 0 < _nr
            - 0 < _nc

        WHAT THIS OBJECT REPRESENTS
            This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
            defined above.  In particular, the output of this layer is simply a copy of
            the input tensor.  However, you can configure the extract layer to output
            only some subset of the input tensor and also to reshape it.  Therefore,
            the dimensions of the tensor output by this layer are as follows (letting
            IN be the input tensor and OUT the output tensor):
                - OUT.num_samples() == IN.num_samples()
                - OUT.k()  == _k 
                - OUT.nr() == _nr 
                - OUT.nc() == _nc 

            So the output will always have the same number of samples as the input, but
            within each sample (the k,nr,nc part) we will copy only a subset of the
            values.  Moreover, the _offset parameter controls which part of each sample
            we take.  To be very precise, we will have:
                - let IN_SIZE   = IN.k()*IN.nr()*IN.nc()
                - let OUT_SIZE  = _k*_nr*_nc 
                - for i in range[0,IN.num_samples()) and j in range[0,OUT_SIZE):
                    - OUT.host()[i*OUT_SIZE+j] == IN.host()[i*IN_SIZE+_offset+j]


            Finally, all this means that the input tensor to this layer must have a big
            enough size to accommodate taking a _k*_nr*_nc slice from each of its
            samples.  
    !*/

public:

    template <typename SUBNET> void **setup** (const SUBNET& sub);
    template <typename SUBNET> void **forward**(const SUBNET& sub, resizable_tensor& output);
    template <typename SUBNET> void **backward**(const tensor& gradient_input, SUBNET& sub, tensor& params_grad);
    const tensor& **get_layer_params**() const; 
    tensor& **get_layer_params**(); 
    /*!
        These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ interface.
    !*/
**}**;

template <
    long offset,
    long k,
    long nr,
    long nc,
    typename SUBNET
    >
using extract = add_layer<extract_<offset,k,nr,nc>, SUBNET>;

// ----------------------------------------------------------------------------------------

template <
    long _offset_k,
    long _offset_nr,
    long _offset_nc,
    long _k,
    long _nr,
    long _nc
    >
class **slice_**
**{**
    /*!
        REQUIREMENTS ON TEMPLATE ARGUMENTS
            - 0 <= _offset_k
            - 0 <= _offset_nr
            - 0 <= _offset_nc
            - 0 < _k
            - 0 < _nr
            - 0 < _nc

        WHAT THIS OBJECT REPRESENTS
            This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
            defined above.  In particular, the output of this layer is simply a copy of
            the input tensor. It is similar to extract in that you can configure the
            slice layer to output only some subset of the input tensor, but slice allows
            copies of non-contiguous regions of the input which enables three dimensional
            cropping of a tensor. The dimensions of the tensor output by this layer
            are as follows (letting IN be the input tensor and OUT the output tensor):
                - OUT.num_samples() == IN.num_samples()
                - OUT.k()  == _k 
                - OUT.nr() == _nr 
                - OUT.nc() == _nc 

            So the output will always have the same number of samples as the input, but
            within each sample (the k,nr,nc part) we will copy only a subset of the
            values. Moreover, the _offset_k, _offset_nr, and _offset_nc parameters
            control which channels, rows, and columns of each sample we take.
            To be very precise, we will have:
                - let IN_SIZE   = IN.k()*IN.nr()*IN.nc()
                - let OUT_SIZE  = _k*_nr*_nc 
                - for i in range[0,IN.num_samples()) and j in range[0,OUT_SIZE):
                    - let k = (j / (OUT.nr()*OUT.nc())) % OUT.k()
                    - let r = (j / OUT.nc()) % IN.nr()
                    - let c = j % OUT.nc()
                    - OUT.host()[i*OUT_SIZE+j] == IN.host()[i*IN_SIZE+
                                                            k_stride*(_offset_k+k)+
                                                            row_stride*(_offset_nr+r)+
                                                            col_stride*(_offset_nc+c)]


