arXiv subjects

Mikhail Burtsev

Publications and source records attributed to Mikhail Burtsev.

At least 19 recordsLinked to original sources

arXiv2026

Recursive Criticality of AI Self-Improvement

AI is increasingly used in the R\&D process that produces future AI systems. We study the conditions under which this feedback becomes self-amplifying. Our model describes how the rate of AI capability growth depends on baseline research productivity, recursive feedback, and the increasing difficulty of research progress. We derive a recursive reproduction number, $\mathcal{R}_{\mathrm{AI}}$, that determines whether improvements are amplified or damped across development cycles. This quantity compares the strength of feedback with the rate at which further progress becomes more difficult. When $\mathcal{R}_{\mathrm{AI}}>1$, the effects of improvements compound across development cycles, placing the system in a self-amplifying regime. When $\mathcal{R}_{\mathrm{AI}}<1$, their effects weaken across cycles. The transition depends on the structure of the AI R\&D feedback loop and need not occur at any particular level of model capability. A system can therefore enter a self-amplifying regime before acceleration becomes visible, while rapid progress can also occur without self-amplification. Higher baseline research productivity can accelerate progress without changing whether the system is self-amplifying, but the duration of the development cycle becomes a limiting timescale for amplification. Increasing research difficulty can end a period of self-amplification. Extending the model to multiple research actors shows that improvements shared across organizations can make the overall research ecosystem self-amplifying even when no individual actor is. The framework identifies measurable properties of AI R\&D systems that can help distinguish recursive amplification from rapid progress driven by other sources, including the strength of recursive feedback, how effectively improvements propagate into successor systems, cycle duration, and the increasing difficulty of further progress.

cs.AI↗

arXiv2026

MARS: Multi-Specialist LLM Relay System for Competitive Programming

Large Language Models excel at code generation, yet competitive programming exposes a persistent failure mode: existing multi-agent pipelines distribute work over generic planner, coder, and debugger roles and delegate the choice of algorithmic technique to the backbone alone. We present MARS (Multi-Agent Relay of Specialized LLMs), a prompt-only framework in which each agent is a topic specialist---dynamic programming, graphs, strings, geometry, and so on---grounded by retrieval-augmented generation over an algorithm-theory corpus. Given a problem, retrieval selects a small team of relevant specialists; a starter writes an initial C++17 solution, and each subsequent turn runs the candidate against public examples in a sandbox, lets the active specialist keep, repair, or hand off the draft, and forwards a structured packet to the next specialist. A single infrastructure-fixer pass normalizes boilerplate at the end. On the CodeContests test split with Gemma 4, MARS reaches $0.624 \pm 0.006$ pass rate at $2.3$ recorded pipeline stages per task ($+14.4$ percentage points over direct prompting), closing most of the gap to CodeSIM ($0.731$) at $3.3{\times}$ lower wall-clock cost and substantially smaller variance in per-task token spend. The source code is available on GitHub: https://github.com/fckand/mars.

cs.AI↗

arXiv2026

Geometry-Guided Layerwise FFN Width Allocation in Transformers

Feed-forward networks (FFNs) account for a large fraction of Transformer parameters, yet their hidden width is usually constant across depth. We ask whether this capacity can instead be allocated from a forward-pass measurement of layer behavior. We view each FFN as transporting a cloud of token representations and quantify the induced geometric change using correspondence-preserving shift, Gromov-Wasserstein distortion, and degree-one persistent homology under raw and scale-normalized metrics. A layerwise approximation surrogate yields an exact fixed-budget optimizer. Across seven pretrained language models, raw Euclidean work largely tracks residual-norm growth, whereas normalized work is predominantly front-loaded. Gromov-Wasserstein work is more consistently associated with perturbation-based layer sensitivity than the finite-sample topological estimate. In paired 128M and 256M training runs, several normalized-work schedules reduce mean validation loss relative to both uniform width and a hand-designed cosine taper. With the amplified paired differences at 440M, the best geometry-based allocations improve over uniform substantially larger than the cosine taper, while the anti-topological raw control is worse than uniform.

