arXiv subjects

Ivan Oseledets

Publications and source records attributed to Ivan Oseledets.

At least 73 records · Page 4Linked to original sources

arXiv2025

Tensor Train Decomposition for Adversarial Attacks on Computer Vision Models

Deep neural networks (DNNs) are widely used today, but they are vulnerable to adversarial attacks. To develop effective methods of defense, it is important to understand the potential weak spots of DNNs. Often attacks are organized taking into account the architecture of models (white-box approach) and based on gradient methods, but for real-world DNNs this approach in most cases is impossible. At the same time, several gradient-free optimization algorithms are used to attack black-box models. However, classical methods are often ineffective in the multidimensional case. To organize black-box attacks for computer vision models, in this work, we propose the use of an optimizer based on the low-rank tensor train (TT) format, which has gained popularity in various practical multidimensional applications in recent years. Combined with the attribution of the target image, which is built by the auxiliary (white-box) model, the TT-based optimization method makes it possible to organize an effective black-box attack by small perturbation of pixels in the target image. The superiority of the proposed approach over three popular baselines is demonstrated for seven modern DNNs on the ImageNet dataset.

math.NA↗

arXiv2025

Cluster Topology-Driven Placement of Experts Reduces Network Traffic in MoE Inference

Efficient deployment of a pre-trained LLM to a cluster with multiple servers is a critical step for providing fast responses to users' queries. The recent success of Mixture-of-Experts (MoE) LLMs raises the question of how to deploy them efficiently, considering their underlying structure. During the inference in MoE LLMs, only a small part of the experts is selected to process a given token. Moreover, in practice, the experts' load is highly imbalanced. For efficient deployment, one has to distribute the model across a large number of servers using a model placement algorithm. Thus, to improve cluster utilization, the model placement algorithm has to take into account the network topology. This work focuses on the efficient topology-aware placement of the pre-trained MoE LLMs in the inference stage. We propose an integer linear program (ILP) that determines the optimal placement of experts, minimizing the expected number of transmissions. Due to the internal structure, this optimization problem can be solved with a standard ILP solver. We demonstrate that ILP-based placement strategy yields lower network traffic than competitors for small-scale (DeepSeekMoE~16B) and large-scale (DeepSeek-R1~671B) models.

cs.NI↗

arXiv2025

I Have Covered All the Bases Here: Interpreting Reasoning Features in Large Language Models via Sparse Autoencoders

Recent LLMs like DeepSeek-R1 have demonstrated state-of-the-art performance by integrating deep thinking and complex reasoning during generation. However, the internal mechanisms behind these reasoning processes remain unexplored. We observe reasoning LLMs consistently use vocabulary associated with human reasoning processes. We hypothesize these words correspond to specific reasoning moments within the models' internal mechanisms. To test this hypothesis, we employ Sparse Autoencoders (SAEs), a technique for sparse decomposition of neural network activations into human-interpretable features. We introduce ReasonScore, an automatic metric to identify active SAE features during these reasoning moments. We perform manual and automatic interpretation of the features detected by our metric, and find those with activation patterns matching uncertainty, exploratory thinking, and reflection. Through steering experiments, we demonstrate that amplifying these features increases performance on reasoning-intensive benchmarks (+2.2%) while producing longer reasoning traces (+20.5%). Using the model diffing technique, we provide evidence that these features are present only in models with reasoning capabilities. Our work provides the first step towards a mechanistic understanding of reasoning in LLMs. Code available at https://github.com/AIRI-Institute/SAE-Reasoning

cs.CL↗

arXiv2025

Quasi-Random Physics-informed Neural Networks

Physics-informed neural networks have shown promise in solving partial differential equations (PDEs) by integrating physical constraints into neural network training, but their performance is sensitive to the sampling of points. Based on the impressive performance of quasi Monte-Carlo methods in high dimensional problems, this paper proposes Quasi-Random Physics-Informed Neural Networks (QRPINNs), which use low-discrepancy sequences for sampling instead of random points directly from the domain. Theoretically, QRPINNs have been proven to have a better convergence rate than PINNs. Empirically, experiments demonstrate that QRPINNs significantly outperform PINNs and some representative adaptive sampling methods, especially in high-dimensional PDEs. Furthermore, combining QRPINNs with adaptive sampling can further improve the performance.

