Alireza Farhadi

Hamed Mahdavi, Pouria Mahdavinia, Alireza Farhadi et al.

State-of-the-art (SOTA) LLMs have progressed from struggling on proof-based Olympiad problems to solving most of the IMO 2025 problems, with leading systems reportedly handling 5 of 6 problems. Given this progress, we assess how well these models can grade proofs: detecting errors, judging their severity, and assigning fair scores beyond binary correctness. We study proof-analysis capabilities using a corpus of 90 Gemini 2.5 Pro-generated solutions that we grade on a 1-4 scale with detailed error annotations, and on MathArena solution sets for IMO/USAMO 2025 scored on a 0-7 scale. Our analysis shows that models can reliably flag incorrect (including subtly incorrect) solutions but exhibit calibration gaps in how partial credit is assigned. To address this, we introduce agentic workflows that extract and analyze reference solutions and automatically derive problem-specific rubrics for a multi-step grading process. We instantiate and compare different design choices for the grading workflows, and evaluate their trade-offs. Across our annotated corpus and MathArena, our proposed workflows achieve higher agreement with human grades and more consistent handling of partial credit across metrics. We release all code, data, and prompts/logs to facilitate future research.

Hamed Mahdavi, Alireza Hashemi, Majid Daliri et al.

Recent advances in large language models (LLMs) have shown impressive progress in mathematical reasoning tasks. However, current evaluation benchmarks predominantly focus on the accuracy of final answers, often overlooking the crucial logical rigor for mathematical problem solving. The claim that state-of-the-art LLMs can solve Math Olympiad-level problems requires closer examination. To explore this, we conducted both qualitative and quantitative human evaluations of proofs generated by LLMs, and developed a schema for automatically assessing their reasoning capabilities. Our study reveals that current LLMs fall significantly short of solving challenging Olympiad-level problems and frequently fail to distinguish correct mathematical reasoning from clearly flawed solutions. Our analyses demonstrate that the occasional correct final answers provided by LLMs often result from pattern recognition or heuristic shortcuts rather than genuine mathematical reasoning. These findings underscore the substantial gap between LLM performance and human expertise in advanced mathematical reasoning and highlight the importance of developing benchmarks that prioritize the soundness of the reasoning used to arrive at an answer rather than the mere correctness of the final answers.

Hamed Mahdavi, Pouria Mahdavinia, Samira Malek et al.

State-of-the-art (SOTA) LLMs have progressed from struggling on proof-based Olympiad problems to solving most of the IMO 2025 problems, with leading systems reportedly handling 5 of 6 problems. Given this progress, we assess how well these models can grade proofs: detecting errors, judging their severity, and assigning fair scores beyond binary correctness. We study proof-analysis capabilities using a corpus of 90 Gemini 2.5 Pro-generated solutions that we grade on a 1-4 scale with detailed error annotations, and on MathArena solution sets for IMO/USAMO 2025 scored on a 0-7 scale. Our analysis shows that models can reliably flag incorrect (including subtly incorrect) solutions but exhibit calibration gaps in how partial credit is assigned. To address this, we introduce agentic workflows that extract and analyze reference solutions and automatically derive problem-specific rubrics for a multi-step grading process. We instantiate and compare different design choices for the grading workflows, and evaluate their trade-offs. Across our annotated corpus and MathArena, our proposed workflows achieve higher agreement with human grades and more consistent handling of partial credit across metrics. We release all code, data, and prompts/logs to facilitate future research.

Alireza Farhadi, MohammadTaghi Hajiaghayi, Elaine Shi

Given a graph, the densest subgraph problem asks for a set of vertices such that the average degree among these vertices is maximized. Densest subgraph has numerous applications in learning, e.g., community detection in social networks, link spam detection, correlation mining, bioinformatics, and so on. Although there are efficient algorithms that output either exact or approximate solutions to the densest subgraph problem, existing algorithms may violate the privacy of the individuals in the network, e.g., leaking the existence/non-existence of edges. In this paper, we study the densest subgraph problem in the framework of the differential privacy, and we derive the first upper and lower bounds for this problem. We show that there exists a linear-time $ε$-differentially private algorithm that finds a $2$-approximation of the densest subgraph with an extra poly-logarithmic additive error. Our algorithm not only reports the approximate density of the densest subgraph, but also reports the vertices that form the dense subgraph. Our upper bound almost matches the famous $2$-approximation by Charikar both in performance and in approximation ratio, but we additionally achieve differential privacy. In comparison with Charikar's algorithm, our algorithm has an extra poly-logarithmic additive error. We partly justify the additive error with a new lower bound, showing that for any differentially private algorithm that provides a constant-factor approximation, a sub-logarithmic additive error is inherent. We also practically study our differentially private algorithm on real-world graphs, and we show that in practice the algorithm finds a solution which is very close to the optimal