cs.LG↗

arXiv2026

Feed-Forward Steering in Transformer Residual Dynamics

Attention-only dynamical theories model Transformer residual directions as particles aggregating on a sphere. We extend this framework by incorporating the feed-forward network (FFN) term as a local steering field acting on each token state. The resulting theory predicts that the tangential component of the FFN field is necessary for motion in residual-direction space, that critical residual directions correspond to nonlinear projective equilibria, and that a commutator defect determines when a finite attention--FFN block can be accurately approximated by a parallel, additive flow. Across GPT-2, Pythia, Mistral, and Llama models, the extended theory improves one-step angular prediction relative to an attention-only baseline, with the contribution of the FFN increasing from GPT-2 to Llama-3-8B. Intervention experiments show that retaining only the tangential FFN component preserves most model quality, whereas retaining only the radial component causes performance to collapse. The tangential component also preserves output diversity under aggregation pressure. As a practical application, layers with small commutator defects can be approximately parallelized with only a modest increase in loss, whereas layers with large defects degrade rapidly. These findings support the interpretation of FFN layers as directional steering fields that shape Transformer residual geometry and govern the feasibility of block-level interventions.

cs.LG↗

arXiv2026

Extending LLM Context via Associative Recurrent Memory

Extending the context length of large language models (LLMs) is critical for many real-world applications, yet standard transformers remain constrained by quadratic compute and linear memory scaling. In this work, we investigate the Associative Recurrent Memory Transformer (ARMT) as a practical approach for enabling long-context processing in LLMs, constant memory scaling, and better efficiency. We make three main contributions. First, we construct two domain-specific long-context datasets designed to evaluate realistic workloads, focusing on narrow-domain fine-tuning scenarios. Second, we propose a comprehensive training recipe for ARMT-based context extension, combining continued pre-training, synthetic long-context data generation, curriculum learning, and selective integration of associative memory into chosen model layers. Third, we present an extensive experimental study demonstrating that ARMT-augmented models: (i) process inputs well beyond their original context limits without degrading performance relative to in-limit baselines; (ii) generalize more effectively to out-of-distribution context lengths; and (iii) need 30% less FLOPs while preserving baseline performance within the original context window.

cs.CL↗

arXiv2026

GradMem: Learning to Write Context into Memory with Test-Time Gradient Descent

Many large language model applications require conditioning on long contexts. Transformers typically support this by storing a large per-layer KV-cache of past activations, which incurs substantial memory overhead. A desirable alternative is compressive memory: read a context once, store it in a compact state, and answer many queries from that state. We study this in a context removal setting, where the model must generate an answer without access to the original context at inference time. We introduce GradMem, which writes context into memory via per-sample test-time optimization. Given a context, GradMem performs a few steps of gradient descent on a small set of prefix memory tokens while keeping model weights frozen. GradMem explicitly optimizes a model-level self-supervised context reconstruction loss, resulting in a loss-driven write operation with iterative error correction, unlike forward-only methods. On associative key--value retrieval, GradMem outperforms forward-only memory writers with the same memory size, and additional gradient steps scale capacity much more effectively than repeated forward writes. We further show that GradMem transfers beyond synthetic benchmarks: with pretrained language models, it attains competitive results on natural language tasks including bAbI and SQuAD variants, relying only on information encoded in memory.

cs.CL↗

arXiv2025

Wikontic: Constructing Wikidata-Aligned, Ontology-Aware Knowledge Graphs with Large Language Models

