# Scaling Test-Time Compute Without Verification or RL is Suboptimal

arXiv: https://arxiv.org/abs/2502.12118 · HTML: https://mlsanity.com/paper/2502.12118/

## Key facts

- Cited by 84 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 50 of its 77 references that are in the map.
- First posted on arXiv 17 Feb 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 50)

- [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)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [SFT Memorizes, RL Generalizes: A Comparative Study of Foundation Model Post-training](https://mlsanity.com/paper/2501.17161/) (2025)
- [DeepSeek LLM: Scaling Open-Source Language Models with Longtermism](https://mlsanity.com/paper/2401.02954/) (2024)
- [Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMs](https://mlsanity.com/paper/2412.21187/) (2024)
- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [LIMO: Less is More for Reasoning](https://mlsanity.com/paper/2502.03387/) (2025)
- [Generative Verifiers: Reward Modeling as Next-Token Prediction](https://mlsanity.com/paper/2408.15240/) (2024)
- [Training Language Models to Self-Correct via Reinforcement Learning](https://mlsanity.com/paper/2409.12917/) (2024)
- [Beyond Human Data: Scaling Self-Training for Problem-Solving with Language Models](https://mlsanity.com/paper/2312.06585/) (2023)
- [Inference Scaling Laws: An Empirical Analysis of Compute-Optimal Inference for Problem-Solving with Language Models](https://mlsanity.com/paper/2408.00724/) (2024)
- [Bridging Offline Reinforcement Learning and Imitation Learning: A Tale of Pessimism](https://mlsanity.com/paper/2103.12021/) (2021)
- [Rewarding Progress: Scaling Automated Process Verifiers for LLM Reasoning](https://mlsanity.com/paper/2410.08146/) (2024)
- [Training Language Models to Reason Efficiently](https://mlsanity.com/paper/2502.04463/) (2025)
- [Monte Carlo Tree Search Boosts Reasoning via Iterative Preference Learning](https://mlsanity.com/paper/2405.00451/) (2024)
- [V-STaR: Training Verifiers for Self-Taught Reasoners](https://mlsanity.com/paper/2402.06457/) (2024)
- [Will we run out of data? Limits of LLM scaling based on human-generated data](https://mlsanity.com/paper/2211.04325/) (2022)
- [VinePPO: Refining Credit Assignment in RL Training of LLMs](https://mlsanity.com/paper/2410.01679/) (2024)
- [Recursive Introspection: Teaching Language Model Agents How to Self-Improve](https://mlsanity.com/paper/2407.18219/) (2024)
- [Free Process Rewards without Process Labels](https://mlsanity.com/paper/2412.01981/) (2024)
- [Beyond Chinchilla-Optimal: Accounting for Inference in Language Model Scaling Laws](https://mlsanity.com/paper/2401.00448/) (2023)
- [Generative Reward Models](https://mlsanity.com/paper/2410.12832/) (2024)

