Simon Park

Vedant Shah, Dingli Yu, Kaifeng Lyu et al. · mila, tsinghua

Current LLM training positions mathematical reasoning as a core capability. With publicly available sources fully tapped, there is unmet demand for diverse and challenging math questions. Relying solely on human experts is both time-consuming and costly, while LLM-generated questions often lack the requisite diversity and difficulty. We present a design framework that combines the strengths of LLMs with a human-in-the-loop approach to generate a diverse array of challenging math questions. We leverage LLM metacognition skills [Didolkar et al., 2024] of a strong LLM to extract core "skills" from existing math datasets. These skills serve as the basis for generating novel and difficult questions by prompting the LLM with random pairs of core skills. The use of two different skills within each question makes finding such questions an "out of distribution" task for both LLMs and humans. Our pipeline employs LLMs to iteratively generate and refine questions and solutions through multiturn prompting. Human annotators then verify and further refine the questions, with their efficiency enhanced via further LLM interactions. Applying this pipeline on skills extracted from the MATH dataset [Hendrycks et al., 2021] resulted in MATH$^2$ - a dataset of higher-quality math questions, as evidenced by: (a) Lower performance of all models on MATH$^2$ than on MATH (b) Higher performance on MATH when using MATH$^2$ questions as in-context examples. Although focused on mathematics, our methodology seems applicable to other domains requiring structured reasoning, and potentially as a component of scalable oversight. Also of interest is a striking relationship observed between models' performance on the new dataset: the success rate on MATH$^2$ is the square on MATH, suggesting that successfully solving the question in MATH$^2$ requires a nontrivial combination of two distinct math skills.

Simon Park, Abhishek Panigrahi, Yun Cheng et al. · princeton

Vision Language Models (VLMs) are impressive at visual question answering and image captioning. But they underperform on multi-step visual reasoning -- even compared to LLMs on the same tasks presented in text form -- giving rise to perceptions of modality imbalance or brittleness. Towards a systematic study of such issues, we introduce a synthetic framework for assessing the ability of VLMs to perform algorithmic visual reasoning, comprising three tasks: Table Readout, Grid Navigation, and Visual Analogy. Each has two levels of difficulty, SIMPLE and HARD, and even the SIMPLE versions are difficult for frontier VLMs. We propose strategies for training on the SIMPLE version of tasks that improve performance on the corresponding HARD task, i.e., simple-to-hard (S2H) generalization. This controlled setup, where each task also has an equivalent text-only version, allows a quantification of the modality imbalance and how it is impacted by training strategy. We show that 1) explicit image-to-text conversion is important in promoting S2H generalization on images, by transferring reasoning from text; 2) conversion can be internalized at test time. We also report results of mechanistic study of this phenomenon. We identify measures of gradient alignment that can identify training strategies that promote better S2H generalization. Ablations highlight the importance of chain-of-thought.