Knowledge graphs (KGs) provide structured, verifiable grounding for large language models (LLMs), but current LLM-based systems commonly use KGs as auxiliary structures for text retrieval, leaving their intrinsic quality underexplored. In this work, we propose Wikontic, a multi-stage pipeline that constructs KGs from open-domain text by extracting candidate triplets with qualifiers, enforcing Wikidata-based type and relation constraints, and normalizing entities to reduce duplication. The resulting KGs are compact, ontology-consistent, and well-connected; on MuSiQue, the correct answer entity appears in 96% of generated triplets. On HotpotQA, our triplets-only setup achieves 76.0 F1, and on MuSiQue 59.8 F1, matching or surpassing several retrieval-augmented generation baselines that still require textual context. In addition, Wikontic attains state-of-the-art information-retention performance on the MINE-1 benchmark (86%), outperforming prior KG construction methods. Wikontic is also efficient at build time: KG construction uses less than 1,000 output tokens, about 3$\times$ fewer than AriGraph and $<$1/20 of GraphRAG. The proposed pipeline enhances the quality of the generated KG and offers a scalable solution for leveraging structured knowledge in LLMs.

cs.CL↗

arXiv2025

Loss Patterns of Neural Networks

We present multi-point optimization: an optimization technique that allows to train several models simultaneously without the need to keep the parameters of each one individually. The proposed method is used for a thorough empirical analysis of the loss landscape of neural networks. By extensive experiments on FashionMNIST and CIFAR10 datasets we demonstrate two things: 1) loss surface is surprisingly diverse and intricate in terms of landscape patterns it contains, and 2) adding batch normalization makes it more smooth. Source code to reproduce all the reported results is available on GitHub: https://github.com/universome/loss-patterns.

cs.LG↗

arXiv2025

Can Stationary Distributions of Scale-Invariant Neural Networks Be Described by the Thermodynamics of an Ideal Gas?

Understanding the training dynamics of deep neural networks remains a major open problem, with physics-inspired approaches offering promising insights. Building on this perspective, we develop a thermodynamic framework to describe the stationary distributions of stochastic gradient descent (SGD) with weight decay for scale-invariant neural networks, a setting that both reflects practical architectures with normalization layers and permits theoretical analysis. We establish analogies between training hyperparameters (e.g., learning rate, weight decay) and thermodynamic variables such as temperature, pressure, and volume. Starting with a simplified isotropic noise model, we uncover a close correspondence between SGD dynamics and ideal gas behavior, validated through theory and simulation. Extending to training of neural networks, we show that key predictions of the framework, including the behavior of stationary entropy, align closely with experimental observations. This framework provides a principled foundation for interpreting training dynamics and may guide future work on hyperparameter tuning and the design of learning rate schedulers.

cs.LG↗

arXiv2025

Q-RAG: Long Context Multi-step Retrieval via Value-based Embedder Training

Retrieval-Augmented Generation (RAG) methods enhance LLM performance by efficiently filtering relevant context for LLMs, reducing hallucinations and inference cost. However, most existing RAG methods focus on single-step retrieval, which is often insufficient for answering complex questions that require multi-step search. Recently, multi-step retrieval approaches have emerged, typically involving the fine-tuning of small LLMs to perform multi-step retrieval. This type of fine-tuning is highly resource-intensive and does not enable the use of larger LLMs. In this work, we propose Q-RAG, a novel approach that fine-tunes the Embedder model for multi-step retrieval using reinforcement learning (RL). Q-RAG offers a competitive, resource-efficient alternative to existing multi-step retrieval methods for open-domain question answering and achieves state-of-the-art results on the popular long-context benchmarks BabiLong and RULER for contexts up to 10M tokens. Code is available at https://github.com/griver/Q-RAG

cs.LG↗

arXiv2025

Limitations of Normalization in Attention Mechanism

This paper investigates the limitations of the normalization in attention mechanisms. We begin with a theoretical framework that enables the identification of the model's selective ability and the geometric separation involved in token selection. Our analysis includes explicit bounds on distances and separation criteria for token vectors under softmax scaling. Through experiments with pre-trained GPT-2 model, we empirically validate our theoretical results and analyze key behaviors of the attention mechanism. Notably, we demonstrate that as the number of selected tokens increases, the model's ability to distinguish informative tokens declines, often converging toward a uniform selection pattern. We also show that gradient sensitivity under softmax normalization presents challenges during training, especially at low temperature settings. These findings advance current understanding of softmax-based attention mechanism and motivate the need for more robust normalization and selection strategies in future attention architectures.

