Intelligent systems at phystech: 2026 graduation

Literature review, comparison, and analysis of existing solutions constitute a significant part of a thesis manuscript.  In the last three years, AI chats have dramatically intervened in the thesis preparation workflow. The ability of AI chats to analyze and compare discourages students from acting as the primary drivers of research and instead encourages their passive reliance on AI-generated content. This situation makes manuscripts eclectic and lacks focus. The theoretical part disconnects from the computational experiments. As a result, the audience is reluctant to read students’ manuscripts. Ironically, they use AI chats to summarise the manuscripts to extract their main contributions. We are proud to say that our thesis works do not suffer from this AI distortion. We are grateful to our students, especially our bachelor’s and master’s alumni, who have carefully prepared and successfully defended their theses, producing clear, well-founded, and meaningful results. Our thesis manuscripts are designed for public discussion and rigorous scientific analysis. Each thesis presents a clear research idea grounded in the fundamentals of machine learning. It includes a theoretical justification, a repository with the source code of the computational experiments, and slides. Videos of the pre-defence sessions are uploaded to our YouTube channel “Intelligent Systems”: Bachelors & Masters.

Applied methods in machine learning

Several of this year’s theses take on hidden dynamics and structure in real-world data — from feedback effects inside deployed ML systems to signals recorded from the human brain and body.

Andrey Veprikov‘s thesis, supervised by Dr. Anton Khritankov, addresses machine learning systems in which the model’s own predictions quietly change the data it will see next. This hidden feedback loop often causes models to degrade over time even as the loss on the current batch keeps improving. He introduces a single control parameter into the training step and proves conditions under which it keeps the system stable, validating the approach both on synthetic tasks and on a real medical-imaging benchmark. Parts of the work appeared in Knowledge and Information Systems (Springer), in Artificial Intelligence and Decision Making, and at the MMRO conference.

Sergey Dementev‘s research, also supervised by Dr. Anton Khritankov,  studies the same class of hidden feedback loops in recommender systems, where models repeatedly learn from data shaped by their own past recommendations. He shows that personalization degradation is not a single effect but arises through two distinct mechanisms: the contraction of user-preference diversity and the retraining-driven reshaping of served content. The work provides mathematical guarantees for these effects, including activation conditions and a measurable threshold for personalization collapse. Experiments on synthetic data and MovieLens-20M confirm the theory and show that explicit diversification can preserve diversity without sacrificing recommendation quality.

Alexander Terentyev‘s thesis, supervised by our alumnus and professor Dr. Roman Isachenko, studies an inverse problem for partial differential equations. It introduces a regularization method that produces physically meaningful solutions and allows control over their spatial structure, tested on an EEG dataset. Unlike other approaches, it does not impose strict assumptions on the properties of the sources — their structure follows directly from the regularization.

Matvei Kreinin‘s work  under supervision of Dr. Aleksandr Beznosikov, D.Sc., addresses bidirectional translation between native (non-contrast) and contrast-enhanced abdominal computed tomography (CT) series by means of conditional flow matching theory. He proposes the Medical Flow Matching (MFM) framework together with a neural-network parameterization of the velocity field, TimeResNet. The method enables single-step deterministic inference via integration of an ordinary differential equation, and a single network realizes both translation directions.

