This project investigates scaling test-time compute through a Generative Verifier (GV) on the Countdown mathematical reasoning task using a computationally constrained 0.5B parameter regime, hypothesizing that the “verification gap” will widen at higher values of N due to the model’s limited semantic capacity.
This project explores the Countdown arithmetic reasoning task: given a set of numbers, produce an arithmetic expression that evaluates to a target value on the Qwen 2.5-0.5B base model and proposes two complementary extensions targeting these failure modes.
Reinforcement learning with verifiable rewards (RLVR) has been effective on tasks with structured solutions like math and coding, but its reliance on simple, rule-based verifiers creates a fundamental bottleneck. We find their applicability is surprisingly narrow even in structured domains, a limitation that is compounded at scale: rule-based systems can paradoxically degrade in performance as multi-domain, free-form training data increases. To overcome these challenges, we propose a new RLVR framework that uses a generative verifier to provide soft, probabilistic rewards. Our key insight is that powerful LLMs show high agreement with human evaluators when judging answer correctness given a ground-truth reference, allowing us to automate reward generation without costly human annotation. Our experiments demonstrate the effectiveness of this approach. We show that a compact 7B generative reward model can guide a 7B policy model to decisively outperform models up to 10x its size, including the 72B Qwen2.5-Instruct (by a margin of +8.6%). This effectiveness is robust, holding true across diverse training datasets with answers sourced from experts, web users, and other LLMs, and generalizes strongly to seven out-of-distribution benchmarks. Our work provides a scalable and effective framework for extending RLVR beyond the limitations of pattern-based verification to complex, noisy, real-world domains.
Yi Su, Dian Yu, Linfeng Song et al.· Annual Meeting of the Associ...· 1 citation
This paper introduces C LUE (Clustering and Experience-based Verification) , a training-free, non-parametric verifier that improves selection and reranking in Large Language Model outputs and finds that correct and incorrect solutions exhibit measurable geometric differences in their hidden-state trajectories.
Zhenwen Liang, Ruosen Li, Yujun Zhou et al.· Annual Meeting of the Associ...· 0 citations
Reinforcement learning (RL) has become a central post-training paradigm for eliciting reasoning capabilities in large language models, yet uniform task sampling allocates compute without regard to differences in how tasks respond to optimization. Existing task-valuation methods mostly rely on snapshot-based signals such as current pass rate or reward, which estimate how solvable a task is under the current policy. However, tasks with similar current solvability can still differ substantially in how positively they respond to further training. We study this residual axis as task learnability: a regime-conditional measure of expected positive response to continued training under a fixed RL post-training regime. By analyzing per-task reward trajectories, we find that learnability is reproducible across independently sampled training contexts and predictive of downstream utility. To make this signal practical before training begins, we propose TrajVal, a lightweight probe-based estimator that approximates per-task learnability from a short probe run and two endpoint evaluations. TrajVal can be used either as a standalone static prior for task sampling or as a multiplicative prior for existing online schedulers. Experiments on mathematical and logical reasoning benchmarks across multiple model scales show that TrajVal improves data efficiency over uniform sampling and provides complementary gains when combined with online scheduling methods.
Ting Zhou, Zhenqing Ling, Daoyuan Chen et al.· 0 citations
This work establishes the first non-vacuous generalization bounds for parameter-efficient RLVR fine-tuning at the billion-parameter scale, and proposes the Progressive RLVR framework, which integrates RLVR with on-policy distillation, TinyLoRA, and model quantization.