Martin Vechev

Yu-Du Feng, Niels Mündler-Sasahara, Mark Vero et al.

Reasoning language models (RLMs) have demonstrated impressive performance in domains such as mathematics and coding. These domains permit reliable verification of model outputs, which is important for enabling the reinforcement learning that drives RLM performance gains. However, training RLMs on domains that lack reliable verifiers remains challenging. Meanwhile, for both verifiable and unverifiable domains, large amounts of unused supervised fine-tuning data with human-written solutions exist. In this work, we show that these data can be used efficiently to further improve RLM performance. For this, we first use classic instruction tuning, supervised fine-tuning without reasoning traces, on the RLM. Next, we merge our instruction-tuned model with the original reasoning model, recovering its reasoning behavior on the target domain. Our extensive evaluation demonstrates that our technique improves RLM performance in both verifiable and hard-to-verify domains, including coding and text summarization, while preserving RLM capabilities across other domains. Importantly, our method is highly cost-effective, enabling such improvements for less than USD $3.

Hanna Yukhymenko, Anton Alexandrov, Martin Vechev

The reliability of multilingual Large Language Model (LLM) evaluation is currently compromised by the inconsistent quality of translated benchmarks. Existing resources often suffer from semantic drift and context loss, which can lead to misleading performance metrics. In this work, we present a fully automated framework designed to address these challenges by enabling scalable, high-quality translation of datasets and benchmarks. We demonstrate that adapting test-time compute scaling strategies, specifically Universal Self-Improvement (USI) and our proposed multi-round ranking method, T-RANK, allows for significantly higher quality outputs compared to traditional pipelines. Our framework ensures that benchmarks preserve their original task structure and linguistic nuances during localization. We apply this approach to translate popular benchmarks and datasets into eight Eastern and Southern European languages (Ukrainian, Bulgarian, Slovak, Romanian, Lithuanian, Estonian, Turkish, Greek). Evaluations using both reference-based metrics and LLM-as-a-judge show that our translations surpass existing resources, resulting in more accurate downstream model assessment. We release both the framework and the improved benchmarks to facilitate robust and reproducible multilingual AI development.

Jasper Dekoninck, Nikola Jovanović, Tim Gehrunger et al.

Large language models (LLMs) are becoming increasingly capable mathematical collaborators, but static benchmarks are no longer sufficient for evaluating progress: they are often narrow in scope, quickly saturated, and rarely updated. This makes it hard to compare models reliably and track progress over time. Instead, we need evaluation platforms: continuously maintained systems that run, aggregate, and analyze evaluations across many benchmarks to give a comprehensive picture of model performance within a broad domain. In this work, we build on the original MathArena benchmark by substantially broadening its scope from final-answer olympiad problems to a continuously maintained evaluation platform for mathematical reasoning with LLMs. MathArena now covers a much wider range of tasks, including proof-based competitions, research-level arXiv problems, and formal proof generation in Lean. Additionally, we maintain a clear evaluation protocol for all models and regularly design new benchmarks as model capabilities improve to ensure that MathArena remains challenging. Notably, the strongest model, GPT-5.5, now reaches 98% on the 2026 USA Math Olympiad and 74% on research-level questions, showing that frontier models can now comfortably solve extremely challenging mathematical problems. This highlights the importance of continuously maintained evaluation platforms like MathArena to track the rapid progress of LLMs in mathematical reasoning.

Ivo Petrov, Jasper Dekoninck, Dimitar I. Dimitrov et al.

Large language models (LLMs) have become capable mathematical problem-solvers, often producing correct proofs for challenging problems. However, correctness alone is not sufficient: mathematical proofs should also be clear, concise, insightful, and transferable to other problems. While this proof quality is subjective and depends on the reader and context, many of its components are concrete and broadly valued. In this work, we identify such components and introduce ProofRank, a benchmark curated from challenging mathematical competitions. ProofRank evaluates several scalable proxies of proof quality: (i) conciseness, measuring whether proofs avoid unnecessary steps; (ii) computational ease, measuring the extent to which a proof relies on tedious calculations; (iii) cognitive simplicity, measuring how accessible the used proof techniques are; (iv) diversity, measuring how varied a model's proofs for a single problem are; and (v) adaptivity, measuring whether a model can follow a specified proof technique. Across models, we find substantial differences in proof quality that are not captured by correctness-only benchmarks. We also observe significant trade-offs between proof-quality metrics and correctness, suggesting that future evaluations of mathematical reasoning should measure how useful LLM-generated proofs are.

