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Maxim Rakhuba

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4 papers

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AAAI Conference 2026 Conference Paper

Matrix-Free Two-to-Infinity and One-to-Two Norms Estimation

Askar Tsyganov
Evgeny Frolov
Sergey Samsonov
Maxim Rakhuba

In this paper, we propose new randomized algorithms for estimating the two-to-infinity and one-to-two norms in a matrix-free setting, using only matrix-vector multiplications. Our methods are based on appropriate modifications of Hutchinson's diagonal estimator and its Hutch++ version. We provide oracle complexity bounds for both modifications. We further illustrate the practical utility of our algorithms for Jacobian-based regularization in deep neural network training on image classification tasks. We also demonstrate that our methodology can be applied to mitigate the effect of adversarial attacks in the domain of recommender systems.

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NeurIPS Conference 2025 Conference Paper

COALA: Numerically Stable and Efficient Framework for Context-Aware Low-Rank Approximation

Uliana Parkina
Maxim Rakhuba

Recent studies suggest that context-aware low-rank approximation is a useful tool for compression and fine-tuning of modern large-scale neural networks. In this type of approximation, a norm is weighted by a matrix of input activations, significantly improving metrics over the unweighted case. Nevertheless, existing methods for neural networks suffer from numerical instabilities due to their reliance on classical formulas involving explicit Gram matrix computation and their subsequent inversion. We demonstrate that this can degrade the approximation quality or cause numerically singular matrices. To address these limitations, we propose a novel inversion-free regularized framework that is based entirely on stable decompositions and overcomes the numerical pitfalls of prior art. Our method can handle all possible challenging scenarios: (1) when calibration matrices exceed GPU memory capacity, (2) when input activation matrices are nearly singular, and even (3) when insufficient data prevents unique approximation. For the latter, we prove that our solution converges to a desired approximation and derive explicit error bounds.

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NeurIPS Conference 2024 Conference Paper

Group and Shuffle: Efficient Structured Orthogonal Parametrization

Mikhail Gorbunov
Nikolay Yudin
Vera Soboleva
Aibek Alanov
Alexey Naumov
Maxim Rakhuba

The increasing size of neural networks has led to a growing demand for methods of efficient finetuning. Recently, an orthogonal finetuning paradigm was introduced that uses orthogonal matrices for adapting the weights of a pretrained model. In this paper, we introduce a new class of structured matrices, which unifies and generalizes structured classes from previous works. We examine properties of this class and build a structured orthogonal parametrization upon it. We then use this parametrization to modify the orthogonal finetuning framework, improving parameter efficiency. We empirically validate our method on different domains, including adapting of text-to-image diffusion models and downstream task finetuning in language modeling. Additionally, we adapt our construction for orthogonal convolutions and conduct experiments with 1-Lipschitz neural networks.

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NeurIPS Conference 2022 Conference Paper

Towards Practical Control of Singular Values of Convolutional Layers

Alexandra Senderovich
Ekaterina Bulatova
Anton Obukhov
Maxim Rakhuba

In general, convolutional neural networks (CNNs) are easy to train, but their essential properties, such as generalization error and adversarial robustness, are hard to control. Recent research demonstrated that singular values of convolutional layers significantly affect such elusive properties and offered several methods for controlling them. Nevertheless, these methods present an intractable computational challenge or resort to coarse approximations. In this paper, we offer a principled approach to alleviating constraints of the prior art at the expense of an insignificant reduction in layer expressivity. Our method is based on the tensor-train decomposition; it retains control over the actual singular values of convolutional mappings while providing structurally sparse and hardware-friendly representation. We demonstrate the improved properties of modern CNNs with our method and analyze its impact on the model performance, calibration, and adversarial robustness. The source code is available at: https: //github. com/WhiteTeaDragon/practical svd conv

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