Lev Goldfarb - Academia.edu (original) (raw)
Papers by Lev Goldfarb
This paper deals with the formulation of an alternative, structural, approach to the speech repre... more This paper deals with the formulation of an alternative, structural, approach to the speech representation and recognition problem. In this approach, we require both the representation and the learning algorithms to be linguistically meaningful and to naturally represent the linguistic data at hand. This allows the speech recognition system to discover the emergent combinatorial structure of the linguistic classes. The proposed approach is developed within the ETS formalism, the first formalism in applied mathematics specifically designed to address the issues of class and object/event representation. We present an initial application of ETS to the articulatory modelling of speech based on elementary physiological gestures that can be reliably represented as the ETS primitives. We discuss the advantages of this gestural approach over prevalent methods and its promising potential to mathematical modelling and representation in linguistics.
I do not know where to start! Lev Golfarb, friend, mentor, and my Ph.D. supervisor comes first. I... more I do not know where to start! Lev Golfarb, friend, mentor, and my Ph.D. supervisor comes first. I must thank Lev deeply for his patience, support, advice, and above all, inspiration over the years. His unwavering faith in the ETS Model inspired and encouraged me throughout. Next come my wife, Rachel, and our children Conrad and Martina. They all had to make many personal sacrifices while I away from home on my frequent, and often lengthy, visits to New Brunswick. I distinctly remember the occasions I would be freezing on a cold November day in Fredericton while they were still having barbecues on the beach back home in Malta. When Conrad was younger he would often come to me while I was pounding away at the keyboard and say "Dada, could you please draw a chou-chou train with three coaches and with an elephant in the wagon at the back-please-so I can colour it? ". Mixing science and family was not always easy. I must thank my mother May, for putting up with my endless complaining-especially at the end, all of my brothers and sisters, and Rachel's parents, Teddy and Louise, for taking the kids away at the weekends so I could finish my work. Very special thanks also go to Prof. Joseph Horton for advice, encouragement, and inspiration. Prof. Horton is also the chairman of my Ph.D. committee. I would also like to thank Prof. Dana W. Wasson who is also on my Ph.D. committee, Dr. Bernie Kurz, the graduate-studies advisor, the Dean of Computer Science, Prof.
We propose to modify the original definition of the inductive learning process proposed by one of... more We propose to modify the original definition of the inductive learning process proposed by one of us to include two modes of operation of the evolving transformation system (ETS), supervised and unsupervised, which we will call external and internal.
What Is a Structural Representation (in preparation) …, 2006
Currently, the only discipline that has dealt with scientific representationsalbeit non-structura... more Currently, the only discipline that has dealt with scientific representationsalbeit non-structural ones-is mathematics (as distinct from logic). I suggest that it is this discipline, only vastly expanded based on a new, structural, foundation, that will also deal with structural representations. Logic (including computability theory) is not concerned with the issues of various representations useful in natural sciences. Artificial intelligence was supposed to address these issues but has, in fact, hardly advanced them at all. How do we, then, approach the development of representational formalisms? It appears that the only reasonable starting point is the primordial point at which all of mathematics began, i.e. we should start with the generalization of the process of construction of natural numbers, replacing the identical structureless units, out of which numbers are built, by structural ones, each signifying an atomic "transforming" event. This paper is conceived as a companion to [1], and is a revised version of [2]. Mathematics is the science of the infinite, its goal is the symbolic comprehension of the infinite with human, that is finite, means. Hermann Weyl The definition of mathematics accepted in the 20 th century, as a science of the infinite, should be replaced by another one, which more accurately captures its nature: it is the science of the relationship between the finite and the infinite.