cs.LG↗

arXiv2025

Beyond Memorization: Extending Reasoning Depth with Recurrence, Memory and Test-Time Compute Scaling

Reasoning is a core capability of large language models, yet how multi-step reasoning is learned and executed remains unclear. We study this question in a controlled cellular-automata (1dCA) framework that excludes memorisation by using disjoint training and test rules. Given a short state sequence, the model is required to infer the hidden local rule and then chain it to predict multiple future steps. Our evaluation shows that LLMs largely fail to reliably solve a natural-language proxy of the proposed task. We find that most neural architectures trained from scratch can learn rule inference and achieve high next-step accuracy, but performance drops sharply as the required number of intermediate reasoning steps increases. Experiments show that increasing model depth is crucial, and extending effective depth via recurrence, memory, or test-time compute improves results but remains bounded. The code is available on github: https://github.com/RodkinIvan/associative-recurrent-memory-transformer/tree/ACT

cs.LG↗

arXiv2025

Cramming 1568 Tokens into a Single Vector and Back Again: Exploring the Limits of Embedding Space Capacity

A range of recent works addresses the problem of compression of sequence of tokens into a shorter sequence of real-valued vectors to be used as inputs instead of token embeddings or key-value cache. These approaches are focused on reduction of the amount of compute in existing language models rather than minimization of number of bits needed to store text. Despite relying on powerful models as encoders, the maximum attainable lossless compression ratio is typically not higher than x10. This fact is highly intriguing because, in theory, the maximum information capacity of large real-valued vectors is far beyond the presented rates even for 16-bit precision and a modest vector size. In this work, we explore the limits of compression by replacing the encoder with a per-sample optimization procedure. We show that vectors with compression ratios up to x1500 exist, which highlights two orders of magnitude gap between existing and practically attainable solutions. Furthermore, we empirically show that the compression limits are determined not by the length of the input but by the amount of uncertainty to be reduced, namely, the cross-entropy loss on this sequence without any conditioning. The obtained limits highlight the substantial gap between the theoretical capacity of input embeddings and their practical utilization, suggesting significant room for optimization in model design.

cs.CL↗

arXiv2025

AriGraph: Learning Knowledge Graph World Models with Episodic Memory for LLM Agents

Advancements in the capabilities of Large Language Models (LLMs) have created a promising foundation for developing autonomous agents. With the right tools, these agents could learn to solve tasks in new environments by accumulating and updating their knowledge. Current LLM-based agents process past experiences using a full history of observations, summarization, retrieval augmentation. However, these unstructured memory representations do not facilitate the reasoning and planning essential for complex decision-making. In our study, we introduce AriGraph, a novel method wherein the agent constructs and updates a memory graph that integrates semantic and episodic memories while exploring the environment. We demonstrate that our Ariadne LLM agent, consisting of the proposed memory architecture augmented with planning and decision-making, effectively handles complex tasks within interactive text game environments difficult even for human players. Results show that our approach markedly outperforms other established memory methods and strong RL baselines in a range of problems of varying complexity. Additionally, AriGraph demonstrates competitive performance compared to dedicated knowledge graph-based methods in static multi-hop question-answering.

cs.AI↗

arXiv2025

Associative Recurrent Memory Transformer

This paper addresses the challenge of creating a neural architecture for very long sequences that requires constant time for processing new information at each time step. Our approach, Associative Recurrent Memory Transformer (ARMT), is based on transformer self-attention for local context and segment-level recurrence for storage of task specific information distributed over a long context. We demonstrate that ARMT outperfors existing alternatives in associative retrieval tasks and sets a new performance record in the recent BABILong multi-task long-context benchmark by answering single-fact questions over 50 million tokens with an accuracy of 79.9%. The source code for training and evaluation is available on github.

