arxiv_ml 95% Match Research Paper AI Researchers,ML Engineers,LLM Developers,Researchers in AI Reasoning and Evaluation 4 days ago

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

large-language-models › reasoning

📄 Abstract

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.

Authors (2)

Md Tanvirul Alam

Nidhi Rastogi

Submitted

October 30, 2025

arXiv Category

cs.LG

arXiv PDF Code

Key Contributions

This study investigates the generalization limits of RLVR for LLM mathematical reasoning using two combinatorial problems. It finds that RLVR often improves metrics by reinforcing superficial heuristics rather than acquiring new reasoning strategies, highlighting the limits of generalization and the need for benchmarks that measure genuine reasoning.

Business Value

Ensuring that AI models truly reason rather than rely on superficial patterns is critical for building reliable and trustworthy AI systems, especially in high-stakes domains like mathematics and science.

Paper Metadata

Innovation Type

Analytical/Evaluative

Deployment Feasibility

High. Focuses on evaluating and improving LLM training methodologies, applicable to current and future models.

Limitations Addressed

Uncertainty about RLVR's ability to foster genuine reasoning,LLMs exploiting shortcuts rather than learning underlying principles,Lack of benchmarks that disentangle reasoning from heuristic exploitation

Performance Gains

Identifies specific failure modes of RLVR in generalization.,Provides evidence that metric improvements may not reflect true reasoning gains.

View Code on GitHub

Technical Tags

LLM GeneralizationReinforcement Learning with Verifiable Rewards (RLVR)Mathematical ReasoningCombinatorial ProblemsActivity SchedulingLongest Increasing SubsequenceSuperficial HeuristicsShortcut ExploitationPass@kVerifiable Solutions

Research Topics

LLM ReasoningGeneralization in AIReinforcement LearningAI EvaluationMathematical Problem Solving

Methods & Architectures

Reinforcement Learning with Verifiable Rewards (RLVR)Analysis of Generalization LimitsCombinatorial Problem SolvingPass@k EvaluationReward Design Analysis Large Language Models (LLMs)

Applications & Tasks

AI Model Development Mathematical Reasoning Algorithm Design Evaluating LLM Reasoning StrategiesUnderstanding Generalization LimitsPreventing Shortcut Learning Assessing RLVR's ability to learn genuine reasoningIdentifying limitations in LLM generalizationDeveloping benchmarks that distinguish reasoning from heuristics

Datasets & Benchmarks

Datasets

Activity Scheduling dataset, Longest Increasing Subsequence dataset

Benchmarks

pass@k evaluations

pass@kAnalysis of learned strategies (heuristics vs. reasoning)

Related Fields

Large Language ModelsReinforcement LearningArtificial IntelligenceMachine LearningReasoningEvaluationCombinatorics

Keywords

LLMReasoningRLVRGeneralizationMathematical ReasoningCombinatoricsHeuristicsAI EvaluationReinforcement LearningPass@kShortcut Learning

Academic Context

#LLM Reasoning#Generalization in AI#Reinforcement Learning#AI Evaluation#Mathematical Problem Solving

Commercial Potential

Potential Products

More robust and generalizable LLMs for reasoningImproved evaluation methodologies for AI reasoning

Target Industries

TechnologyAI ResearchSoftware DevelopmentEducation

Use Case Examples

Developing LLMs that can solve novel mathematical problems without relying on memorized patternsCreating evaluation suites that accurately measure true reasoning capabilities

Competitive Edge

Provides critical insights into the limitations of current RL techniques for LLM reasoning, guiding future research towards more robust and generalizable solutions.

Market Opportunity

The market for advanced AI reasoning capabilities is substantial.

Revenue Models

Improved AI models leading to better products and services.

Resource Requirements

Compute Needs

High, for training and evaluating LLMs on complex reasoning tasks.

Data Requirements

Carefully curated datasets for combinatorial problems, potentially synthetic data generation.

Deployment Constraints

Computational cost of extensive evaluation,Difficulty in designing truly disentangled benchmarks

Scalability

Scalability is tied to the underlying LLM training and evaluation infrastructure.

Production Readiness

Maturity Level

Research

Time to Market

Ongoing research, findings inform future LLM development and evaluation.

Patent Potential

Low, primarily analytical and methodological.

View Full Paper Back to Papers