A recently developed formalism for structural representation-called Evolving Transformations Syst... more A recently developed formalism for structural representation-called Evolving Transformations System (ETS)-is discussed as suggesting a radically different direction for the development of computer/information science. One can gain an initial intuitive understanding of the ETS object representation by generalizing the temporal process of the (Peano) construction of natural numbers: replace the single 'structureless' unit out of which a number is built by one of several more general structural units. The new formalism points to the informational view of nature in which the basic object encoding is temporal, event-based, while the ubiquitous in science 'spatial' object instantiation can be constructed on the basis of the former. Thus, this far-reaching structural generalization of natural numbers emerges as a universal form of both temporal and structural representation that can be variously instantiated, depending on the desired target medium, e.g. 3D-space, biotic, network, etc. Moreover, the ETS representation satisfies a unique and very desirable property not possessed by any other known language, scientific or spoken: its syntax and semantics are congruent.
Abstract. Currently, the only discipline that deals with scientific representations— albeit non-s... more Abstract. Currently, the only discipline that deals with scientific representations— albeit non-structural ones—is mathematics (as distinct from logic). I suggest that it is this discipline, only vastly expanded based on a new, structural, foundation, that will also be dealing with structural representations. Logic (including computability theory) is not concerned with the issues of various representations useful in natural sciences. Artificial intelligence was supposed to address these issues but has, in fact, hardly advanced them at all. How do we, then, approach the development of representational formalisms? It appears that the only reasonable starting point is the primordial point at which all of mathematics began, i.e. we should start with the generalization of the process of construction of natural numbers, replacing the identical structureless units, out of which numbers are built, by structural ones, each signifying an elementary “transforming” event. Mathematics is the sci...
Our main objective is to propose a recently-developed representational formalism, the Evolving Tr... more Our main objective is to propose a recently-developed representational formalism, the Evolving Transformation System (ETS), as a general structural tool for decision and risk analysis, as opposed to the conventional numeric tools. We believe ETS to be the first formalism developed specifically with the goal of (properly understood) structural representation in mind. We outline the use of ETS in the representation of an “insider’s view ” of a terrorist plot. The example should be treated as that of an internal view of a generic planning process. We emphasize that the same tools can be used for modeling the external view of a decision process (and its execution). The “atomic ” representational unit of ETS is a structured event, and sequences of such events form processes that represent real human (including business) activities consisting of a series of various human actions. Each such action can be viewed structurally as an event transforming several “incoming ” information processes...
As one of us has already repeatedly stressed ([10], [12], [13], [15]), we believe, together with ... more As one of us has already repeatedly stressed ([10], [12], [13], [15]), we believe, together with Hermann von Helmholtz [23], that the central and the most pressing issue confronting cognitive science and artificial intelligence is the development of a satisfactory unified inductive learning model (see also [5], [34], [43]). Unfortunately, this issue was not perceived to be the central issue by the three leading (and founding) schools of AI, which had a very negative effect on the development of AI up to now. In particular, due only to the difference between the formal models used originally in some areas of AI and pattern recognition, AI had severed practically all ties with pattern recognition, which was very counter-productive to the development of both areas and particularly to AI.
Numbers have emerged historically as by far the most popular form of representation. All our basi... more Numbers have emerged historically as by far the most popular form of representation. All our basic scientific paradigms are built on the foundation of these, numeric, or quantitative, concepts. Measurement, as conventionally understood, is the corresponding process for (numeric) representation of objects or events, i.e., it is a procedure or device that realizes the mapping from the set of objects to the set of numbers. Any (including a future) measurement device is constructed based on the underlying mathematical structure that is thought appropriate for the purpose. It has gradually become clear to us that the classical numeric mathematical structures, and hence the corresponding (including all present) measurement devices, impose on “real” events/objects a very rigid form of representation, which cannot be modified dynamically in order to capture their combinative, or compositional, structure. To remove this fundamental limitation, a new mathematical structure—evolving transforma...
