Maksim Nekrashevich

Xavier Aramayo Carrasco, Maksim Nekrashevich, Petr Mokrov et al.

Recently, the Gromov-Wasserstein Optimal Transport (GWOT) problem has attracted the special attention of the ML community. In this problem, given two distributions supported on two (possibly different) spaces, one has to find the most isometric map between them. In the discrete variant of GWOT, the task is to learn an assignment between given discrete sets of points. In the more advanced continuous formulation, one aims at recovering a parametric mapping between unknown continuous distributions based on i.i.d. samples derived from them. The clear geometrical intuition behind the GWOT makes it a natural choice for several practical use cases, giving rise to a number of proposed solvers. Some of them claim to solve the continuous version of the problem. At the same time, GWOT is notoriously hard, both theoretically and numerically. Moreover, all existing continuous GWOT solvers still heavily rely on discrete techniques. Natural questions arise: to what extent do existing methods unravel the GWOT problem, what difficulties do they encounter, and under which conditions they are successful? Our benchmark paper is an attempt to answer these questions. We specifically focus on the continuous GWOT as the most interesting and debatable setup. We crash-test existing continuous GWOT approaches on different scenarios, carefully record and analyze the obtained results, and identify issues. Our findings experimentally testify that the scientific community is still missing a reliable continuous GWOT solver, which necessitates further research efforts. As the first step in this direction, we propose a new continuous GWOT method which does not rely on discrete techniques and partially solves some of the problems of the competitors.

Alexander Golubev, Maria Trofimova, Sergei Polezhaev et al.

Research on applications of reinforcement learning (RL) to large language models has mostly been focused on single-turn problems, such as mathematical reasoning or single-shot code generation. While these problems can be viewed as token-level multi-turn Markov decision processes (MDPs), this view corresponds to a degenerate case of multi-turn interaction where the environment provides no feedback. This contrasts with many real-world domains, such as software engineering (SWE), which require rich multi-turn interactions with a stateful environment that responds to each action with a non-trivial observation. To bridge this gap, we demonstrate the successful application of RL to this general regime. Our methodology begins with rejection fine-tuning (RFT) using execution feedback to train a policy to follow instructions and formatting effectively, followed by a synchronous RL pipeline using DAPO for iterative improvement. Applying this pipeline to Qwen2.5-72B-Instruct, we increase its Pass@1 on the SWE-bench Verified benchmark from 11% to 39%, substantially improving upon the 20% RFT baseline. On the May and June splits of SWE-rebench, the resulting agent achieves Pass@1 of 35% and 31% respectively, competitive with even larger models such as DeepSeek-V3-0324 or Qwen3-235B-A22B, demonstrating that our methodology offers a practical approach for training capable agents for multi-turn interactive tasks using open-weight models.

Karina Zainullina, Alexander Golubev, Maria Trofimova et al.

Large language models (LLMs) have recently achieved remarkable results in complex multi-step tasks, such as mathematical reasoning and agentic software engineering. However, they often struggle to maintain consistent performance across multiple solution attempts. One effective approach to narrow the gap between average-case and best-case performance is guided test-time search, which explores multiple solution paths to identify the most promising one. Unfortunately, effective search techniques (e.g. MCTS) are often unsuitable for non-serializable RL environments, such as Docker containers, where intermediate environment states cannot be easily saved and restored. We investigate two complementary search strategies applicable to such environments: 1-step lookahead and trajectory selection, both guided by a learned action-value function estimator. On the SWE-bench Verified benchmark, a key testbed for agentic software engineering, we find these methods to double the average success rate of a fine-tuned Qwen-72B model, achieving 40.8%, the new state-of-the-art for open-weights models. Additionally, we show that these techniques are transferable to more advanced closed models, yielding similar improvements with GPT-4o.