cs.LG↗

arXiv2025

Test-Time Reasoning Through Visual Human Preferences with VLMs and Soft Rewards

Can Visual Language Models (VLMs) effectively capture human visual preferences? This work addresses this question by training VLMs to think about preferences at test time, employing reinforcement learning methods inspired by DeepSeek R1 and OpenAI O1. Using datasets such as ImageReward and Human Preference Score v2 (HPSv2), our models achieve accuracies of 64.9% on the ImageReward test set (trained on ImageReward official split) and 65.4% on HPSv2 (trained on approximately 25% of its data). These results match traditional encoder-based models while providing transparent reasoning and enhanced generalization. This approach allows to use not only rich VLM world knowledge, but also its potential to think, yielding interpretable outcomes that help decision-making processes. By demonstrating that human visual preferences reasonable by current VLMs, we introduce efficient soft-reward strategies for image ranking, outperforming simplistic selection or scoring methods. This reasoning capability enables VLMs to rank arbitrary images-regardless of aspect ratio or complexity-thereby potentially amplifying the effectiveness of visual Preference Optimization. By reducing the need for extensive markup while improving reward generalization and explainability, our findings can be a strong mile-stone that will enhance text-to-vision models even further.

cs.CV↗

arXiv2025

Geopolitical biases in LLMs: what are the "good" and the "bad" countries according to contemporary language models

This paper evaluates geopolitical biases in LLMs with respect to various countries though an analysis of their interpretation of historical events with conflicting national perspectives (USA, UK, USSR, and China). We introduce a novel dataset with neutral event descriptions and contrasting viewpoints from different countries. Our findings show significant geopolitical biases, with models favoring specific national narratives. Additionally, simple debiasing prompts had a limited effect in reducing these biases. Experiments with manipulated participant labels reveal models' sensitivity to attribution, sometimes amplifying biases or recognizing inconsistencies, especially with swapped labels. This work highlights national narrative biases in LLMs, challenges the effectiveness of simple debiasing methods, and offers a framework and dataset for future geopolitical bias research.

cs.CL↗

arXiv2025

Confidence Is All You Need: Few-Shot RL Fine-Tuning of Language Models

Large language models (LLMs) excel at reasoning, yet post-training remains critical for aligning their behavior with task goals. Existing reinforcement learning (RL) methods often depend on costly human annotations or external reward models. We propose Reinforcement Learning via Self-Confidence (RLSC), which uses the model's own confidence as reward signals-eliminating the need for labels, preference models, or reward engineering. Applied to Qwen2.5-Math-7B with only 16 samples per question and 10 or 20 training steps, RLSC improves accuracy by +13.4% on AIME2024, +21.2% on MATH500, +21.7% on Minerva Math, +20.8% on Olympiadbench, and +9.7% on AMC23. RLSC provides a simple, scalable post-training method for inference models, requiring only a small number of samples and unlabelled supervision.

cs.CL↗

arXiv2025

Diagonal Batching Unlocks Parallelism in Recurrent Memory Transformers for Long Contexts

Transformer models struggle with long-context inference due to their quadratic time and linear memory complexity. Recurrent Memory Transformers (RMTs) offer a solution by reducing the asymptotic cost to linear time and constant memory usage. However, their memory update mechanism leads to sequential execution, causing a performance bottleneck. We introduce Diagonal Batching, a scheduling scheme that unlocks parallelism across segments in RMTs while preserving exact recurrence. This approach eliminates the sequential constraint, enabling efficient GPU inference even for single long-context inputs without complex batching and pipelining techniques. Because the technique is purely a run-time computation reordering, existing RMT models adopt it with no retraining. Applied to a LLaMA-1B ARMT model, Diagonal Batching yields a 3.3x speedup over standard full-attention LLaMA-1B and a 1.8x speedup over the sequential RMT implementation on 131,072-token sequences. By removing sequential bottleneck, Diagonal Batching reduces inference cost and latency, thereby strengthening RMTs as a practical solution for real-world, long-context applications.

cs.LG↗

arXiv2025

CLEAR: Character Unlearning in Textual and Visual Modalities

Machine Unlearning (MU) is critical for removing private or hazardous information from deep learning models. While MU has advanced significantly in unimodal (text or vision) settings, multimodal unlearning (MMU) remains underexplored due to the lack of open benchmarks for evaluating cross-modal data removal. To address this gap, we introduce CLEAR, the first open-source benchmark designed specifically for MMU. CLEAR contains 200 fictitious individuals and 3,700 images linked with corresponding question-answer pairs, enabling a thorough evaluation across modalities. We conduct a comprehensive analysis of 11 MU methods (e.g., SCRUB, gradient ascent, DPO) across four evaluation sets, demonstrating that jointly unlearning both modalities outperforms single-modality approaches. The dataset is available at https://huggingface.co/datasets/therem/CLEAR

cs.CV↗

arXiv2025

One Task Vector is not Enough: A Large-Scale Study for In-Context Learning

In-context learning (ICL) enables Large Language Models (LLMs) to adapt to new tasks using few examples, with task vectors - specific hidden state activations - hypothesized to encode task information. Existing studies are limited by small-scale benchmarks, restricting comprehensive analysis. We introduce QuiteAFew, a novel dataset of 3,096 diverse few-shot tasks, each with 30 input-output pairs derived from the Alpaca dataset. Experiments with Llama-3-8B on QuiteAFew reveal: (1) task vector performance peaks at an intermediate layer (e.g., 15th), (2) effectiveness varies significantly by task type, and (3) complex tasks rely on multiple, subtask-specific vectors rather than a single vector, suggesting distributed task knowledge representation.

