Limits of Generalization in RLVR: Two Case Studies in Mathematical Reasoning

2025-10-30

AI Summary

This work investigates whether Reinforcement Learning with Verifiable Rewards (RLVR) genuinely enhances large language models’ mathematical reasoning capabilities—or merely optimizes superficial metrics. Method: We construct combinatorial optimization benchmarks (e.g., activity scheduling, longest increasing subsequence) with unique optimal solutions to rigorously distinguish genuine reasoning from heuristic shortcuts. Using fully verifiable mathematical tasks, we systematically design multiple reward types and conduct RLVR training and ablation analysis. Contribution/Results: Although RLVR substantially improves evaluation scores, it fails to induce novel reasoning strategies; instead, it reinforces reliance on task-specific surface patterns. This study introduces the first reasoning-capability discrimination framework grounded in uniqueness of optimal solutions, exposing a fundamental limitation in RLVR’s generalization to complex reasoning tasks. Our benchmark and methodology provide a more rigorous foundation for trustworthy evaluation of mathematical reasoning in foundation models.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Metareasoning and Metaheuristics

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

Abstract

Mathematical reasoning is a central challenge for large language models (LLMs), requiring not only correct answers but also faithful reasoning processes. Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a promising approach for enhancing such capabilities; however, its ability to foster genuine reasoning remains unclear. We investigate RLVR on two combinatorial problems with fully verifiable solutions: emph{Activity Scheduling} and the emph{Longest Increasing Subsequence}, using carefully curated datasets with unique optima. Across multiple reward designs, we find that RLVR improves evaluation metrics but often by reinforcing superficial heuristics rather than acquiring new reasoning strategies. These findings highlight the limits of RLVR generalization, emphasizing the importance of benchmarks that disentangle genuine mathematical reasoning from shortcut exploitation and provide faithful measures of progress. Code available at https://github.com/xashru/rlvr-seq-generalization.

Problem

• Investigating RLVR's generalization limits in mathematical reasoning tasks
• Assessing whether RLVR fosters genuine reasoning versus superficial heuristics
• Developing benchmarks to distinguish true reasoning from shortcut exploitation

Innovation

• RLVR improves metrics via superficial heuristics
• Benchmarks needed to separate reasoning from shortcuts
• Case studies on Activity Scheduling and LIS problems