# How Much Can Language Models Gain from Test-Time Computation?

arXiv: https://arxiv.org/abs/2610.01110 · HTML: https://mlsanity.com/paper/2610.01110/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 49 of its 66 references that are in the map.
- First posted on arXiv 1 Oct 2026.

## Builds on (most cited first, 30 of 49)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Teaching Large Language Models to Self-Debug](https://mlsanity.com/paper/2304.05128/) (2023)
- [FrugalGPT: How to Use Large Language Models While Reducing Cost and Improving Performance](https://mlsanity.com/paper/2305.05176/) (2023)
- [CRITIC: Large Language Models Can Self-Correct with Tool-Interactive Critiquing](https://mlsanity.com/paper/2305.11738/) (2023)
- [RouteLLM: Learning to Route LLMs with Preference Data](https://mlsanity.com/paper/2406.18665/) (2024)
- [Terminal-Bench: Benchmarking Agents on Hard, Realistic Tasks in Command Line Interfaces](https://mlsanity.com/paper/2601.11868/) (2026)
- [Generative Verifiers: Reward Modeling as Next-Token Prediction](https://mlsanity.com/paper/2408.15240/) (2024)
- [AppWorld: A Controllable World of Apps and People for Benchmarking Interactive Coding Agents](https://mlsanity.com/paper/2407.18901/) (2024)
- [CodeT: Code Generation with Generated Tests](https://mlsanity.com/paper/2207.10397/) (2022)
- [Hybrid LLM: Cost-Efficient and Quality-Aware Query Routing](https://mlsanity.com/paper/2404.14618/) (2024)
- [MathArena: Evaluating LLMs on Uncontaminated Math Competitions](https://mlsanity.com/paper/2505.23281/) (2025)
- [Inference Scaling Laws: An Empirical Analysis of Compute-Optimal Inference for Problem-Solving with Language Models](https://mlsanity.com/paper/2408.00724/) (2024)
- [Omni-MATH: A Universal Olympiad Level Mathematic Benchmark For Large Language Models](https://mlsanity.com/paper/2410.07985/) (2024)
- [Token-Budget-Aware LLM Reasoning](https://mlsanity.com/paper/2412.18547/) (2024)
- [When Can LLMs Actually Correct Their Own Mistakes? A Critical Survey of Self-Correction of LLMs](https://mlsanity.com/paper/2406.01297/) (2024)
- [AI Agents That Matter](https://mlsanity.com/paper/2407.01502/) (2024)
- [Universal Self-Consistency for Large Language Model Generation](https://mlsanity.com/paper/2311.17311/) (2023)
- [Beyond Chinchilla-Optimal: Accounting for Inference in Language Model Scaling Laws](https://mlsanity.com/paper/2401.00448/) (2023)
- [Large Language Model Cascades with Mixture of Thoughts Representations for Cost-efficient Reasoning](https://mlsanity.com/paper/2310.03094/) (2023)
- [On the Self-Verification Limitations of Large Language Models on Reasoning and Planning Tasks](https://mlsanity.com/paper/2402.08115/) (2024)

## Abstract (arXiv)

How much can test-time computation improve a language model, and at what cost? Test-time scaling is widely proposed as a substitute for larger models, but existing comparisons mostly evaluate one domain at a time and rarely charge selection to the budget. We introduce SELF-POT, a benchmark and evaluation framework that measures the test-time potential of a model across competition mathematics, competitive programming, and agentic workflows. SELF-POT separates candidate coverage from final accuracy on static tasks, tracks correctness transitions under revision, and measures protocol completion alongside task success in agentic environments. Under a unified budget rule, it compares Direct inference with parallel sampling and self-revision under fixed multiples of the Direct budget, and charges every model call, including selection and critique, in dollars. This design supports two kinds of comparison: the gain a model obtains from additional inference, and a lower-cost model with additional inference against a stronger model. Across five low-cost reasoning models on 350 sealed tasks, with Claude Opus 5.5 Direct as the reference, the returns depend on the domain, the selection rule, and failure handling. When we replay the retained programming candidate pools, public-example selection raises correct submissions from 376 to 453 of 500 scheduled cells while saving 12-49% of logical API cost across models, and simply retaining an available candidate when judging fails recovers 61 submissions at unchanged cost. On identical mathematics pools, judging with fallback yields 186 correct submissions versus 182 for voting, while voting saves 12-21% of logical API cost. These controlled replays show how selection and failure handling change the gains realized from the same generated candidates, and they quantify the marginal value of a model judge.