Daniil Dorin‘s thesis, supervised by our alumnus and professor Dr. Andrey Grabovoy, is devoted to decoding and reconstructing visual stimuli from brain activity recorded simultaneously with fMRI and EEG — two neuroimaging modalities whose spatial and temporal resolutions complement each other. He frames decoding as a single problem approached in three stages of increasing structural complexity: estimating the hemodynamic delay of the BOLD signal, extracting spatiotemporal features of fMRI through Riemannian geometry and class-specific activity masks that stay robust under limited sample sizes, and finally a multimodal architecture that contrastively aligns joint fMRI–EEG embeddings with the CLIP space and reconstructs the stimulus via a two-stage diffusion generation. Experiments show that combining the two modalities outperforms single-modality decoding, and that adding a diffusion prior further improves the semantic fidelity of the reconstructions. The thesis is based on 3 papers published during Daniil’s study. The three stages of the work, ordered by the structure each one is able to represent: stage 1 models time alone, recovering the hemodynamic delay Δt from a linear autoregressive forecast of fMRI given the stimulus; stage 2 adds space, describing class-specific activity masks through the Riemannian geometry of their covariance matrices, which keeps the feature dimension independent of sample size; stage 3 adds a second modality, contrastively aligning the joint fMRI–EEG embedding with CLIP space before a two-stage diffusion reconstruction. The stages are sequential rather than parallel — the delay estimated in the first is what temporally aligns the two modalities in the third.

Anastasia German‘s work, also supervised by Dr. Andrey Grabovoy, addresses the prediction of fMRI images — more precisely, increments of the BOLD signal — from the audio and video streams of a naturalistic audiovisual film, using simple, interpretable voxel-wise linear models. Three models of increasing complexity are built: a unimodal audio baseline, based on MFCC features, a multimodal banded-ridge regression with separate penalties for audio and video, and — the central model — a voxel-wise gated model in which predictions from the two modalities are mixed by a scalar gate, whose optimal value is derived analytically in closed form. The key result: banded-ridge regression yields only a marginal improvement, while the gated model consistently outperforms both unimodal baselines across all nine subjects, confirmed statistically. The analysis also shows that the gate favors audio almost everywhere, that the contribution of video is weak and distributed, and that the gain is achieved specifically through local, voxel-wise modality selection unavailable to a globally fitted joint model.

Kirill Semkin in his thesis, supervised by Dr. Roman Isachenko, proposes a method for time series classification under the assumption that series from different classes are generated by distinct dynamical systems, modeled as ordinary or stochastic differential equations whose noisy phase trajectories form the observed data. The classifier assigns each series to the class whose dynamics best fit it in a certain sense. Since exact trajectories are rarely available, they are replaced with conditional expectations obtained by solving a smoothing problem. The method is validated on synthetic linear systems, on human activity recognition from inertial sensors, and on heart failure detection from ECG recordings.

Anastasiia Vozniuk’s thesis under supervision of Dr. Andrey Grabovoy focuses on possibilities of analysing text coherence and cohesion based on graph structure of the text. It operates on building a tree of the logical structure of the text with Rhetorical Structure Theory and then calculating various values of semantic and structural coherence, as well as entity cohesion. At the end, one can obtain a unified measure of text cohesion that is flexible and interpretable.

Optimization

This year’s optimization theses range from projection-free first-order methods to budget-constrained bandit learning and new matrix optimizers.

Igor Ignashin‘s thesis under supervision of Dr. Andrey Grabovoy is devoted to projection-free Frank–Wolfe methods for machine learning and large-scale network optimization. It develops and analyzes conjugate, stochastic block-coordinate, and decentralized block-coordinate variants, focusing on reducing the computational cost per iteration while preserving O(1/t)-type convergence guarantees. The work combines theoretical convergence proofs with experiments on machine-learning tasks and traffic-assignment networks. The traffic-assignment part was developed into the paper in the peer-reviewed journal.

Ilgam Latypov‘s work, supervised by Dr. Yuriy Dorn, addresses the problem of allocating a limited training budget across multiple adaptive online-learning experts while still identifying the best-performing one. He proposes M-LCB, a UCB-style meta-algorithm that selectively trains the most promising experts and achieves near-optimal regret guarantees in the stochastic setting. Theoretical results are complemented by experiments showing that adaptive budget allocation substantially accelerates convergence to the optimal expert compared to existing approaches. The full paper is available on arXiv.

Machine learning fundamentals and computational mathematics

The largest group of theses this year develops theory — new estimators, generalization bounds, and structural models for representation learning, architecture search, and generative modeling.