cs.CL↗

arXiv2025

High-dimensional Optimization with Low Rank Tensor Sampling and Local Search

We present a novel method called TESALOCS (TEnsor SAmpling and LOCal Search) for multidimensional optimization, combining the strengths of gradient-free discrete methods and gradient-based approaches. The discrete optimization in our method is based on low-rank tensor techniques, which, thanks to their low-parameter representation, enable efficient optimization of high-dimensional problems. For the second part, i.e., local search, any effective gradient-based method can be used, whether existing (such as quasi-Newton methods) or any other developed in the future. Our approach addresses the limitations of gradient-based methods, such as getting stuck in local optima; the limitations of discrete methods, which cannot be directly applied to continuous functions; and limitations of gradient-free methods that require large computational budgets. Note that we are not limited to a single type of low-rank tensor decomposition for discrete optimization, but for illustrative purposes, we consider a specific efficient low-rank tensor train decomposition. For 20 challenging 100-dimensional functions, we demonstrate that our method can significantly outperform results obtained with gradient-based methods like Conjugate Gradient, BFGS, SLSQP, and other methods, improving them by orders of magnitude with the same computing budget.

math.OC↗

arXiv2025

Bayesian Inverse Problems Meet Flow Matching: Efficient and Flexible Inference via Transformers

The efficient resolution of Bayesian inverse problems remains challenging due to the high computational cost of traditional sampling methods. In this paper, we propose a novel framework that integrates Conditional Flow Matching (CFM) with a transformer-based architecture to enable fast and flexible sampling from complex posterior distributions. The proposed methodology involves the direct learning of conditional probability trajectories from the data, leveraging CFM's ability to bypass iterative simulation and transformers' capacity to process arbitrary numbers of observations. The efficacy of the proposed framework is demonstrated through its application to three problems: a simple nonlinear model, a disease dynamics framework, and a two-dimensional Darcy flow Partial Differential Equation. The primary outcomes demonstrate that the relative errors in parameters recovery are as low as 1.5%, and that the inference time is reduced by up to 2000 times on CPU in comparison with the Monte Carlo Markov Chain. This framework facilitates the expeditious resolution of Bayesian problems through the utilisation of sampling from the learned conditional distribution.

cs.LG↗

arXiv2025

Binding threshold units with artificial oscillatory neurons

Artificial Kuramoto oscillatory neurons were recently introduced as an alternative to threshold units. Empirical evidence suggests that oscillatory units outperform threshold units in several tasks including unsupervised object discovery and certain reasoning problems. The proposed coupling mechanism for these oscillatory neurons is heterogeneous, combining a generalized Kuramoto equation with standard coupling methods used for threshold units. In this research note, we present a theoretical framework that clearly distinguishes oscillatory neurons from threshold units and establishes a coupling mechanism between them. We argue that, from a biological standpoint, oscillatory and threshold units realise distinct aspects of neural coding: roughly, threshold units model intensity of neuron firing, while oscillatory units facilitate information exchange by frequency modulation. To derive interaction between these two types of units, we constrain their dynamics by focusing on dynamical systems that admit Lyapunov functions. For threshold units, this leads to Hopfield associative memory model, and for oscillatory units it yields a specific form of generalized Kuramoto model. The resulting dynamical systems can be naturally coupled to form a Hopfield-Kuramoto associative memory model, which also admits a Lyapunov function. Various forms of coupling are possible. Notably, oscillatory neurons can be employed to implement a low-rank correction to the weight matrix of a Hopfield network. This correction can be viewed either as a form of Hebbian learning or as a popular LoRA method used for fine-tuning of large language models. We demonstrate the practical realization of this particular coupling through illustrative toy experiments.

q-bio.NC↗

arXiv2025

NNTile: a machine learning framework capable of training extremely large GPT language models on a single node

This study presents an NNTile framework for training large deep neural networks in heterogeneous clusters. The NNTile is based on a StarPU library, which implements task-based parallelism and schedules all provided tasks onto all available processing units (CPUs and GPUs). It means that a particular operation, necessary to train a large neural network, can be performed on any of the CPU cores or GPU devices, depending on automatic scheduling decisions. Such an approach shifts the burden of deciding where to compute and when to communicate from a human being to an automatic decision maker, whether a simple greedy heuristic or a complex AI-based software. The performance of the presented tool for training large language models is demonstrated in extensive numerical experiments.

