arXiv subjects

Sergei Kudriashov

Publications and source records attributed to Sergei Kudriashov.

6 recordsLinked to original sources

arXiv2026

Fast Differentiable SVD on GPU via Polar Decomposition

We present a fully GPU-oriented SVD pipeline based on polar decomposition, motivated by iterative methods that rely solely on matrix multiplications, such as the Newton-Schulz iteration. We show that this approach enables up to a $2\times$ speedup compared to standard implementations. Furthermore, we derive a numerically stable backward pass for the polar decomposition and leverage it to obtain a fully differentiable SVD. Our methods are released as open-source implementations in both PyTorch and JAX: https://github.com/fallnlove/cans_svd.

math.NA↗

arXiv2026

Tensorion: A Tensor-Aware Generalization of the Muon Optimizer

Common first-order optimizers, such as Adam, implicitly treat each parameter block as an unstructured vector, which disregards the multilinear weight structure present in many modern machine learning models. Recent work has shown that exploiting matrix structure can improve optimization dynamics. A notable example is Muon, which performs steepest descent under the spectral norm constraint. We take the next step and introduce Tensorion, a tensor-aware optimizer that extends Muon's constrained optimization perspective from matrices to higher-order tensors. Tensorion is built around a linear minimization oracle (LMO) over a tensor norm ball. The norm is carefully chosen to balance two objectives: tightly bounding the tensor spectral norm, while still keeping the LMO tractable. This LMO becomes computable because it reduces to operations on adaptively selected unfolding matrices. Notably, when restricted to order-2 tensors (i.e., matrices), Tensorion recovers Muon exactly. Experiments on tensor-based computer vision problems suggest that Tensorion can offer improved convergence behavior and more stable gradient updates compared with Adam-based and existing tensor-aware baselines in the evaluated settings.

cs.LG↗

arXiv2026

Pay Attention to Attention Distribution: A New Local Lipschitz Bound for Transformers

We introduce a novel upper bound on the local Lipschitz constant of the dot-product self-attention block showing its dependence on the attention map distributions. The proposed bound is not only tighter than the prior art, but for the first time, reveals how the distribution of attention probabilities shapes the local Lipschitz constant of the self-attention block. The theoretical basis of the proposed upper bound lies in the refined closed-form upper bounds on singular values of the Jacobian of softmax function. Leveraging these theoretical insights, we introduce JaSMin (Jacobian Softmax norm Minimization), a lightweight regularizer that directly controls the local Lipschitz constant of each block and, consequently, the entire model. Additionally, we discuss how the nature of the attention map distribution contributes to the gradient dynamics and, consequently, transformer training stability.

cs.LG↗

arXiv2025

FiMMIA: scaling semantic perturbation-based membership inference across modalities

Membership Inference Attacks (MIAs) aim to determine whether a specific data point was included in the training set of a target model. Although there are have been numerous methods developed for detecting data contamination in large language models (LLMs), their performance on multimodal LLMs (MLLMs) falls short due to the instabilities introduced through multimodal component adaptation and possible distribution shifts across multiple inputs. In this work, we investigate multimodal membership inference and address two issues: first, by identifying distribution shifts in the existing datasets, and second, by releasing an extended baseline pipeline to detect them. We also generalize the perturbation-based membership inference methods to MLLMs and release \textbf{FiMMIA} -- a modular \textbf{F}ramework for \textbf{M}ultimodal \textbf{MIA}.\footnote{The source code and framework have been made publicly available under the MIT license via \href{https://github.com/ai-forever/data_leakage_detect}{link}.The video demonstration is available on \href{https://youtu.be/a9L4-H80aSg}{YouTube}.} Our approach trains a neural network to analyze the target model's behavior on perturbed inputs, capturing distributional differences between members and non-members. Comprehensive evaluations on various fine-tuned multimodal models demonstrate the effectiveness of our perturbation-based membership inference attacks in multimodal domains.

cs.LG↗

arXiv2025

Shrink the longest: improving latent space isotropy with symplicial geometry

Although transformer-based models have been dominating the field of deep learning, various studies of their embedding space have shown that they suffer from "representation degeneration problem": embeddings tend to be distributed in a narrow cone, making the latent space highly anisotropic. Increasing the isotropy has shown to improve performance in downstream tasks both in static and contextual language models. However, most of approaches either add inference overhead or require substantial amount of data for model reparametrization. We propose a novel regularization technique based on simplicial geometry to improve the isotropy of latent representations. The core idea of our method is based on maximizing the persistent entropy of barcodes obtained using Vietoris-Rips filtration from contextual embeddings in the underlying latent space. We demonstrate that the method leads to an increase in downstream performance while significantly lowering the anisotropy during fine-tuning by exploiting existing geometric structures instead of reparametrization.

cs.LG↗

arXiv2025

The more polypersonal the better -- a short look on space geometry of fine-tuned layers

The interpretation of deep learning models is a rapidly growing field, with particular interest in language models. There are various approaches to this task, including training simpler models to replicate neural network predictions and analyzing the latent space of the model. The latter method allows us to not only identify patterns in the model's decision-making process, but also understand the features of its internal structure. In this paper, we analyze the changes in the internal representation of the BERT model when it is trained with additional grammatical modules and data containing new grammatical structures (polypersonality). We find that adding a single grammatical layer causes the model to separate the new and old grammatical systems within itself, improving the overall performance on perplexity metrics.

cs.CL↗