Iryna Zabarianska‘s work under supervision of Dr. Alexander Korotin, addresses the estimation of mutual information (MI) between discrete random variables, which remains challenging for conventional methods as dimensionality or alphabet size grows. Leveraging recent advances in discrete bridge matching — a generative framework for domain transfer — she constructs a novel MI estimator, DBMI (Discrete Bridge Mutual Information). By expressing MI as a KL divergence between two reciprocal processes and using their Markov-chain representation, DBMI naturally handles discrete data. The method is evaluated on both a low-dimensional benchmark and a high-dimensional image benchmark with known ground truth, demonstrating superior performance over existing discrete MI estimators. The work is presented at the ICLR delta workshop.

Maksim Ivanov‘s bachelor’s thesis, supervised by our alumnus and professor Dr. Oleg Bakhteev, proposes a method for structural pruning in neural networks, based on analyzing a deep-learning computation graph and estimating the information flow propagated through it. Compared with existing baselines, the proposed approach better preserves the monotonic relationship between the true and predicted losses.

Nikita Okhotnikov‘s master’s thesis, supervised by Dr. Andrey Grabovoy, investigates the theoretical foundations of LoRA, one of the most widely used parameter-efficient fine-tuning techniques. The study builds on the previously observed implicit low-stable-rank bias of LoRA training and derives new expressivity and generalization bounds that incorporate this bias into theoretical estimates. Nikita argues that stable rank, rather than conventional algebraic rank, provides a more realistic measure of an adapter’s capacity and generalization ability.

Nikita Kiselev‘s thesis https://github.com/intsystems/Kiselev-MS-Thesis/blob/main/paper/main.pdf, also supervised by Dr. Andrey Grabovoy, asks how much training data a parametric model actually needs, and answers this through the stabilization of the empirical loss surface: once one more object no longer reshapes the landscape near the minimum, the sample can be called sufficient. Existing quantitative criteria average the loss increment isotropically over the entire parameter space, which makes them impractical for large networks. He introduces a unified p-convergence criterion equipped with a preference function over the parameter space, recovering existing estimates as special cases and adding a new one: probing restricted to the subspace spanned by the leading Hessian eigenvectors. For this criterion he proves the same convergence guarantees as before, but now scaling with the subspace size rather than the full number of parameters, along with several efficient estimation algorithms that avoid computing the full Hessian. Experiments on MLP/MNIST and on the nanochat d6 transformer confirm the theory, with the subspace-based estimator several orders of magnitude faster than direct Monte Carlo at no loss of accuracy. The results of his master’s thesis are based on five papers published in peer-reviewed journals [1, 2, 3, 4] and conference proceedings.

Egor Petrov‘s bachelor’s thesis, also supervised by Dr. Andrey Grabovoy, studies the loss landscape of Transformer architectures from a second-order theoretical perspective. The work derives exact Jacobian and Hessian matrices for all components of a full post-norm Transformer block — including self-attention, residual connections, LayerNorm, and the feed-forward network — by applying and extending tools from matrix calculus. The analytical formulas are verified against PyTorch autograd with accuracy up to numerical precision, while also providing faster computation for several derivative blocks. These results open the way to a more detailed theoretical analysis of Transformers, including their optimization stability, curvature-aware training methods, and scaling behavior.

Petr Babkin‘s master’s thesis, supervised by Dr. Oleg Bakhteev, studies neural architecture search for Mixture-of-Experts (MoE) models that accounts for the cluster structure of the data. Since changing an expert’s architecture changes its routing — and thus the data it trains on — the architectures and the data partition must be optimized jointly. The work introduces a surrogate function that takes an expert architecture and a binary vector encoding a subset of data clusters, and predicts the quality the architecture would attain on that subset without actual training. A Surrogate-assisted Generalized EM (SGEM) algorithm then uses this surrogate to jointly find the optimal data subsets for the experts and their architectures, with a proven convergence guarantee. On a CIFAR-100/SVHN mixture, the method turns experts into domain specialists without any source labels, outperforming random-MoE and shared-architecture baselines.