A fundamentally new formal framework for structural representation of organic compounds based on ... more A fundamentally new formal framework for structural representation of organic compounds based on the rst \true" (general) formalism for structural object representation recently proposed by us|evolving transformation system (ETS) model|is outlined. The applied orientation of the paper is towards the molecular design in general and computer aided drug design (CADD) in particular. Inadequacies of the conventional models used in (CADD) for molecular representation and classi cation as well as the advantages of the proposed ETS model are discussed. Some advantages of the ETS model is its capability to represent naturally all important structural features of molecules, e.g. di erent atoms and their bonding types (including hydrogen bonding), basic 2D and 3D isometries, the molecular class structure. The model allows one not only to classify a new compound, but also to construct a chemically valid new compound from the class of compounds that was previously learned based on a small s...
My objective is to explain why a completely inadequate focus on the two central and inseparable c... more My objective is to explain why a completely inadequate focus on the two central and inseparable concepts—the concepts of class (of objects) and class representation—is responsible for the lack of adequate progress in machine learning, and AI in general. I suggest that the main reason for this lack of progress is reliance on conventional formalisms, mainly the vector space and logical, which cannot in principle support a satisfactory concept of class. On the other hand, the orientation towards new, class-oriented, representational formalisms—if the underlying informational hypothesis about the nature of classes in the universe is vindicated—would establish machine learning as a new kind of natural science. An example of a class-oriented representational formalism is not considered here, since a special issue of Pattern Recognition is addressing such new formalism, Evolving Transformation System (ETS).
A recently developed formalism for structural representation, called Evolving Transformations Sys... more A recently developed formalism for structural representation, called Evolving Transformations System (ETS)—in which syntax and semantics are congruent—suggests an unforeseen constructive resolution to the ubiquitous syntax/semantics incompatibility issue raised by Searle’s Chinese Room argument. The ETS is an outcome of long-term research work directed at the development of a category-oriented formalism for structural object representation, which turned out to be an event-based representation.
Neural Computing Surveys, 1999
In August 1998 Dave Touretzky asked on the connectionists e-mailing list," Is connectionist ... more In August 1998 Dave Touretzky asked on the connectionists e-mailing list," Is connectionist symbol processing dead?" This query lead to an interesting discussion and exchange of ideas. We thought it might be useful to capture this exchange in an article. We solicited contributions, and this collective article is the result. Contributions were solicited by a public call on the connectionists e-mailing list. All contributions received were subjected to two to three informal reviews. Almost all were accepted with varying degrees of revision. Given ...
We outline a formalism for structural, or symbolic, representation, the necessity of which has be... more We outline a formalism for structural, or symbolic, representation, the necessity of which has been acutely felt not just in artificial intelligence and pattern recognition, but also in the natural sciences, particularly biology. At the same time, biology has been gradually edging to the forefront of sciences, although the reasons obviously have nothing to do with its state of formalization or maturity. Rather, the reasons have to do with the growing realization that the objects of biology are not only more important (to society) and interesting (to science), but that they also more explicitly exhibit the evolving nature of all objects in the Universe. It is this view of objects as evolving structural entities/processes that we aim to formally address here, in contrast to the ubiquitous mathematical view of objects as points in some abstract space. In light of the above, the paper is addressed to a very broad group of scientists. One can gain an initial intuitive understanding of th...
1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes
ABSTRACT In this paper, we study the theoretical aspects of modelling analysis of relations of a ... more ABSTRACT In this paper, we study the theoretical aspects of modelling analysis of relations of a system. In our approach, we study systems which can be represented as weighted multigraphs whose nodes are systems/components, whose edges represent abstract binary relations and whose edge weights are generalized measurements. Using concepts of pattern recognition the state patterns and evolution trajectory are analyzed through the projections onto a discrete and a continuous phase spaces.
Abstract We outline a formalism for" structural", or&am... more Abstract We outline a formalism for" structural", or" symbolic", representation, the necessity of which is acutely felt in all sciences. One can develop an initial intuitive understanding of the proposed representation by simply generalizing the process of construction of natural numbers: replace the identical structureless units out of which numbers are built by several structural ones, attached consecutively. Now, however, the resulting constructions embody the corresponding formative/generative histories, since we can see what was attached ...
