Hakob Tamazyan | Yerevan State University (original) (raw)

Papers by Hakob Tamazyan

Research paper thumbnail of Some New Proof System for Propositional Modal Logic

Zekuyts’ner - Haykakan SSṚ gitut’yunneri akademia, Apr 23, 2024

Research paper thumbnail of A Hierarchy of Determinative Sequent Systems with Different Substitution Rules

Some determinative sequent system (DS) for classical propositional calculus is introduced on the ... more Some determinative sequent system (DS) for classical propositional calculus is introduced on the base of wellknown Tseytin's transformation. It is proved that the system DS is polynomial equivalent to the resolution system R and cut-free sequent system PK-. Then we define the system SDS (DS with a substitution rule) and the systems SkDS (DS with restricted substitution rules, where the number of connectives in substituted formulas is bounded by). It is proved that for every ≥ the system Sk+1DS has an exponential speed-up over the system SkDS in the tree form, and the system SDS is polynomially equivalent to the Frege systems.

Research paper thumbnail of Analyzing Local Representations of Self-supervised Vision Transformers

arXiv (Cornell University), Dec 30, 2023

In this paper, we present a comparative analysis of various self-supervised Vision Transformers (... more In this paper, we present a comparative analysis of various self-supervised Vision Transformers (ViTs), focusing on their local representative power. Inspired by large language models, we examine the abilities of ViTs to perform various computer vision tasks with little to no fine-tuning. We design evaluation framework to analyze the quality of local, i.e. patch-level, representations in the context of few-shot semantic segmentation, instance identification, object retrieval and tracking. We discover that contrastive learning based methods like DINO produce more universal patch representations that can be immediately applied for downstream tasks with no parameter tuning, compared to masked image modeling. The embeddings learned using the latter approach, e.g. in masked autoencoders, have high variance features that harm distance-based algorithms, such as k-NN, and do not contain useful information for most downstream tasks. Furthermore, we demonstrate that removing these high-variance features enhances k-NN for MAE, as well as for its recent extension Scale-MAE. Finally, we find an object instance retrieval setting where DINOv2, a model pretrained on two orders of magnitude more data, falls short of its less compute intensive counterpart DINO.

Research paper thumbnail of On Proof Complexities Relations in Some Systems of Propositional Calculus

Mathematical problems of computer science, Dec 25, 2020

Research paper thumbnail of The Relationship Between the Proof Complexities of Linear Proofs in Quantified Sequent Calculus and Substitution Frege Systems

Mathematical problems of computer science, May 31, 2023

It has formerly been proved that there is an exponential speed-up in the number of lines of the q... more It has formerly been proved that there is an exponential speed-up in the number of lines of the quantified propositional sequent calculus over substitution Frege systems when considering proofs as trees. This paper shows that a linear proof of any quantifierfree tautology in quantified propositional sequent calculus can be transformed into a linear proof of the same tautology in a substitution Frege systems with no more than polynomially increasing proof lines and size.

Research paper thumbnail of The Relationship Between the Proof Complexities of Linear Proofs in Quantified Sequent Calculus and Substitution Frege Systems

Mathematical Problems of Computer Science

It has formerly been proved that there is an exponential speed-up in the number of lines of the q... more It has formerly been proved that there is an exponential speed-up in the number of lines of the quantified propositional sequent calculus over substitution Frege systems when considering proofs as trees. This paper shows that a linear proof of any quantifierfree tautology in quantified propositional sequent calculus can be transformed into a linear proof of the same tautology in a substitution Frege systems with no more than polynomially increasing proof lines and size.

Research paper thumbnail of On Proof Complexities Relations in Some Systems of Propositional Calculus

The number of linear proofs steps for some sets of formulas is compared in the folowing systems o... more The number of linear proofs steps for some sets of formulas is compared in the folowing systems of propositional calculus: PK – seguent system with cut rule, PK— - the same system without cut rule, SPK – the same system with substitution rule, QPK – the same system with quantifier rules. The number of steps of tree-like proofs in the same systems for some considered set of formulas is compared from Alessandra Carbone in [1] and some distinctive property of the system QPK is revealed: QPK has an exponential speed-up over the systems SPK and PK, which, in their turn, have an exponential speed-up over the system PK—. This result drew the heavy interest for the study of the system QPK. In this work for linear proofs steps in the same systems the other relations are received: it is showed that the system QPK has no preference over the system SPK, it is showed also that for the considered formula sets the system PK has no preference over the system PK—, which, in its turn, has no preferen...

Research paper thumbnail of On Proof Complexities Relations in Some Systems of Propositional Calculus

Mathematical Problems of Computer Science, 2020

The number of linear proofs steps for some sets of formulas is compared in the folowing systems o... more The number of linear proofs steps for some sets of formulas is compared in the folowing systems of propositional calculus: PK – seguent system with cut rule, PK— - the same system without cut rule, SPK – the same system with substitution rule, QPK – the same system with quantifier rules. The number of steps of tree-like proofs in the same systems for some considered set of formulas is compared from Alessandra Carbone in [1] and some distinctive property of the system QPK is revealed: QPK has an exponential speed-up over the systems SPK and PK, which, in their turn, have an exponential speed-up over the system PK—. This result drew the heavy interest for the study of the system QPK. In this work for linear proofs steps in the same systems the other relations are received: it is showed that the system QPK has no preference over the system SPK, it is showed also that for the considered formula sets the system PK has no preference over the system PK—, which, in its turn, has no preferen...

