# SCALE: Selective Resource Allocation for Overcoming Performance Bottlenecks in Mathematical Test-time Scaling

arXiv: https://arxiv.org/abs/2512.00466 · HTML: https://mlsanity.com/paper/2512.00466/

## Key facts

- Cited by 1 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 16 of its 16 references that are in the map.
- First posted on arXiv 29 Nov 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, 16 of 16)

- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [Multimodal Chain-of-Thought Reasoning in Language Models](https://mlsanity.com/paper/2302.00923/) (2023)
- [Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMs](https://mlsanity.com/paper/2412.21187/) (2024)
- [LIMO: Less is More for Reasoning](https://mlsanity.com/paper/2502.03387/) (2025)
- [Stop Overthinking: A Survey on Efficient Reasoning for Large Language Models](https://mlsanity.com/paper/2503.16419/) (2025)
- [DAST: Difficulty-Adaptive Slow-Thinking for Large Reasoning Models](https://mlsanity.com/paper/2503.04472/) (2025)
- [Think When You Need: Self-Adaptive Chain-of-Thought Learning](https://mlsanity.com/paper/2504.03234/) (2025)
- [ThinkSwitcher: When to Think Hard, When to Think Fast](https://mlsanity.com/paper/2505.14183/) (2025)
- [TL;DR: Too Long, Do Re-weighting for Efficient LLM Reasoning Compression](https://mlsanity.com/paper/2506.02678/) (2025)
- [LIMOPro: Reasoning Refinement for Efficient and Effective Test-time Scaling](https://mlsanity.com/paper/2505.19187/) (2025)
- [KAT-V1: Kwai-AutoThink Technical Report](https://mlsanity.com/paper/2507.08297/) (2025)
- [Self-Route: Automatic Mode Switching via Capability Estimation for Efficient Reasoning](https://mlsanity.com/paper/2505.20664/) (2025)

## Built on by (most cited first, 1 of 1)

- [AgencyBench: Benchmarking the Frontiers of Autonomous Agents in 1M-Token Real-World Contexts](https://mlsanity.com/paper/2601.11044/) (2026)

## Abstract (arXiv)

Test-time compute scaling has emerged as a powerful paradigm for enhancing mathematical reasoning in large language models (LLMs) by allocating additional computational resources during inference. However, current methods employ uniform resource distribution across all reasoning sub-problems, creating fundamental bottlenecks where challenging sub-problems receive insufficient attention while routine operations consume disproportionate resources. This uniform allocation creates performance bottlenecks where additional computational resources yield diminishing returns. Inspired by dual-process theory, we propose SCALE (Selective Resource Allocation), a framework that selectively allocates computational resources based on sub-problem difficulty. SCALE operates through four stages: (1) problem decomposition into sequential reasoning sub-problems, (2) difficulty assessment of each sub-problem to distinguish between routine operations and computationally challenging sub-problems, (3) selective processing mode assignment between System 1 for simple sub-problems and System 2 for complex ones, and (4) sequential execution with context propagation. By concentrating resources on challenging sub-problems while processing routine operations efficiently, SCALE achieves substantial performance improvements with superior resource utilization. Extensive experiments demonstrate that SCALE significantly outperforms uniform scaling baselines, achieving accuracy improvements of up to 13.75 percentage points (57.50% to 71.25% on AIME25) while reducing computational costs by 33%-53%, representing a major advance in test-time scaling that addresses fundamental limitations of current approaches.