This paper deals with the formulation of an alternative, structural, approach to the speech repre... more This paper deals with the formulation of an alternative, structural, approach to the speech representation and recognition problem. In this approach, we require both the representation and the learning algorithms to be linguistically meaningful and to naturally represent the linguistic data at hand. This allows the speech recognition system to discover the emergent combinatorial structure of the linguistic classes. The proposed approach is developed within the ETS formalism, the first formalism in applied mathematics specifically designed to address the issues of class and object/event representation. We present an initial application of ETS to the articulatory modelling of speech based on elementary physiological gestures that can be reliably represented as the ETS primitives. We discuss the advantages of this gestural approach over prevalent methods and its promising potential to mathematical modelling and representation in linguistics.
I do not know where to start! Lev Golfarb, friend, mentor, and my Ph.D. supervisor comes first. I... more I do not know where to start! Lev Golfarb, friend, mentor, and my Ph.D. supervisor comes first. I must thank Lev deeply for his patience, support, advice, and above all, inspiration over the years. His unwavering faith in the ETS Model inspired and encouraged me throughout. Next come my wife, Rachel, and our children Conrad and Martina. They all had to make many personal sacrifices while I away from home on my frequent, and often lengthy, visits to New Brunswick. I distinctly remember the occasions I would be freezing on a cold November day in Fredericton while they were still having barbecues on the beach back home in Malta. When Conrad was younger he would often come to me while I was pounding away at the keyboard and say "Dada, could you please draw a chou-chou train with three coaches and with an elephant in the wagon at the back-please-so I can colour it? ". Mixing science and family was not always easy. I must thank my mother May, for putting up with my endless complaining-especially at the end, all of my brothers and sisters, and Rachel's parents, Teddy and Louise, for taking the kids away at the weekends so I could finish my work. Very special thanks also go to Prof. Joseph Horton for advice, encouragement, and inspiration. Prof. Horton is also the chairman of my Ph.D. committee. I would also like to thank Prof. Dana W. Wasson who is also on my Ph.D. committee, Dr. Bernie Kurz, the graduate-studies advisor, the Dean of Computer Science, Prof.
We propose to modify the original definition of the inductive learning process proposed by one of... more We propose to modify the original definition of the inductive learning process proposed by one of us to include two modes of operation of the evolving transformation system (ETS), supervised and unsupervised, which we will call external and internal.
What Is a Structural Representation (in preparation) …, 2006
Currently, the only discipline that has dealt with scientific representationsalbeit non-structura... more Currently, the only discipline that has dealt with scientific representationsalbeit non-structural ones-is mathematics (as distinct from logic). I suggest that it is this discipline, only vastly expanded based on a new, structural, foundation, that will also deal with structural representations. Logic (including computability theory) is not concerned with the issues of various representations useful in natural sciences. Artificial intelligence was supposed to address these issues but has, in fact, hardly advanced them at all. How do we, then, approach the development of representational formalisms? It appears that the only reasonable starting point is the primordial point at which all of mathematics began, i.e. we should start with the generalization of the process of construction of natural numbers, replacing the identical structureless units, out of which numbers are built, by structural ones, each signifying an atomic "transforming" event. This paper is conceived as a companion to [1], and is a revised version of [2]. Mathematics is the science of the infinite, its goal is the symbolic comprehension of the infinite with human, that is finite, means. Hermann Weyl The definition of mathematics accepted in the 20 th century, as a science of the infinite, should be replaced by another one, which more accurately captures its nature: it is the science of the relationship between the finite and the infinite.