Alexander Udeneev‘s research, supervised by Dr. Oleg Bakhteev, «Surrogate assisted diversity estimation in neural ensemble search,» introduces a surrogate-assisted framework for Neural Ensemble Search (NES) that jointly optimizes predictive accuracy and architectural diversity to overcome the computational intractability of traditional ensemble methods. Two independent surrogate functions are employed: one predicts individual model accuracy via regression, while the other maps architectures into a latent space using triplet loss to estimate diversity based on predictive dissimilarity. A greedy selection algorithm then constructs ensembles by filtering candidates for high predicted accuracy and iteratively adding models that maximize geometric distance in the diversity latent space. Experimental results on FashionMNIST, CIFAR-10, and CIFAR-100 demonstrate that the approach achieves competitive or superior performance compared to Deep Ensembles and Random Search by effectively balancing individual model quality with collective diversity. Alexander’s bachelor’s thesis was later published and presented at the AIAI 2026 international conference.

Aleksandr Astakhov‘s thesis under supervision of our professor Dr. Vadim Strijov, D.Sc., proposes a model for distributed dynamical systems whose connectivity operator switches among a finite set of matrices, motivated by the observation that any symmetric approximation incurs an irreducible error once interactions become directed. The model combines Takens-embedding-based dimensionality reduction with a set of K low-rank, asymmetric bilinear operators, one per regime. The resulting model improves forecasting accuracy over a symmetric correlation baseline.

Danila Chernousov‘s bachelor’s thesis, supervised by Dr. Andrey Grabovoy, proposes an unsupervised, label-free measure of dataset complexity, motivated by the fact that the size of a training set says little about how diverse and informative it actually is. A valid complexity measure is defined as a non-negative function that is invariant to the order of the objects, subadditive, and monotone, so that adding an object never decreases complexity. The main result is that any embedding of the objects into a Hilbert space produces such a measure, built from the embedding’s Gaussian kernel. The required semantic embedding is supplied by a pretrained diffusion model, which maps every object to its deterministic probability-flow ODE trajectory in the Hilbert space, so the diffusion trajectory itself serves as the embedding.

Maria Nikitina work, supervised by Dr. Oleg Bakhteev and co-supervised by our alumnus Anton Bishuk, examines the relationship between the matrices of an autoencoder’s parameters and the statistical properties of the data it is trained on. The parameters of a trained model are proposed as a dense vector representation of the corresponding data sample. The resulting vector space is shown to be invariant to symmetries of the parameter space, to preserve information about mixtures present in the original data distribution, and to yield vector sets that are linearly separable when the underlying models are trained on data from different distributions. The results of Maria’s work were published in a peer-reviewed journal.

Daniil Kazachkov‘s thesis under supervision of Dr. Alexander Korotin, studies how to recover hidden pairwise dependencies between two sets of observations when the original matching within each group has been lost. The problem is formulated as probabilistic inference, and two approaches are developed: a categorical variational autoencoder with a Gumbel–Sinkhorn latent permutation, and a global shift-mixture model trained with a modified EM algorithm. Experiments on synthetic periodic data show that both methods can recover latent pairs and the underlying data distribution. The neural model generalizes to new groups without re-optimization, while the explicit mixture model achieves higher accuracy when its assumptions match the data structure.

Conclusion

The thesis defence process starts long before the final presentation. At the beginning of the academic year, each student is already in contact with thesis supervisors and has a research topic. All thesis supervisors in the Intelligent Systems group hold a Ph.D. or D.Sc. degree in Physics and Mathematics and have an extensive publication record. During the academic year, each student presents their work several times: at the Department’s reporting seminars and at scientific conferences. Every student also takes part in teaching activities to improve their scientific communication and pedagogical skills.

Links to the thesis manuscripts from recent years.