S. Welleck
Famous AuthorPublications
Reasoning over mathematical objects: on-policy reward modeling and test time aggregation
The ability to precisely derive mathematical objects is a core requirement for downstream STEM applications, including mathematics, physics, and chemistry, where reasoning must culminate in formally structured expressions. Yet, current LM evaluations of mathematical and scientific reasoning rely heavily on simplified answer formats such as numerical values or multiple choice options due to the convenience of automated assessment. In this paper we provide three contributions for improving reasoning over mathematical objects: (i) we build and release training data and benchmarks for deriving mathematical objects, the Principia suite; (ii) we provide training recipes with strong LLM-judges and verifiers, where we show that on-policy judge training boosts performance; (iii) we show how on-policy training can also be used to scale test-time compute via aggregation. We find that strong LMs such as Qwen3-235B and o3 struggle on Principia, while our training recipes can bring significant improvements over different LLM backbones, while simultaneously improving results on existing numerical and MCQA tasks, demonstrating cross-format generalization of reasoning abilities.
GradAlign: Gradient-Aligned Data Selection for LLM Reinforcement Learning
Reinforcement learning (RL) has become a central post-training paradigm for large language models (LLMs), but its performance is highly sensitive to the quality of training problems. This sensitivity stems from the non-stationarity of RL: rollouts are generated by an evolving policy, and learning is shaped by exploration and reward feedback, unlike supervised fine-tuning (SFT) with fixed trajectories. As a result, prior work often relies on manual curation or simple heuristic filters (e.g., accuracy), which can admit incorrect or low-utility problems. We propose GradAlign, a gradient-aligned data selection method for LLM reinforcement learning that uses a small, trusted validation set to prioritize training problems whose policy gradients align with validation gradients, yielding an adaptive curriculum. We evaluate GradAlign across three challenging data regimes: unreliable reward signals, distribution imbalance, and low-utility training corpus, showing that GradAlign consistently outperforms existing baselines, underscoring the importance of directional gradient signals in navigating non-stationary policy optimization and yielding more stable training and improved final performance. We release our implementation at https://github.com/StigLidu/GradAlign