Philipp Mondorf
Publications
AIMO Interpretability Challenge
We propose the AIMO Interpretability Challenge, a competition on distinguishing robust from spurious reasoning in frontier mathematical language models based on the models' internal mechanisms. The challenge is motivated by a central limitation of standard reasoning benchmarks: strong final-answer accuracy does not reveal whether a model relies on stable reasoning mechanisms or exploits brittle reasoning shortcuts. Building on AI Mathematical Olympiad (AIMO) problems and submissions, together with resources from the Fields Model Initiative, the competition will provide (1) newly-published olympiad-level math reasoning problems and their symbolic representations, allowing generation of novel functional variants, (2) access to frontier reasoning models, and (3) assessments of models' adversarial robustness on these problems. Participants will use these resources, along with our computing infrastructure support, to develop methods for identifying which models solve problems robustly. Our competition will also create a new, open robustness benchmark and baseline systems, aiming to provide a lasting foundation for standard benchmarking in mathematical reasoning and interpretability. Scientifically, the competition connects interpretability and generalization research around a central question in AI research: can we determine if, and to what extent, the decision-making of frontier AI models is generalizable and thus, reliable?
Tracing Uncertainty in Language Model "Reasoning"
Language model (LM) "reasoning", commonly described as Chain-of-Thought or test-time scaling, often improves benchmark performance, but the dynamics underlying this process remain poorly understood. We study these dynamics through the lens of uncertainty quantification by treating the "reasoning" traces, the intermediate token sequences generated by LMs, as evolving model states. We summarize each trace by an uncertainty trace profile: a small set of features describing the shape of the uncertainty signal over its trace, such as its slope and linearity. We find that across five LMs evaluated on GSM8K and ProntoQA, these profiles predict whether a trace yields a correct final answer with AUROC up to 0.807, improving markedly on recent related work. We reach AUROC 0.801 using only the first few hundred tokens of full traces, suggesting that errors can be detected early in the generation. A detailed comparison of correct and incorrect traces further reveals qualitatively distinct uncertainty profiles, with correct traces showing a steeper and less linear decline in uncertainty. Together, the results suggest that our method, grounded in decision-making under uncertainty, provides a principled lens for studying the generative process underlying LM "reasoning".
LogicSkills: A Structured Benchmark for Formal Reasoning in Large Language Models
Large language models have demonstrated notable performance across various logical reasoning benchmarks. However, it remains unclear which core logical skills they truly master. To address this, we introduce LogicSkills, a unified benchmark designed to isolate three fundamental skills in formal reasoning: (i) $\textit{formal symbolization}\unicode{x2014}$translating premises into first-order logic; (ii) $\textit{countermodel construction}\unicode{x2014}$formulating a finite structure in which all premises are true while the conclusion is false; and (iii) $\textit{validity assessment}\unicode{x2014}$deciding whether a conclusion follows from a given set of premises. Items are drawn from the two-variable fragment of first-order logic (without identity) and are presented in both natural English and a Carroll-style language with nonce words. All examples are verified for correctness and non-triviality using the SMT solver Z3. Across leading models, performance is high on validity but substantially lower on symbolization and countermodel construction, suggesting reliance on surface-level patterns rather than genuine symbolic or rule-based reasoning.