# Predicting and improving test-time scaling laws via reward tail-guided search

arXiv: https://arxiv.org/abs/2602.01485 · HTML: https://mlsanity.com/paper/2602.01485/

## Key facts

- Cited by 2 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 27 of its 40 references that are in the map.
- First posted on arXiv 1 Feb 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)
- LLM alignment / RLHF / preference optimisation / [Process reward models for reasoning](https://mlsanity.com/alignment/process-reward-models-for-reasoning/)

## Builds on (most cited first, 27 of 27)

- [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)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [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)
- [Language Agent Tree Search Unifies Reasoning Acting and Planning in Language Models](https://mlsanity.com/paper/2310.04406/) (2023)
- [OpenThoughts: Data Recipes for Reasoning Models](https://mlsanity.com/paper/2506.04178/) (2025)
- [Inference Scaling Laws: An Empirical Analysis of Compute-Optimal Inference for Problem-Solving with Language Models](https://mlsanity.com/paper/2408.00724/) (2024)
- [Training Language Models to Reason Efficiently](https://mlsanity.com/paper/2502.04463/) (2025)
- [Skywork-Reward-V2: Scaling Preference Data Curation via Human-AI Synergy](https://mlsanity.com/paper/2507.01352/) (2025)
- [Can 1B LLM Surpass 405B LLM? Rethinking Compute-Optimal Test-Time Scaling](https://mlsanity.com/paper/2502.06703/) (2025)
- [Process Reward Models That Think](https://mlsanity.com/paper/2504.16828/) (2025)
- [Is Best-of-N the Best of Them? Coverage, Scaling, and Optimality in Inference-Time Alignment](https://mlsanity.com/paper/2503.21878/) (2025)
- [TreeBoN: Enhancing Inference-Time Alignment with Speculative Tree-Search and Best-of-N Sampling](https://mlsanity.com/paper/2410.16033/) (2024)
- [How Do Large Language Monkeys Get Their Power (Laws)?](https://mlsanity.com/paper/2502.17578/) (2025)
- [A Simple Model of Inference Scaling Laws](https://mlsanity.com/paper/2410.16377/) (2024)
- [PAG: Multi-Turn Reinforced LLM Self-Correction with Policy as Generative Verifier](https://mlsanity.com/paper/2506.10406/) (2025)
- [Learning quadratic neural networks in high dimensions: SGD dynamics and scaling laws](https://mlsanity.com/paper/2508.03688/) (2025)
- [Uncertainty-Aware Step-wise Verification with Generative Reward Models](https://mlsanity.com/paper/2502.11250/) (2025)
- [M1: Towards Scalable Test-Time Compute with Mamba Reasoning Models](https://mlsanity.com/paper/2504.10449/) (2025)
- [Efficient Prediction of Pass@k Scaling in Large Language Models](https://mlsanity.com/paper/2510.05197/) (2025)
- [Improved Scaling Laws in Linear Regression via Data Reuse](https://mlsanity.com/paper/2506.08415/) (2025)
- [AdaBoN: Adaptive Best-of-N Alignment](https://mlsanity.com/paper/2505.12050/) (2025)
- [First Finish Search: Efficient Test-Time Scaling in Large Language Models](https://mlsanity.com/paper/2505.18149/) (2025)
- [Best-of-Majority: Minimax-Optimal Strategy for Pass@k Inference Scaling](https://mlsanity.com/paper/2510.03199/) (2025)
- [On the Limits of Test-Time Compute: Sequential Reward Filtering for Better Inference](https://mlsanity.com/paper/2512.04558/) (2025)
- [Demystifying LLM-as-a-Judge: Analytically Tractable Model for Inference-Time Scaling](https://mlsanity.com/paper/2512.19905/) (2025)

## Built on by (most cited first, 2 of 2)

- [What should post-training optimize? A test-time scaling law perspective](https://mlsanity.com/paper/2605.10716/) (2026)
- [Collaborative Learning and Reasoning over Model Slices](https://mlsanity.com/paper/2610.12927/) (2026)

## Abstract (arXiv)

Test-time scaling has emerged as a critical avenue for enhancing the reasoning capabilities of Large Language Models (LLMs). Though the straight-forward ''best-of-N'' (BoN) strategy has already demonstrated significant improvements in performance, it lacks principled guidance on the choice of N, budget allocation, and multi-stage decision-making, thereby leaving substantial room for optimization. While many works have explored such optimization, rigorous theoretical guarantees remain limited. In this work, we propose new methodologies to predict and improve scaling properties via tail-guided search. By estimating the tail distribution of rewards, our method predicts the scaling law of LLMs without the need for exhaustive evaluations. Leveraging this prediction tool, we introduce Scaling-Law Guided (SLG) Search, a new test-time algorithm that dynamically allocates compute to identify and exploit intermediate states with the highest predicted potential. We theoretically prove that SLG achieves vanishing regret compared to perfect-information oracles, and achieves expected rewards that would otherwise require a polynomially larger compute budget required when using BoN. Empirically, we validate our framework across different LLMs and reward models, confirming that tail-guided allocation consistently achieves higher reward yields than Best-of-N under identical compute budgets. Our code is available at https://github.com/PotatoJnny/Scaling-Law-Guided-search.