A. Naumov

A. Naumov, Ar. Melnikov, V. Abronin et al.

Neural networks have revolutionized many aspects of society but in the era of huge models with billions of parameters, optimizing and deploying them for commercial applications can require significant computational and financial resources. To address these challenges, we introduce the Tetra-AML toolbox, which automates neural architecture search and hyperparameter optimization via a custom-developed black-box Tensor train Optimization algorithm, TetraOpt. The toolbox also provides model compression through quantization and pruning, augmented by compression using tensor networks. Here, we analyze a unified benchmark for optimizing neural networks in computer vision tasks and show the superior performance of our approach compared to Bayesian optimization on the CIFAR-10 dataset. We also demonstrate the compression of ResNet-18 neural networks, where we use 14.5 times less memory while losing just 3.2% of accuracy. The presented framework is generic, not limited by computer vision problems, supports hardware acceleration (such as with GPUs and TPUs) and can be further extended to quantum hardware and to hybrid quantum machine learning models.

A. Chervov, D. Fedoriaka, E. Konstantinova et al.

This is the third paper of the CayleyPy project applying artificial intelligence to problems in group theory. We announce the first public release of CayleyPy, an open source Python library for computations with Cayley and Schreier graphs. Compared with systems such as GAP and Sage, CayleyPy handles much larger graphs and performs several orders of magnitude faster. Using CayleyPy we obtained about 200 new conjectures on Cayley and Schreier graphs, focused on diameters and growth. For many Cayley graphs of symmetric groups Sn we observe quasi polynomial diameter formulas: a small set of quadratic or linear polynomials indexed by n mod s. We conjecture that this is a general phenomenon, giving efficient diameter computation despite the problem being NP hard. We propose a refinement of the Babai type conjecture on diameters of Sn: n^2/2 + 4n upper bounds in the undirected case, compared to previous O(n^2) bounds. We also provide explicit generator families, related to involutions in a square with whiskers pattern, conjectured to maximize the diameter; search confirms this for all n up to 15. We further conjecture an answer to a question posed by V M Glushkov in 1968 on directed Cayley graphs generated by a cyclic shift and a transposition. For nilpotent groups we conjecture an improvement of J S Ellenberg's results on upper unitriangular matrices over Z/pZ, showing linear dependence of diameter on p. Moreover. Some conjectures are LLM friendly, naturally stated as sorting problems verifiable by algorithms or Python code. To benchmark path finding we created more than 10 Kaggle datasets. CayleyPy works with arbitrary permutation or matrix groups and includes over 100 predefined generators. Our growth computation code outperforms GAP and Sage up to 1000 times in speed and size.

V. Abronin, A. Naumov, D. Mazur et al.

We introduce TQCompressor, a novel method for neural network model compression with improved tensor decompositions. We explore the challenges posed by the computational and storage demands of pre-trained language models in NLP tasks and propose a permutation-based enhancement to Kronecker decomposition. This enhancement makes it possible to reduce loss in model expressivity which is usually associated with factorization. We demonstrate this method applied to the GPT-2$_{small}$. The result of the compression is TQCompressedGPT-2 model, featuring 81 mln. parameters compared to 124 mln. in the GPT-2$_{small}$. We make TQCompressedGPT-2 publicly available. We further enhance the performance of the TQCompressedGPT-2 through a training strategy involving multi-step knowledge distillation, using only a 3.1% of the OpenWebText. TQCompressedGPT-2 surpasses DistilGPT-2 and KnGPT-2 in comparative evaluations, marking an advancement in the efficient and effective deployment of models in resource-constrained environments.

D. Belomestny, L. Iosipoi, E. Moulines et al.

In this paper we propose a novel variance reduction approach for additive functionals of Markov chains based on minimization of an estimate for the asymptotic variance of these functionals over suitable classes of control variates. A distinctive feature of the proposed approach is its ability to significantly reduce the overall finite sample variance. This feature is theoretically demonstrated by means of a deep non asymptotic analysis of a variance reduced functional as well as by a thorough simulation study. In particular we apply our method to various MCMC Bayesian estimation problems where it favourably compares to the existing variance reduction approaches.