ReNCE: Learning to Reason by Noise Contrastive Estimation

TL;DR

ReNCE reframes LLM reasoning post-training as an explicit multi-label noise-contrastive objective, replacing advantage estimation with contrast between positives and hard negatives drawn from the model’s own rollouts. By dynamically filtering prompts, partitioning trajectories, and applying a log-ratio based score with a reward-aware margin under a trust region, ReNCE achieves strong performance across six challenging math benchmarks. The study shows that multi-label NCE with a reward-scaled margin and on-policy updates outperforms GRPO, DAPO, and online DPO, highlighting the practical benefits of explicit contrastive learning for reasoning tasks. The approach offers a scalable, on-policy alternative to reward-based policy gradients with robust ablations validating its key design choices.

Abstract

GRPO is a standard approach to endowing pretrained LLMs with reasoning capabilities. It estimates the advantage of an outcome from a group of $K$ outcomes, and promotes those with positive advantages inside a trust region. Since GRPO discriminates between good and bad outcomes softly, it benefits from additional refinements such as asymmetric clipping and zero-variance data filtering. While effective, these refinements require significant empirical insight and can be challenging to identify. We instead propose an explicit contrastive learning approach. Instead of estimating advantages, we bifurcate $K$ outcomes into positive and negative sets, then maximize the likelihood of positive outcomes. Our approach can be viewed as an online instantiation of (multi-label) noise contrastive estimation for LLM reasoning. We validate our method by demonstrating competitive performance on a suite of challenging math benchmarks against strong baselines such as DAPO and online DPO.