cs.CL↗

arXiv2025

SRMT: Shared Memory for Multi-agent Lifelong Pathfinding

Coordination in decentralized multi-agent reinforcement learning (MARL) necessitates that agents share information about their behavior and intentions. Existing approaches rely on communication protocols with domain or resource constraints or centralized training that poorly scales to large agent populations. We introduce the Shared Recurrent Memory Transformer (SRMT), which enables coordination through unconstrained communication. SRMT provides a global memory workspace where agents broadcast their learned working memory states and query others' memory representations to exchange information and coordinate while maintaining decentralized training and execution. We evaluate SRMT on the Partially Observable Multi-Agent Pathfinding (PO-MAPF) problem, where coordination is vital for optimal path planning and deadlock avoidance. We demonstrate that shared memory enables emergent coordination even when the reward function provides minimal or no guidance. On the specifically constructed Bottleneck task that requires negotiation, SRMT consistently outperforms communicative and memory-augmented baselines, particularly under sparse reward signals, and successfully generalizes to longer corridors unseen during training. On POGEMA maps, SRMT scales with the increasing agents' population and map size, achieving competitive performance with recent MARL, hybrid, and planning-based methods while requiring no domain-specific heuristics. These results demonstrate that a transformer with shared recurrent memory enhances coordination in decentralized multi-agent systems. The source code for training and evaluation is available on GitHub: https://github.com/Aloriosa/srmt.

cs.LG↗

arXiv2024

Learning Elementary Cellular Automata with Transformers

Large Language Models demonstrate remarkable mathematical capabilities but at the same time struggle with abstract reasoning and planning. In this study, we explore whether Transformers can learn to abstract and generalize the rules governing Elementary Cellular Automata. By training Transformers on state sequences generated with random initial conditions and local rules, we show that they can generalize across different Boolean functions of fixed arity, effectively abstracting the underlying rules. While the models achieve high accuracy in next-state prediction, their performance declines sharply in multi-step planning tasks without intermediate context. Our analysis reveals that including future states or rule prediction in the training loss enhances the models' ability to form internal representations of the rules, leading to improved performance in longer planning horizons and autoregressive generation. Furthermore, we confirm that increasing the model's depth plays a crucial role in extended sequential computations required for complex reasoning tasks. This highlights the potential to improve LLM with inclusion of longer horizons in loss function, as well as incorporating recurrence and adaptive computation time for dynamic control of model depth.

cs.NE↗

arXiv2024

BABILong: Testing the Limits of LLMs with Long Context Reasoning-in-a-Haystack

In recent years, the input context sizes of large language models (LLMs) have increased dramatically. However, existing evaluation methods have not kept pace, failing to comprehensively assess the efficiency of models in handling long contexts. To bridge this gap, we introduce the BABILong benchmark, designed to test language models' ability to reason across facts distributed in extremely long documents. BABILong includes a diverse set of 20 reasoning tasks, including fact chaining, simple induction, deduction, counting, and handling lists/sets. These tasks are challenging on their own, and even more demanding when the required facts are scattered across long natural text. Our evaluations show that popular LLMs effectively utilize only 10-20\% of the context and their performance declines sharply with increased reasoning complexity. Among alternatives to in-context reasoning, Retrieval-Augmented Generation methods achieve a modest 60\% accuracy on single-fact question answering, independent of context length. Among context extension methods, the highest performance is demonstrated by recurrent memory transformers after fine-tuning, enabling the processing of lengths up to 50 million tokens. The BABILong benchmark is extendable to any length to support the evaluation of new upcoming models with increased capabilities, and we provide splits up to 10 million token lengths.

cs.CL↗