# When Does Longer Reasoning Help? Predicting Mathematical Reasoning Through Discovery and Execution

arXiv: https://arxiv.org/abs/2610.05322 · HTML: https://mlsanity.com/paper/2610.05322/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 19 of its 21 references that are in the map.
- First posted on arXiv 4 Oct 2026.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 19 of 19)

- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Inference Scaling Laws: An Empirical Analysis of Compute-Optimal Inference for Problem-Solving with Language Models](https://mlsanity.com/paper/2408.00724/) (2024)
- [Planning In Natural Language Improves LLM Search For Code Generation](https://mlsanity.com/paper/2409.03733/) (2024)
- [Winning Gold at IMO 2025 with a Model-Agnostic Verification-and-Refinement Pipeline](https://mlsanity.com/paper/2507.15855/) (2025)
- [Can Language Models Solve Olympiad Programming?](https://mlsanity.com/paper/2404.10952/) (2024)
- [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)
- [How Do Large Language Monkeys Get Their Power (Laws)?](https://mlsanity.com/paper/2502.17578/) (2025)
- [Efficient Prediction of Pass@k Scaling in Large Language Models](https://mlsanity.com/paper/2510.05197/) (2025)
- [Let Me Think! A Long Chain-of-Thought Can Be Worth Exponentially Many Short Ones](https://mlsanity.com/paper/2505.21825/) (2025)
- [Give me a hint: Can LLMs take a hint to solve math problems?](https://mlsanity.com/paper/2410.05915/) (2024)
- [Understanding Performance Gap Between Parallel and Sequential Sampling in Large Reasoning Models](https://mlsanity.com/paper/2604.05868/) (2026)
- [Mitigating Strategy-Selection Bias in Reasoning for More Effective Test-Time Scaling](https://mlsanity.com/paper/2509.17905/) (2025)
- [More Bang for the Buck: Improving the Inference of Large Language Models at a Fixed Budget using Reset and Discard (ReD)](https://mlsanity.com/paper/2601.21522/) (2026)
- [Strategy Executability in Mathematical Reasoning: Leveraging Human-Model Differences for Effective Guidance](https://mlsanity.com/paper/2602.22583/) (2026)
- [AutoFyn Technical Report: Non-Parametric Expert Iteration for Long-Horizon Agents](https://mlsanity.com/paper/2609.05446/) (2026)

## Abstract (arXiv)

Test-time compute can improve mathematical reasoning, but can short-budget runs predict how mathematical reasoning scales with additional compute? We introduce a Discovery--Execution (DE) framework that predicts the aggregate held-out scaling curves through a convolution of strategy discovery and conditional execution. From independent short-budget attempts and oracle-sketch-conditioned runs, the framework estimates cumulative success along held-out reasoning trajectories under alternate compute allocations. We evaluate four models on 35 fresh Olympiad problems and non-geometry problems from IMO-ProofBench Advanced. Under the DE framework, near-saturated execution predicts geometric scaling, as observed for the GPT models. For Claude Opus 4.8, incorporating measured execution substantially improves held-out forecasts over geometric extrapolation across one- and two-arm allocations. As a secondary application, regularized DE (R-DE) decisions to continue or restart yield lower average regret than the best model-specific retrospective policy. Together, these results show that measuring conditional execution provides information about longer reasoning that short-budget success rates do not always capture.