Research paper thumbnail of Some New Proof System for Propositional Modal Logic

Zekuyts’ner - Haykakan SSṚ gitut’yunneri akademia, Apr 23, 2024

Research paper thumbnail of A Hierarchy of Determinative Sequent Systems with Different Substitution Rules

Some determinative sequent system (DS) for classical propositional calculus is introduced on the ... more Some determinative sequent system (DS) for classical propositional calculus is introduced on the base of wellknown Tseytin's transformation. It is proved that the system DS is polynomial equivalent to the resolution system R and cut-free sequent system PK-. Then we define the system SDS (DS with a substitution rule) and the systems SkDS (DS with restricted substitution rules, where the number of connectives in substituted formulas is bounded by). It is proved that for every ≥ the system Sk+1DS has an exponential speed-up over the system SkDS in the tree form, and the system SDS is polynomially equivalent to the Frege systems.

Research paper thumbnail of Analyzing Local Representations of Self-supervised Vision Transformers

arXiv (Cornell University), Dec 30, 2023

In this paper, we present a comparative analysis of various self-supervised Vision Transformers (... more In this paper, we present a comparative analysis of various self-supervised Vision Transformers (ViTs), focusing on their local representative power. Inspired by large language models, we examine the abilities of ViTs to perform various computer vision tasks with little to no fine-tuning. We design evaluation framework to analyze the quality of local, i.e. patch-level, representations in the context of few-shot semantic segmentation, instance identification, object retrieval and tracking. We discover that contrastive learning based methods like DINO produce more universal patch representations that can be immediately applied for downstream tasks with no parameter tuning, compared to masked image modeling. The embeddings learned using the latter approach, e.g. in masked autoencoders, have high variance features that harm distance-based algorithms, such as k-NN, and do not contain useful information for most downstream tasks. Furthermore, we demonstrate that removing these high-variance features enhances k-NN for MAE, as well as for its recent extension Scale-MAE. Finally, we find an object instance retrieval setting where DINOv2, a model pretrained on two orders of magnitude more data, falls short of its less compute intensive counterpart DINO.

Research paper thumbnail of On Proof Complexities Relations in Some Systems of Propositional Calculus

Mathematical problems of computer science, Dec 25, 2020

Research paper thumbnail of The Relationship Between the Proof Complexities of Linear Proofs in Quantified Sequent Calculus and Substitution Frege Systems

Mathematical problems of computer science, May 31, 2023

It has formerly been proved that there is an exponential speed-up in the number of lines of the q... more It has formerly been proved that there is an exponential speed-up in the number of lines of the quantified propositional sequent calculus over substitution Frege systems when considering proofs as trees. This paper shows that a linear proof of any quantifierfree tautology in quantified propositional sequent calculus can be transformed into a linear proof of the same tautology in a substitution Frege systems with no more than polynomially increasing proof lines and size.

Research paper thumbnail of The Relationship Between the Proof Complexities of Linear Proofs in Quantified Sequent Calculus and Substitution Frege Systems

Mathematical Problems of Computer Science

It has formerly been proved that there is an exponential speed-up in the number of lines of the q... more It has formerly been proved that there is an exponential speed-up in the number of lines of the quantified propositional sequent calculus over substitution Frege systems when considering proofs as trees. This paper shows that a linear proof of any quantifierfree tautology in quantified propositional sequent calculus can be transformed into a linear proof of the same tautology in a substitution Frege systems with no more than polynomially increasing proof lines and size.

Research paper thumbnail of On Proof Complexities Relations in Some Systems of Propositional Calculus

The number of linear proofs steps for some sets of formulas is compared in the folowing systems o... more The number of linear proofs steps for some sets of formulas is compared in the folowing systems of propositional calculus: PK – seguent system with cut rule, PK— - the same system without cut rule, SPK – the same system with substitution rule, QPK – the same system with quantifier rules. The number of steps of tree-like proofs in the same systems for some considered set of formulas is compared from Alessandra Carbone in [1] and some distinctive property of the system QPK is revealed: QPK has an exponential speed-up over the systems SPK and PK, which, in their turn, have an exponential speed-up over the system PK—. This result drew the heavy interest for the study of the system QPK. In this work for linear proofs steps in the same systems the other relations are received: it is showed that the system QPK has no preference over the system SPK, it is showed also that for the considered formula sets the system PK has no preference over the system PK—, which, in its turn, has no preferen...

Research paper thumbnail of On Proof Complexities Relations in Some Systems of Propositional Calculus

Mathematical Problems of Computer Science, 2020

The number of linear proofs steps for some sets of formulas is compared in the folowing systems o... more The number of linear proofs steps for some sets of formulas is compared in the folowing systems of propositional calculus: PK – seguent system with cut rule, PK— - the same system without cut rule, SPK – the same system with substitution rule, QPK – the same system with quantifier rules. The number of steps of tree-like proofs in the same systems for some considered set of formulas is compared from Alessandra Carbone in [1] and some distinctive property of the system QPK is revealed: QPK has an exponential speed-up over the systems SPK and PK, which, in their turn, have an exponential speed-up over the system PK—. This result drew the heavy interest for the study of the system QPK. In this work for linear proofs steps in the same systems the other relations are received: it is showed that the system QPK has no preference over the system SPK, it is showed also that for the considered formula sets the system PK has no preference over the system PK—, which, in its turn, has no preferen...