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

arXiv: https://arxiv.org/abs/2504.01005 · HTML: https://mlsanity.com/paper/2504.01005/

## Key facts

- Cited by 42 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 31 of its 48 references that are in the map.
- First posted on arXiv 1 Apr 2025.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 30 of 31)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Large Language Diffusion Models](https://mlsanity.com/paper/2502.09992/) (2025)
- [Generative Verifiers: Reward Modeling as Next-Token Prediction](https://mlsanity.com/paper/2408.15240/) (2024)
- [Improve Mathematical Reasoning in Language Models by Automated Process Supervision](https://mlsanity.com/paper/2406.06592/) (2024)
- [Inference Scaling Laws: An Empirical Analysis of Compute-Optimal Inference for Problem-Solving with Language Models](https://mlsanity.com/paper/2408.00724/) (2024)
- [Think before you speak: Training Language Models With Pause Tokens](https://mlsanity.com/paper/2310.02226/) (2023)
- [V-STaR: Training Verifiers for Self-Taught Reasoners](https://mlsanity.com/paper/2402.06457/) (2024)
- [Universal Self-Consistency for Large Language Model Generation](https://mlsanity.com/paper/2311.17311/) (2023)
- [Free Process Rewards without Process Labels](https://mlsanity.com/paper/2412.01981/) (2024)
- [Generative Reward Models](https://mlsanity.com/paper/2410.12832/) (2024)
- [Critique-out-Loud Reward Models](https://mlsanity.com/paper/2408.11791/) (2024)
- [Easy-to-Hard Generalization: Scalable Alignment Beyond Human Supervision](https://mlsanity.com/paper/2403.09472/) (2024)
- [Scaling Test-Time Compute Without Verification or RL is Suboptimal](https://mlsanity.com/paper/2502.12118/) (2025)
- [TICKing All the Boxes: Generated Checklists Improve LLM Evaluation and Generation](https://mlsanity.com/paper/2410.03608/) (2024)
- [Smaller, Weaker, Yet Better: Training LLM Reasoners via Compute-Optimal Sampling](https://mlsanity.com/paper/2408.16737/) (2024)
- [Evolving Deeper LLM Thinking](https://mlsanity.com/paper/2501.09891/) (2025)
- [SETS: Leveraging Self-Verification and Self-Correction for Improved Test-Time Scaling](https://mlsanity.com/paper/2501.19306/) (2025)

## Built on by (most cited first, 30 of 42)

- [Process Reward Models That Think](https://mlsanity.com/paper/2504.16828/) (2025)
- [RewardAnything: Generalizable Principle-Following Reward Models](https://mlsanity.com/paper/2506.03637/) (2025)
- [Agentic Rubrics as Contextual Verifiers for SWE Agents](https://mlsanity.com/paper/2601.04171/) (2026)
- [Group Think: Multiple Concurrent Reasoning Agents Collaborating at Token Level Granularity](https://mlsanity.com/paper/2505.11107/) (2025)
- [Can Slow-thinking LLMs Reason Over Time? Empirical Studies in Time Series Forecasting](https://mlsanity.com/paper/2505.24511/) (2025)
- [Variation in Verification: Understanding Verification Dynamics in Large Language Models](https://mlsanity.com/paper/2509.17995/) (2025)
- [The Price of a Second Thought: On the Evaluation of Reasoning Efficiency in Large Language Models](https://mlsanity.com/paper/2505.22017/) (2025)
- [Generative AI Act II: Test Time Scaling Drives Cognition Engineering](https://mlsanity.com/paper/2504.13828/) (2025)
- [When Does Verification Pay Off? A Closer Look at LLMs as Solution Verifiers](https://mlsanity.com/paper/2512.02304/) (2025)
- [T1: Tool-integrated Verification for Test-time Compute Scaling in Small Language Models](https://mlsanity.com/paper/2504.04718/) (2025)
- [RLAC: Reinforcement Learning with Adversarial Critic for Free-Form Generation Tasks](https://mlsanity.com/paper/2511.01758/) (2025)
- [Falcon-H1R: Pushing the Reasoning Frontiers with a Hybrid Model for Efficient Test-Time Scaling](https://mlsanity.com/paper/2601.02346/) (2026)
- [RE-TRAC: REcursive TRAjectory Compression for Deep Search Agents](https://mlsanity.com/paper/2602.02486/) (2026)
- [Faster and Better LLMs via Latency-Aware Test-Time Scaling](https://mlsanity.com/paper/2505.19634/) (2025)
- [Solve-Detect-Verify: Inference-Time Scaling with Flexible Generative Verifier](https://mlsanity.com/paper/2505.11966/) (2025)
- [Enhancing Large Language Model Reasoning with Reward Models: An Analytical Survey](https://mlsanity.com/paper/2510.01925/) (2025)
- [MITS: Enhanced Tree Search Reasoning for LLMs via Pointwise Mutual Information](https://mlsanity.com/paper/2510.03632/) (2025)
- [AutoChemSchematic AI: Agentic Physics-Aware Automation for Chemical Manufacturing Scale-Up](https://mlsanity.com/paper/2505.24584/) (2025)
- [Rethinking Optimal Verification Granularity for Compute-Efficient Test-Time Scaling](https://mlsanity.com/paper/2505.11730/) (2025)
- [A Theory of Inference Compute Scaling: Reasoning through Directed Stochastic Skill Search](https://mlsanity.com/paper/2507.00004/) (2025)
- [CoT2-Meta: Budgeted Metacognitive Control for Test-Time Reasoning](https://mlsanity.com/paper/2603.28135/) (2026)
- [Falsification, Not Exposure: An Internally Preregistered Placebo-Controlled Decomposition of Self-Repair Feedback in Frozen Small Code Models](https://mlsanity.com/paper/2606.31511/) (2026)
- [On the Shelf Life of Fine-Tuned LLM-Judges: Future-Proofing, Backward-Compatibility, and Question Generalization](https://mlsanity.com/paper/2509.23542/) (2025)
- [Self-Reflective Generation at Test Time](https://mlsanity.com/paper/2510.02919/) (2025)
- [Think Twice, Act Once: Verifier-Guided Action Selection For Embodied Agents](https://mlsanity.com/paper/2605.12620/) (2026)
- [Locating Hidden Failures Makes Long-Horizon Agents More Reliable](https://mlsanity.com/paper/2609.17930/) (2026)
- [Budget-aware Test-time Scaling via Discriminative Verification](https://mlsanity.com/paper/2510.14913/) (2025)
- [ScalePRM: Training Process Reward Models by Scaling Verification Compute Without Ground Truth](https://mlsanity.com/paper/2512.03244/) (2025)
- [Oracle Gap and Signal Fidelity: A Fixed-Pool Diagnostic for Test-Time Collaboration](https://mlsanity.com/paper/2607.17531/) (2026)
- [Claim-Level Reliability Assessment for Efficient Test-Time Reasoning](https://mlsanity.com/paper/2608.11994/) (2026)

## Abstract (arXiv)

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.