## Built on by (most cited first, 30 of 84)

- [Why Do Multi-Agent LLM Systems Fail?](https://mlsanity.com/paper/2503.13657/) (2025)
- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [ReasoningBank: Scaling Agent Self-Evolving with Reasoning Memory](https://mlsanity.com/paper/2509.25140/) (2025)
- [Learning to Reason under Off-Policy Guidance](https://mlsanity.com/paper/2504.14945/) (2025)
- [The Unreasonable Effectiveness of Entropy Minimization in LLM Reasoning](https://mlsanity.com/paper/2505.15134/) (2025)
- [The Surprising Effectiveness of Negative Reinforcement in LLM Reasoning](https://mlsanity.com/paper/2506.01347/) (2025)
- [Advances and Challenges in Foundation Agents: From Brain-Inspired Intelligence to Evolutionary, Collaborative, and Safe Systems](https://mlsanity.com/paper/2504.01990/) (2025)
- [OpenVLThinker: Complex Vision-Language Reasoning via Iterative SFT-RL Cycles](https://mlsanity.com/paper/2503.17352/) (2025)
- [Optimizing Test-Time Compute via Meta Reinforcement Fine-Tuning](https://mlsanity.com/paper/2503.07572/) (2025)
- [OpenCodeReasoning: Advancing Data Distillation for Competitive Coding](https://mlsanity.com/paper/2504.01943/) (2025)
- [Inducing Programmatic Skills for Agentic Tasks](https://mlsanity.com/paper/2504.06821/) (2025)
- [Big-Math: A Large-Scale, High-Quality Math Dataset for Reinforcement Learning in Language Models](https://mlsanity.com/paper/2502.17387/) (2025)
- [All Roads Lead to Likelihood: The Value of Reinforcement Learning in Fine-Tuning](https://mlsanity.com/paper/2503.01067/) (2025)
- [e3: Learning to Explore Enables Extrapolation of Test-Time Compute for LLMs](https://mlsanity.com/paper/2506.09026/) (2025)
- [Does Thinking More always Help? Mirage of Test-Time Scaling in Reasoning Models](https://mlsanity.com/paper/2506.04210/) (2025)
- [Reinforcement Learning Finetunes Small Subnetworks in Large Language Models](https://mlsanity.com/paper/2505.11711/) (2025)
- [When To Solve, When To Verify: Compute-Optimal Problem Solving and Generative Verification for LLM Reasoning](https://mlsanity.com/paper/2504.01005/) (2025)
- [RaC: Robot Learning for Long-Horizon Tasks by Scaling Recovery and Correction](https://mlsanity.com/paper/2509.07953/) (2025)
- [Harnessing the Reasoning Economy: A Survey of Efficient Reasoning for Large Language Models](https://mlsanity.com/paper/2503.24377/) (2025)
- [Thinking vs. Doing: Agents that Reason by Scaling Test-Time Interaction](https://mlsanity.com/paper/2506.07976/) (2025)
- [Visual Document Understanding and Reasoning: A Multi-Agent Collaboration Framework with Agent-Wise Adaptive Test-Time Scaling](https://mlsanity.com/paper/2508.03404/) (2025)
- [OpenCodeReasoning-II: A Simple Test Time Scaling Approach via Self-Critique](https://mlsanity.com/paper/2507.09075/) (2025)
- [Differential Smoothing Mitigates Sharpening and Improves LLM Reasoning](https://mlsanity.com/paper/2511.19942/) (2025)
- [Latent Thinking Optimization: Your Latent Reasoning Language Model Secretly Encodes Reward Signals in Its Latent Thoughts](https://mlsanity.com/paper/2509.26314/) (2025)
- [LoVeC: Reinforcement Learning for Better Verbalized Confidence in Long-Form Generations](https://mlsanity.com/paper/2505.23912/) (2025)
- [Reuse your FLOPs: Scaling RL on Hard Problems by Conditioning on Very Off-Policy Prefixes](https://mlsanity.com/paper/2601.18795/) (2026)
- [Generative AI Act II: Test Time Scaling Drives Cognition Engineering](https://mlsanity.com/paper/2504.13828/) (2025)
- [Every Rollout Counts: Optimal Resource Allocation for Efficient Test-Time Scaling](https://mlsanity.com/paper/2506.15707/) (2025)
- [Putting the Value Back in RL: Better Test-Time Scaling by Unifying LLM Reasoners With Verifiers](https://mlsanity.com/paper/2505.04842/) (2025)
- [Making Small Language Models Efficient Reasoners: Intervention, Supervision, Reinforcement](https://mlsanity.com/paper/2505.07961/) (2025)

## Abstract (arXiv)

Despite substantial advances in scaling test-time compute, an ongoing debate in the community is how it should be scaled up to enable continued and efficient improvements with scaling. There are largely two approaches: first, distilling successful search or thinking traces; and second, using verification (e.g., 0/1 outcome rewards, reward models, or verifiers) to guide reinforcement learning (RL) and search algorithms. In this paper, we prove that finetuning LLMs with verifier-based (VB) methods based on RL or search is far superior to verifier-free (VF) approaches based on distilling or cloning search traces, given a fixed amount of compute/data budget. Further, we show that as we scale test-time compute (measured as the output token length) and training data, suboptimality of VF methods scales poorly compared to VB when the base pre-trained LLM presents a heterogeneous distribution over correct solution traces (e.g., different lengths, styles, etc.) and admits a non-sharp distribution over rewards on traces sampled from it. We formalize this condition using anti-concentration [ErdHos, 1945]. This implies a stronger result that VB methods scale better asymptotically, with the performance gap between VB and VF methods widening as test-time budget grows. We corroborate our theory empirically on both didactic and math reasoning problems with 3/8/32B-sized pre-trained LLMs, where we find verification is crucial for scaling test-time compute.