When To Solve, When To Verify: Compute-Optimal Problem Solving and Generative Verification for LLM Reasoning

2025-04-01

AI Summary

This work investigates the optimal allocation of fixed computational budgets between solution generation and generative verification in large language models (LLMs). Focusing on Self-Consistency (SC) and Generative Reward Models (GenRM), we propose an inference-time scaling analysis framework. Our key contributions are threefold: (1) We establish, for the first time, that SC consistently outperforms GenRM under typical inference budgets; (2) We derive a formal scaling law for GenRM, proving that expanding the number of generated solutions yields greater marginal gains than increasing the number of verification chains; (3) Empirical evaluation across multiple models and datasets shows GenRM requires up to 8× more computation to match SC’s accuracy—results that are robust and reproducible. All code and empirically validated scaling laws are publicly released to support reproducible research.

Technology Category

• Natural Language Processing: Generation
• Machine Learning: Large Multimodal Models (LMMs)
• Planning, Routing, and Scheduling: Planning with Language Models

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation

Abstract

Scaling test-time compute has emerged as a key strategy for enhancing the reasoning capabilities of large language models (LLMs), particularly in tasks like mathematical problem-solving. A traditional approach, Self-Consistency (SC), generates multiple solutions to a problem and selects the most common answer via majority voting. Another common method involves scoring each solution with a reward model (verifier) and choosing the best one. Recent advancements in Generative Reward Models (GenRM) reframe verification as a next-token prediction task, enabling inference-time scaling along a new axis. Specifically, GenRM generates multiple verification chains-of-thought to score each solution. Under a limited inference budget, this introduces a fundamental trade-off: should you spend the budget on scaling solutions via SC or generate fewer solutions and allocate compute to verification via GenRM? To address this, we evaluate GenRM against SC under a fixed inference budget. Interestingly, we find that SC is more compute-efficient than GenRM for most practical inference budgets across diverse models and datasets. For instance, GenRM first matches SC after consuming up to 8x the inference compute and requires significantly more compute to outperform it. Furthermore, we derive inference scaling laws for the GenRM paradigm, revealing that compute-optimal inference favors scaling solution generation more aggressively than scaling the number of verifications. Our work provides practical guidance on optimizing test-time scaling by balancing solution generation and verification. The code is available at https://github.com/nishadsinghi/sc-genrm-scaling.

Problem

• Balancing compute between solution generation and verification in LLMs
• Comparing Self-Consistency and Generative Reward Models efficiency
• Optimizing test-time compute for enhanced LLM reasoning performance

Innovation

• Generative Reward Models for verification scaling
• Self-Consistency for compute-efficient solution generation
• Inference scaling laws balancing solutions and verifications