Kazuki Egashira, Mark Vero, Jasper Dekoninck et al.

Reinforcement Learning with Verifiable Rewards (RLVR) has become a powerful approach for improving the reasoning capabilities of large language models (LLMs). While RLVR is designed for tasks with verifiable ground-truth answers, real-world verifiers (e.g., static code checkers) can introduce errors into the reward signal. Prior analyses have largely treated such errors as random and independent across samples, concluding that errors merely slow training with limited effect on final performance. However, practical verifiers tend to exhibit systematic errors. This introduces a risk of models learning unwanted consistent behavior from a structurally incorrect reward signal. In this work, we study the impact of such systematic verification errors on RLVR. Through controlled experiments on arithmetic tasks, we show that systematic false negatives lead to similar effects as random noise. On the other hand, systematic false positives can cause a wide range of behaviors from sub-optimal plateaus to performance collapse. Crucially, these outcomes are not determined by the overall error rate but by the specific pattern of introduced errors, making pre-hoc mitigation difficult. Our results show that, in contrast to prior conclusions, realistic verification errors can critically shape RLVR outcomes and that verifier quality has to be understood beyond its sample-level error rate.

Hanno Hiss, Jasper Dekoninck, Martin Vechev

The growing capabilities of large language models (LLMs) have led to the saturation of many benchmarks and training datasets used to improve them. Motivated by this, we investigate whether questions solved with perfect empirical accuracy can nevertheless be used to improve downstream performance. To do so, we replace binary correctness with two sources of more fine-grained quality signals: (1) pairwise LLM self-judgments, in which the model evaluates the relative quality of its own solutions, and (2) token-level entropy, where token-level uncertainty is used as a proxy for solution quality. We incorporate these signals into several training algorithms and evaluate them on Qwen3-1.7B-Base. When training exclusively on a simple arithmetic task, quality-based signals improve performance by up to $18.6\%$ over the base model, substantially outperforming SFT. On GSM8K, however, gains are more modest and depend strongly on the quality signal. For instance, self-judgments show poor agreement with a stronger external judge and can even degrade performance below the base model. Overall, our results suggest that quality-based training can extract useful signal from saturated questions for base models, but that applying such signals to more complex tasks requires careful calibration and further study.

Nikolay Georgiev, Maria Drencheva, Kseniia Ibragimova et al.

As agentic AI systems tackle more complex mathematical tasks, they increasingly rely on information retrieval (IR) to search problem databases, theorem libraries, and educational resources. However, choosing the right retriever remains difficult, as it is infeasible to directly isolate its effect on downstream performance. On the other hand, existing retrieval-specific benchmarks often fail to capture fine-grained mathematical relevance, penalizing relevant documents. We address this gap by introducing SABER-Math, the first fully automated benchmark for evaluating mathematical IR without expert annotation. Starting from 283K high-school-level math problems with solutions, SABER-Math builds challenging reranking tasks in three steps: (i) first, LLMs extract concise solution summaries and mathematical topics for each problem; (ii) then, per-query relevant documents are discovered using ontology topic-based and lexical solutions-summary-based similarities, and (iii) finally, a Swiss-style LLM preference tournament produces fine-grained relevance ratings for the documents. We evaluate lexical retrievers, specialized mathematical retrieval systems, and recent embedding models. We find that while modern embedding models substantially outperform classical and math-specific baselines, even the strongest systems struggle in symbol-heavy domains like Algebra and Calculus. Importantly, we show that general-purpose IR benchmarks such as MTEB do not reliably predict mathematical performance, especially for recent embedding models, highlighting the need for math-specific retrieval benchmarks.