A recently developed formalism for structural representation-called Evolving Transformations Syst... more A recently developed formalism for structural representation-called Evolving Transformations System (ETS)-is discussed as suggesting a radically different direction for the development of computer/information science. One can gain an initial intuitive understanding of the ETS object representation by generalizing the temporal process of the (Peano) construction of natural numbers: replace the single 'structureless' unit out of which a number is built by one of several more general structural units. The new formalism points to the informational view of nature in which the basic object encoding is temporal, event-based, while the ubiquitous in science 'spatial' object instantiation can be constructed on the basis of the former. Thus, this far-reaching structural generalization of natural numbers emerges as a universal form of both temporal and structural representation that can be variously instantiated, depending on the desired target medium, e.g. 3D-space, biotic, network, etc. Moreover, the ETS representation satisfies a unique and very desirable property not possessed by any other known language, scientific or spoken: its syntax and semantics are congruent.
Abstract. Currently, the only discipline that deals with scientific representations— albeit non-s... more Abstract. Currently, the only discipline that deals with scientific representations— albeit non-structural ones—is mathematics (as distinct from logic). I suggest that it is this discipline, only vastly expanded based on a new, structural, foundation, that will also be dealing with structural representations. Logic (including computability theory) is not concerned with the issues of various representations useful in natural sciences. Artificial intelligence was supposed to address these issues but has, in fact, hardly advanced them at all. How do we, then, approach the development of representational formalisms? It appears that the only reasonable starting point is the primordial point at which all of mathematics began, i.e. we should start with the generalization of the process of construction of natural numbers, replacing the identical structureless units, out of which numbers are built, by structural ones, each signifying an elementary “transforming” event. Mathematics is the sci...
Our main objective is to propose a recently-developed representational formalism, the Evolving Tr... more Our main objective is to propose a recently-developed representational formalism, the Evolving Transformation System (ETS), as a general structural tool for decision and risk analysis, as opposed to the conventional numeric tools. We believe ETS to be the first formalism developed specifically with the goal of (properly understood) structural representation in mind. We outline the use of ETS in the representation of an “insider’s view ” of a terrorist plot. The example should be treated as that of an internal view of a generic planning process. We emphasize that the same tools can be used for modeling the external view of a decision process (and its execution). The “atomic ” representational unit of ETS is a structured event, and sequences of such events form processes that represent real human (including business) activities consisting of a series of various human actions. Each such action can be viewed structurally as an event transforming several “incoming ” information processes...
As one of us has already repeatedly stressed ([10], [12], [13], [15]), we believe, together with ... more As one of us has already repeatedly stressed ([10], [12], [13], [15]), we believe, together with Hermann von Helmholtz [23], that the central and the most pressing issue confronting cognitive science and artificial intelligence is the development of a satisfactory unified inductive learning model (see also [5], [34], [43]). Unfortunately, this issue was not perceived to be the central issue by the three leading (and founding) schools of AI, which had a very negative effect on the development of AI up to now. In particular, due only to the difference between the formal models used originally in some areas of AI and pattern recognition, AI had severed practically all ties with pattern recognition, which was very counter-productive to the development of both areas and particularly to AI.
Numbers have emerged historically as by far the most popular form of representation. All our basi... more Numbers have emerged historically as by far the most popular form of representation. All our basic scientific paradigms are built on the foundation of these, numeric, or quantitative, concepts. Measurement, as conventionally understood, is the corresponding process for (numeric) representation of objects or events, i.e., it is a procedure or device that realizes the mapping from the set of objects to the set of numbers. Any (including a future) measurement device is constructed based on the underlying mathematical structure that is thought appropriate for the purpose. It has gradually become clear to us that the classical numeric mathematical structures, and hence the corresponding (including all present) measurement devices, impose on “real” events/objects a very rigid form of representation, which cannot be modified dynamically in order to capture their combinative, or compositional, structure. To remove this fundamental limitation, a new mathematical structure—evolving transforma...
