arXiv subjects

Evgeny Dantsin

Publications and source records attributed to Evgeny Dantsin.

3 recordsLinked to original sources

arXiv2024

Extensional Properties of Recurrent Neural Networks

A property of a recurrent neural network (RNN) is called \emph{extensional} if, loosely speaking, it is a property of the function computed by the RNN rather than a property of the RNN algorithm. Many properties of interest in RNNs are extensional, for example, robustness against small changes of input or good clustering of inputs. Given an RNN, it is natural to ask whether it has such a property. We give a negative answer to the general question about testing extensional properties of RNNs. Namely, we prove a version of Rice's theorem for RNNs: any nontrivial extensional property of RNNs is undecidable.

cs.NE↗

arXiv2022

An AlphaZero-Inspired Approach to Solving Search Problems

AlphaZero and its extension MuZero are computer programs that use machine-learning techniques to play at a superhuman level in chess, go, and a few other games. They achieved this level of play solely with reinforcement learning from self-play, without any domain knowledge except the game rules. It is a natural idea to adapt the methods and techniques used in AlphaZero for solving search problems such as the Boolean satisfiability problem (in its search version). Given a search problem, how to represent it for an AlphaZero-inspired solver? What are the "rules of solving" for this search problem? We describe possible representations in terms of easy-instance solvers and self-reductions, and we give examples of such representations for the satisfiability problem. We also describe a version of Monte Carlo tree search adapted for search problems.

cs.AI↗

arXiv2020

Similarity Between Points in Metric Measure Spaces

This paper is about similarity between objects that can be represented as points in metric measure spaces. A metric measure space is a metric space that is also equipped with a measure. For example, a network with distances between its nodes and weights assigned to its nodes is a metric measure space. Given points x and y in different metric measure spaces or in the same space, how similar are they? A well known approach is to consider x and y similar if their neighborhoods are similar. For metric measure spaces, similarity between neighborhoods is well captured by the Gromov-Hausdorff-Prokhorov distance, but it is NP-hard to compute this distance even in quite simple cases. We propose a tractable alternative: the radial distribution distance between the neighborhoods of x and y. The similarity measure based on the radial distribution distance is coarser than the similarity based on the Gromov-Hausdorff-Prokhorov distance but much easier to compute.

cs.DM↗