            Finally, all this means that the input tensor to this layer must have a big
            enough size to accommodate taking a _k*_nr*_nc slice from each of its
            samples.  
    !*/

public:

    template <typename SUBNET> void **setup** (const SUBNET& sub);
    template <typename SUBNET> void **forward**(const SUBNET& sub, resizable_tensor& output);
    template <typename SUBNET> void **backward**(const tensor& gradient_input, SUBNET& sub, tensor& params_grad);
    const tensor& **get_layer_params**() const; 
    tensor& **get_layer_params**(); 
    /*!
        These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ interface.
    !*/
**}**;

template <
    long offset_k,
    long offset_nr,
    long offset_nc,
    long k,
    long nr,
    long nc,
    typename SUBNET
    >
using slice = add_layer<slice_<offset_k,offset_nr,offset_nc,k,nr,nc>, SUBNET>;

// ----------------------------------------------------------------------------------------

template <long long row_stride = 2, long long col_stride = 2>
class **reorg_**
**{**
    /*!
        REQUIREMENTS ON TEMPLATE ARGUMENTS
            - row_stride >= 1
            - col_stride >= 1

        WHAT THIS OBJECT REPRESENTS
            This class implements the EXAMPLE_COMPUTATIONAL_LAYER_ interface, performing a 
            reorganization of tensor data. It rearranges spatial information along the channel
            dimension, effectively "folding" spatial dimensions into channels.
            
            The dimensions of the output tensor are as follows (letting IN be the input tensor
            and OUT the output tensor):
                - OUT.num_samples() == IN.num_samples()
                - OUT.k()  == IN.k() * row_stride * col_stride
                - OUT.nr() == IN.nr() / row_stride
                - OUT.nc() == IN.nc() / col_stride

            Therefore, the output tensor maintains the same number of samples as the input but
            alters the channel and spatial dimensions based on the specified strides.
            
            Specifically, for all n, k, r, c in OUT:
                OUT.host[tensor_index(OUT, n, k, r, c)] ==
                IN.host[tensor_index(IN,
                                    n,
                                    k % IN.k(),
                                    r * row_stride + (k / IN.k()) / col_stride,
                                    c * col_stride + (k / IN.k()) % col_stride)]

            **Enhancement Note:**  
            The underlying utility functions (`reorg` and `reorg_gradient`) now include an
            optional `bool add_to` parameter. While the current implementation uses the default
            value to maintain existing behavior, this parameter allows for future reversible
            operations and gradient accumulation flexibility within neural network layers.

            You can think of this layer as an alternative to a strided convolutional layer for
            downsampling tensors, offering similar spatial reduction with different internal
            gradient propagation mechanics.
    !*/

public:

    template <typename SUBNET> void **setup** (const SUBNET& sub);
    template <typename SUBNET> void **forward**(const SUBNET& sub, resizable_tensor& output);
    template <typename SUBNET> void **backward**(const tensor& gradient_input, SUBNET& sub, tensor& params_grad);
    dpoint **map_input_to_output** (dpoint p) const;
    dpoint **map_output_to_input** (dpoint p) const;
    const tensor& **get_layer_params**() const;
    tensor& **get_layer_params**();
    /*!
        These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ interface.
    !*/
**}**;

template <typename SUBNET>
using reorg = add_layer<reorg_<2, 2>, SUBNET>;

// ----------------------------------------------------------------------------------------

class **transpose_**
**{**
    /*!
        WHAT THIS OBJECT REPRESENTS
            This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface
            defined above. In particular, this layer performs a 2D matrix transposition
            on each of the k planes within each sample of a 4D tensor.

            The dimensions of the tensor output by this layer are as follows (letting
            IN be the input tensor and OUT the output tensor):
                - OUT.num_samples() == IN.num_samples()
                - OUT.k()  == IN.k()
                - OUT.nr() == IN.nc()
                - OUT.nc() == IN.nr()

            The transposition is performed as follows:
                - For each sample i and each k-plane j:
                    - OUT[i][j][r][c] = IN[i][j][c][r] for all r in [0, IN.nc()) and c in [0, IN.nr())

            This layer does not have any learnable parameters.
    !*/

public:

    **transpose_**() = default;

    template <typename SUBNET> void **setup** (const SUBNET& sub);
    template <typename SUBNET> void **forward**(const SUBNET& sub, resizable_tensor& output);
    template <typename SUBNET> void **backward**(const tensor& gradient_input, SUBNET& sub, tensor& params_grad);
    
    inline dpoint **map_input_to_output**(dpoint p) const;
    inline dpoint **map_output_to_input**(dpoint p) const;

    const tensor& **get_layer_params**() const; 
    tensor& **get_layer_params**(); 

    friend void **serialize**(const transpose_& item, std::ostream& out);
    friend void **deserialize**(transpose_& item, std::istream& in);

    friend std::ostream& **operator**<<(std::ostream& out, const transpose_& item);
    friend void **to_xml**(const transpose_& item, std::ostream& out);