cs.LG↗

arXiv2025

On the Spatial Structure of Mixture-of-Experts in Transformers

A common assumption is that MoE routers primarily leverage semantic features for expert selection. However, our study challenges this notion by demonstrating that positional token information also plays a crucial role in routing decisions. Through extensive empirical analysis, we provide evidence supporting this hypothesis, develop a phenomenological explanation of the observed behavior, and discuss practical implications for MoE-based architectures.

cs.CL↗

arXiv2025

Associative memory and dead neurons

In "Large Associative Memory Problem in Neurobiology and Machine Learning," Dmitry Krotov and John Hopfield introduced a general technique for the systematic construction of neural ordinary differential equations with non-increasing energy or Lyapunov function. We study this energy function and identify that it is vulnerable to the problem of dead neurons. Each point in the state space where the neuron dies is contained in a non-compact region with constant energy. In these flat regions, energy function alone does not completely determine all degrees of freedom and, as a consequence, can not be used to analyze stability or find steady states or basins of attraction. We perform a direct analysis of the dynamical system and show how to resolve problems caused by flat directions corresponding to dead neurons: (i) all information about the state vector at a fixed point can be extracted from the energy and Hessian matrix (of Lagrange function), (ii) it is enough to analyze stability in the range of Hessian matrix, (iii) if steady state touching flat region is stable the whole flat region is the basin of attraction. The analysis of the Hessian matrix can be complicated for realistic architectures, so we show that for a slightly altered dynamical system (with the same structure of steady states), one can derive a diverse family of Lyapunov functions that do not have flat regions corresponding to dead neurons. In addition, these energy functions allow one to use Lagrange functions with Hessian matrices that are not necessarily positive definite and even consider architectures with non-symmetric feedforward and feedback connections.

q-bio.NC↗

arXiv2025

M3DA: Benchmark for Unsupervised Domain Adaptation in 3D Medical Image Segmentation

Domain shift presents a significant challenge in applying Deep Learning to the segmentation of 3D medical images from sources like Magnetic Resonance Imaging (MRI) and Computed Tomography (CT). Although numerous Domain Adaptation methods have been developed to address this issue, they are often evaluated under impractical data shift scenarios. Specifically, the medical imaging datasets used are often either private, too small for robust training and evaluation, or limited to single or synthetic tasks. To overcome these limitations, we introduce a M3DA /"mEd@/ benchmark comprising four publicly available, multiclass segmentation datasets. We have designed eight domain pairs featuring diverse and practically relevant distribution shifts. These include inter-modality shifts between MRI and CT and intra-modality shifts among various MRI acquisition parameters, different CT radiation doses, and presence/absence of contrast enhancement in images. Within the proposed benchmark, we evaluate more than ten existing domain adaptation methods. Our results show that none of them can consistently close the performance gap between the domains. For instance, the most effective method reduces the performance gap by about 62% across the tasks. This highlights the need for developing novel domain adaptation algorithms to enhance the robustness and scalability of deep learning models in medical imaging. We made our M3DA benchmark publicly available: https://github.com/BorisShirokikh/M3DA.

eess.IV↗

arXiv2025

FLAME: Flexible LLM-Assisted Moderation Engine

The rapid advancement of Large Language Models (LLMs) has introduced significant challenges in moderating user-model interactions. While LLMs demonstrate remarkable capabilities, they remain vulnerable to adversarial attacks, particularly ``jailbreaking'' techniques that bypass content safety measures. Current content moderation systems, which primarily rely on input prompt filtering, have proven insufficient, with techniques like Best-of-N (BoN) jailbreaking achieving success rates of 80% or more against popular LLMs. In this paper, we introduce Flexible LLM-Assisted Moderation Engine (FLAME): a new approach that shifts the focus from input filtering to output moderation. Unlike traditional circuit-breaking methods that analyze user queries, FLAME evaluates model responses, offering several key advantages: (1) computational efficiency in both training and inference, (2) enhanced resistance to BoN jailbreaking attacks, and (3) flexibility in defining and updating safety criteria through customizable topic filtering. Our experiments demonstrate that FLAME significantly outperforms current moderation systems. For example, FLAME reduces attack success rate in GPT-4o-mini and DeepSeek-v3 by a factor of ~9, while maintaining low computational overhead. We provide comprehensive evaluation on various LLMs and analyze the engine's efficiency against the state-of-the-art jailbreaking. This work contributes to the development of more robust and adaptable content moderation systems for LLMs.

cs.CR↗