A fundamentally new formal framework for structural representation of organic compounds based on ... more A fundamentally new formal framework for structural representation of organic compounds based on the rst \true" (general) formalism for structural object representation recently proposed by us|evolving transformation system (ETS) model|is outlined. The applied orientation of the paper is towards the molecular design in general and computer aided drug design (CADD) in particular. Inadequacies of the conventional models used in (CADD) for molecular representation and classi cation as well as the advantages of the proposed ETS model are discussed. Some advantages of the ETS model is its capability to represent naturally all important structural features of molecules, e.g. di erent atoms and their bonding types (including hydrogen bonding), basic 2D and 3D isometries, the molecular class structure. The model allows one not only to classify a new compound, but also to construct a chemically valid new compound from the class of compounds that was previously learned based on a small s...
My objective is to explain why a completely inadequate focus on the two central and inseparable c... more My objective is to explain why a completely inadequate focus on the two central and inseparable concepts—the concepts of class (of objects) and class representation—is responsible for the lack of adequate progress in machine learning, and AI in general. I suggest that the main reason for this lack of progress is reliance on conventional formalisms, mainly the vector space and logical, which cannot in principle support a satisfactory concept of class. On the other hand, the orientation towards new, class-oriented, representational formalisms—if the underlying informational hypothesis about the nature of classes in the universe is vindicated—would establish machine learning as a new kind of natural science. An example of a class-oriented representational formalism is not considered here, since a special issue of Pattern Recognition is addressing such new formalism, Evolving Transformation System (ETS).
A recently developed formalism for structural representation, called Evolving Transformations Sys... more A recently developed formalism for structural representation, called Evolving Transformations System (ETS)—in which syntax and semantics are congruent—suggests an unforeseen constructive resolution to the ubiquitous syntax/semantics incompatibility issue raised by Searle’s Chinese Room argument. The ETS is an outcome of long-term research work directed at the development of a category-oriented formalism for structural object representation, which turned out to be an event-based representation.
Neural Computing Surveys, 1999
In August 1998 Dave Touretzky asked on the connectionists e-mailing list," Is connectionist ... more In August 1998 Dave Touretzky asked on the connectionists e-mailing list," Is connectionist symbol processing dead?" This query lead to an interesting discussion and exchange of ideas. We thought it might be useful to capture this exchange in an article. We solicited contributions, and this collective article is the result. Contributions were solicited by a public call on the connectionists e-mailing list. All contributions received were subjected to two to three informal reviews. Almost all were accepted with varying degrees of revision. Given ...
We outline a formalism for structural, or symbolic, representation, the necessity of which has be... more We outline a formalism for structural, or symbolic, representation, the necessity of which has been acutely felt not just in artificial intelligence and pattern recognition, but also in the natural sciences, particularly biology. At the same time, biology has been gradually edging to the forefront of sciences, although the reasons obviously have nothing to do with its state of formalization or maturity. Rather, the reasons have to do with the growing realization that the objects of biology are not only more important (to society) and interesting (to science), but that they also more explicitly exhibit the evolving nature of all objects in the Universe. It is this view of objects as evolving structural entities/processes that we aim to formally address here, in contrast to the ubiquitous mathematical view of objects as points in some abstract space. In light of the above, the paper is addressed to a very broad group of scientists. One can gain an initial intuitive understanding of th...
1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes
ABSTRACT In this paper, we study the theoretical aspects of modelling analysis of relations of a ... more ABSTRACT In this paper, we study the theoretical aspects of modelling analysis of relations of a system. In our approach, we study systems which can be represented as weighted multigraphs whose nodes are systems/components, whose edges represent abstract binary relations and whose edge weights are generalized measurements. Using concepts of pattern recognition the state patterns and evolution trajectory are analyzed through the projections onto a discrete and a continuous phase spaces.
Abstract We outline a formalism for" structural", or&am... more Abstract We outline a formalism for" structural", or" symbolic", representation, the necessity of which is acutely felt in all sciences. One can develop an initial intuitive understanding of the proposed representation by simply generalizing the process of construction of natural numbers: replace the identical structureless units out of which numbers are built by several structural ones, attached consecutively. Now, however, the resulting constructions embody the corresponding formative/generative histories, since we can see what was attached ...