    /*!
        These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ interface.
    !*/
private:
    resizable_tensor params; // unused
**}**;

template <typename SUBNET>
using transpose = add_layer<transpose_, SUBNET>;

// ----------------------------------------------------------------------------------------

class **positional_encodings_**
**{**
    /*!
        WHAT THIS OBJECT REPRESENTS
            This is an implementation of the EXAMPLE_COMPUTATIONAL_LAYER_ interface.
            It defines a positional encoding layer that adds position information to
            the input tensor. This is particularly useful in transformer architectures
            where the order of the sequence matters.

            The dimensions of the tensors output by this layer are the same as the input
            tensor dimensions.

            This implementation is based on the positional encoding described in:
            Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A. N., 
            Kaiser, Ł., & Polosukhin, I. (2017). Attention is all you need. In Advances 
            in neural information processing systems (pp. 5998-6008).

            The encoding uses sine and cosine functions of different frequencies:
            PE(pos, 2i)   = sin(pos / 10000^(2i/d_model))
            PE(pos, 2i+1) = cos(pos / 10000^(2i/d_model))
            where pos is the position and i is the dimension.
    !*/

public:

    **positional_encodings_**(
        unsigned long sequence_dim_ = 1,
        unsigned long embedding_dim_ = 1
    );
    /*!
        ensures
            - #sequence_dim == sequence_dim_
            - #embedding_dim == embedding_dim_
    !*/

    **positional_encodings_** (
        const positional_encodings_& item
    );
    /*!
        ensures
            - EXAMPLE_COMPUTATIONAL_LAYER_ objects are copy constructable
    !*/

    positional_encodings_& **operator**=(
        const positional_encodings_& item
    );
    /*!
        ensures
            - EXAMPLE_COMPUTATIONAL_LAYER_ objects are assignable
    !*/

    template <typename SUBNET>
    void **setup** (
        const SUBNET& sub
    );
    /*!
        requires
            - SUBNET implements the SUBNET interface defined at the top of this file.
        ensures
            - performs any necessary setup for the layer, including the calculation
            of positional encodings based on the dimensions of the input.
    !*/

    template <typename SUBNET>
    void **forward**(
        const SUBNET& sub,
        resizable_tensor& output
    );
    /*!
        requires
            - SUBNET implements the SUBNET interface defined at the top of this file.
            - setup() has been called.
        ensures
            - Adds the positional encodings to the output of the subnetwork and 
            stores the results into #output.
    !*/

    template <typename SUBNET>
    void **backward**(
        const tensor& gradient_input,
        SUBNET& sub,
        tensor& params_grad
    );
    /*!
        requires
            - SUBNET implements the SUBNET interface defined at the top of this file.
            - setup() has been called.
            - #params_grad is unused in this layer as there are no learnable parameters.
        ensures
            - Computes the gradient of the layer with respect to the input, which
            is simply the input gradient itself as positional encodings are constant.
    !*/

    const tensor& **get_layer_params**(
    ) const;
    /*!
        ensures
            - returns the parameters that define the behavior of forward().
            Note: This layer has no learnable parameters, so this returns an empty tensor.
    !*/

    tensor& **get_layer_params**(
    );
    /*!
        ensures
            - returns the parameters that define the behavior of forward().
            Note: This layer has no learnable parameters, so this returns an empty tensor.
    !*/

    const tensor& **get_positional_encodings**(
    ) const;
    /*!
        ensures
            - returns the computed positional encodings.
    !*/

    tensor& **get_positional_encodings**(
    );
    /*!
        ensures
            - returns the computed positional encodings.
    !*/

    friend void **serialize**(const positional_encodings_& item, std::ostream& out);
    friend void **deserialize**(positional_encodings_& item, std::istream& in);
    /*!
        provides serialization support
    !*/

    friend std::ostream& **operator**<<(std::ostream& out, const positional_encodings_& item);
    /*!
        print a string describing this layer.
    !*/

    friend void **to_xml**(const positional_encodings_& item, std::ostream& out);
    /*!
        This function is optional, but required if you want to print your networks with
        net_to_xml(). It prints a layer as XML.
    !*/
**}**;

template <typename SUBNET>
using positional_encodings = add_layer<positional_encodings_, SUBNET>;

