Maria Drencheva

Ivo Petrov, Jasper Dekoninck, Lyuben Baltadzhiev et al.

Recent math benchmarks for large language models (LLMs) such as MathArena indicate that state-of-the-art reasoning models achieve impressive performance on mathematical competitions like AIME, with the leading model, Gemini-2.5-Pro, achieving scores comparable to top human competitors. However, these benchmarks evaluate models solely based on final numerical answers, neglecting rigorous reasoning and proof generation which are essential for real-world mathematical tasks. To address this, we introduce a comprehensive evaluation of full-solution reasoning for challenging mathematical problems. Using expert human annotators, we evaluated several state-of-the-art reasoning models on the six problems from the 2025 USAMO within hours of their release. Our results reveal that all tested models struggled significantly: only Gemini-2.5-Pro achieves a non-trivial score of 25%, while all other models achieve less than 5%. Through detailed analysis of reasoning traces, we identify the most common failure modes and find several unwanted artifacts arising from the optimization strategies employed during model training. Overall, our results suggest that current LLMs are inadequate for rigorous mathematical reasoning tasks, highlighting the need for substantial improvements in reasoning and proof generation capabilities.

Jasper Dekoninck, Ivo Petrov, Kristian Minchev et al.

In recent months, large language models (LLMs) have made significant progress in mathematical proof generation, but further advancement is hindered by the lack of a large-scale, high-quality dataset of human-evaluated proofs. While expensive to create, such a dataset is essential for driving improvements in training and enabling a rigorous analysis of proof generation capabilities. In this work, we present the Open Proof Corpus (OPC), a dataset comprising over 5,000 human-evaluated proofs produced by state-of-the-art LLMs. The OPC was specifically designed for broad applicability and downstream usage in proof generation research and is the first to include a substantial number of correct, LLM-generated solutions to problems from prestigious mathematics competitions such as the USAMO and IMO. Using the OPC, we explore critical questions in automated proof generation: (1) the performance gap between natural language and formal proof generation, (2) the discrepancy between final-answer accuracy and full-proof validity, and (3) the impact of best-of-n selection on proof quality. Finally, to showcase the utility of the OPC, we finetune an 8B-parameter model on the dataset, obtaining a model that performs on par with the best model, Gemini-2.5-Pro, on the task of evaluating proof correctness.

Maria Drencheva, Ivo Petrov, Maximilian Baader et al.

Federated learning claims to enable collaborative model training among multiple clients with data privacy by transmitting gradient updates instead of the actual client data. However, recent studies have shown the client privacy is still at risk due to the, so called, gradient inversion attacks which can precisely reconstruct clients' text and image data from the shared gradient updates. While these attacks demonstrate severe privacy risks for certain domains and architectures, the vulnerability of other commonly-used data types, such as graph-structured data, remain under-explored. To bridge this gap, we present GRAIN, the first exact gradient inversion attack on graph data in the honest-but-curious setting that recovers both the structure of the graph and the associated node features. Concretely, we focus on Graph Convolutional Networks (GCN) and Graph Attention Networks (GAT) -- two of the most widely used frameworks for learning on graphs. Our method first utilizes the low-rank structure of GNN gradients to efficiently reconstruct and filter the client subgraphs which are then joined to complete the input graph. We evaluate our approach on molecular, citation, and social network datasets using our novel metric. We show that GRAIN reconstructs up to 80% of all graphs exactly, significantly outperforming the baseline, which achieves up to 20% correctly positioned nodes.