// ----------------------------------------------------------------------------------------

template <
    unsigned long num_embeddings_,
    unsigned long embedding_dim_
    >
class **embeddings_**
**{**
    /*!
        WHAT THIS OBJECT REPRESENTS
            This object represents an embedding layer in a neural network. It maps discrete
            tokens to continuous vector representations. This is a fundamental technique in
            natural language processing and other domains dealing with categorical data.

            The layer takes as input a tensor of integer indices and outputs a tensor of 
            the same shape (except for the last dimension) where each index is replaced by 
            its corresponding embedding vector.

            For more information on embeddings, see:
            Mikolov, T., Sutskever, I., Chen, K., Corrado, G. S., & Dean, J. (2013). 
            Distributed representations of words and phrases and their compositionality. 
            In Advances in neural information processing systems (pp. 3111-3119).

        TEMPLATE PARAMETERS
            - num_embeddings_: The size of the embedding dictionary, i.e., the number of 
                            discrete tokens that can be embedded.
            - embedding_dim_: The dimensionality of each embedding vector.

        CONVENTION
            - get_embeddings() returns the tensor of embedding vectors.
            - get_num_embeddings() == num_embeddings_
            - get_embedding_dim() == embedding_dim_
            - get_learning_rate_multiplier() returns the learning rate multiplier for this layer.
            - get_scale_by_freq() returns whether to scale gradients by token frequency.
    */        
public:
    **embeddings_**() = default;

    unsigned long **get_num_embeddings**() const;
    unsigned long **get_embedding_dim**() const;
    double **get_learning_rate_multiplier**() const;
    bool **get_scale_by_freq**() const;

    void **set_num_embeddings**(unsigned long num);
    void **set_embedding_dim**(unsigned long dim);
    void **set_learning_rate_multiplier**(double val);
    void **set_scale_by_freq**(bool val);

    template <typename SUBNET> void **setup**(const SUBNET& sub);
    template <typename SUBNET> void **forward**(const SUBNET& sub, resizable_tensor& output);
    template <typename SUBNET> void **backward**(const tensor& gradient_input, SUBNET& sub, tensor& params_grad);

    const tensor& **get_layer_params**() const;
    tensor& **get_layer_params**();
    const tensor& **get_embeddings**() const;
    tensor& **get_embeddings**();

    friend void **serialize**(const embeddings_& item, std::ostream& out);
    friend void **deserialize**(embeddings_& item, std::istream& in);
    friend std::ostream& **operator**<<(std::ostream& out, const embeddings_& item);
    friend void **to_xml**(const embeddings_& item, std::ostream& out);

    /*!
        These functions are implemented as described in the EXAMPLE_COMPUTATIONAL_LAYER_ interface.
    !*/
**}**;

template <
    unsigned long num_embeddings,
    unsigned long embedding_dim,
    typename SUBNET
    >
using embeddings = add_layer<embeddings_<num_embeddings, embedding_dim>, SUBNET>;

// ----------------------------------------------------------------------------------------

struct **neg_infinity_tag** **{** **}**;
struct **zero_tag** **{** **}**;

template<typename T>
struct **is_special_value** : std::false_type **{** **}**;
template<>
struct **is_special_value**<neg_infinity_tag> : std::true_type **{** **}**;
template<>
struct **is_special_value**<zero_tag> : std::true_type **{** **}**;

template<long diag_, typename tag_, long num_ = 0, long den_ = 1>
class **tril_**
**{**
    /*!
        TEMPLATE PARAMETERS
            - diag_: A long integer specifying the diagonal offset.
            - tag_: A type tag specifying special values or void for numeric values.
            - num_: Numerator for numeric diagonal value (default is 0, only used if tag_ is void).
            - den_: Denominator for numeric diagonal value (default is 1, only used if tag_ is void).

        REQUIREMENTS
            - diag_ must be an integer.
            - tag_ must be either neg_infinity_tag, zero_tag, or void.
            - If tag_ is void, num_ and den_ are used to compute the diagonal value.
            - If tag_ is neg_infinity_tag or zero_tag, num_ and den_ are ignored.

        WHAT THIS OBJECT REPRESENTS
            This object implements a layer in a deep neural network that applies a lower triangular mask to
            its input tensor. The mask is defined such that all elements above the specified diagonal are set
            to a given value. The diagonal offset and the mask value are determined by the template parameters.

        DIAGONAL VALUE DETERMINATION
            - If tag_ is neg_infinity_tag: diagonal value is set to negative infinity.
            - If tag_ is zero_tag: diagonal value is set to zero.
            - If tag_ is void: diagonal value is set to num_ / den_ as a float.

        DIAGONAL OFFSET
            The diag_ parameter determines the diagonal above which elements are masked:
            - diag_ = 0: main diagonal
            - diag_ > 0: diag_ steps above the main diagonal
            - diag_ < 0: |diag_| steps below the main diagonal

        EXAMPLE USAGE
            // Create a layer that masks all elements above the main diagonal with -inf
            tril_<0, neg_infinity_tag> layer1;

            // Create a layer that masks all elements above the main diagonal with 0
            tril_<0, zero_tag> layer2;

            // Create a layer that masks all elements above the main diagonal with 0.5
            tril_<0, void, 1, 2> layer3;

            // Create a layer that masks all elements 5 positions above the main diagonal with -inf
            tril_<5, neg_infinity_tag> layer4;

            // Create a layer that masks all elements 3 positions below the main diagonal with 0.25
            tril_<-3, void, 1, 4> layer5;

        SERIALIZATION SUPPORT
            This object supports serialization and deserialization via the serialize() and deserialize() functions.
    !*/

public:
    **tril_**() = default;
    /*!
        ensures
            - This object is properly initialized.
    !*/

    template <typename SUBNET>
    void **setup**(const SUBNET& sub);
    /*!
        requires
            - SUBNET is a valid network layer type.
        ensures
            - Initializes the mask based on the dimensions of the input tensor from sub.
    !*/

    template <typename SUBNET>
    void **forward**(const SUBNET& sub, resizable_tensor& output);
    /*!
        requires
            - SUBNET is a valid network layer type.
        ensures
            - Applies the lower triangular mask to the input tensor from sub and stores the result in output.
    !*/

    template <typename SUBNET>
    void **backward**(const tensor& gradient_input, SUBNET& sub, tensor& params_grad);
    /*!
        requires
            - SUBNET is a valid network layer type.
        ensures
            - Computes the gradient of the loss with respect to the input tensor and stores it in sub.
    !*/

    inline dpoint **map_input_to_output**(const dpoint& p) const;
    /*!
        ensures
            - Maps a point from the input tensor to the corresponding point in the output tensor.
    !*/

    inline dpoint **map_output_to_input**(const dpoint& p) const;
    /*!
        ensures
            - Maps a point from the output tensor to the corresponding point in the input tensor.
    !*/

    const tensor& **get_layer_params**() const;
    /*!
        ensures
            - Returns the parameters of this layer.
    !*/

    tensor& **get_layer_params**();
    /*!
        ensures
            - Returns the parameters of this layer.
    !*/

    friend void **serialize**(const tril_& item, std::ostream& out);
    /*!
        ensures
            - Serializes the state of this object to the given output stream.
    !*/

    friend void **deserialize**(tril_& item, std::istream& in);
    /*!
        ensures
            - Deserializes the state of this object from the given input stream.
    !*/

    friend std::ostream& **operator**<<(std::ostream& out, const tril_& item);
    /*!
        ensures
            - Prints a human-readable representation of this object to the given output stream.
    !*/

    friend void **to_xml**(const tril_& item, std::ostream& out);
    /*!
        ensures
            - Serializes the state of this object to XML format and writes it to the given output stream.
    !*/
**}**;

template <typename SUBNET>
using tril = add_layer<tril_<0, zero_tag>, SUBNET>;

template <typename SUBNET>
using tril_mask = add_layer<tril_<0, neg_infinity_tag>, SUBNET>;

template <long diag, long num, long den, typename SUBNET>
using tril_diag = add_layer<tril_<diag, void, num, den>, SUBNET>;

// ----------------------------------------------------------------------------------------

}

#endif // DLIB_DNn_LAYERS_ABSTRACT_H_