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

AAAI 2026 · Large language models › Reasoning and chain of thought · approach: Routing, pruning and distillation for reasoning · 0 citations (OpenAlex)

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Proposes SCALE, a prompt-based framework that decomposes math problems into sub-problems, rates their difficulty, routes each to System 1 or System 2 thinking mode, and executes them sequentially with context propagation; it also generates SCALE traces for SFT of non-reasoning models.

Problem

Test-time compute scaling for math reasoning allocates resources uniformly across sub-problems, so hard sub-problems get too little compute while routine steps waste tokens.

Approach

Inspired by dual-process theory, decompose a problem into sequential sub-problems, score each sub-problem's difficulty with the LLM, and selectively assign System 1 (fast) or System 2 (deliberate) thinking modes, propagating previous solutions as context.

Key results

• On AIME25 with Qwen3-32B, SCALE reaches 71.25% vs 57.50% for CoT (+13.75 points), using 26,643 tokens vs InftyThink's 36,640 at 70.00%.
• Fine-tuning Llama3.3-70B-Instruct on 800 SCALE traces raises AIME24 accuracy from 24.58% to 63.51%.
• SCALE reduces total tokens by 33-53% relative to InftyThink across the reported model-dataset combinations, per the paper's claim.

Surprising findings

• Lower difficulty thresholds (more sub-problems sent to System 2, around 75% hard) gave the highest accuracy, with accuracy falling as the threshold rises.
• On AIME25, SCALE with Qwen3-32B is reported at 71.25% while Majority-Voting for Distill-Qwen-32B reaches 60.00%, and SCALE underperforms Majority-Voting on AIME24 for Distill-Llama-70B (71.25% vs 76.67%).

Limitations

• Difficulty assessment and decomposition rely on the LLM's own prompted judgments, with no external validation of difficulty labels.
• Gains over Majority-Voting are inconsistent; SCALE does not beat it on several AIME24 entries.
• Evaluation limited to three math benchmarks with 8 samples per problem, so small differences (e.g., 1-2 points) may be within noise.

Experimental setup

Datasets: LIMOPro problem set AIME24 AIME25 AMC23

Benchmarks: AIME24 AIME25 AMC23

Metrics: pass@1 accuracy (8 samples) tokens per problem tokens per iteration

Baselines: CoT InftyThink Majority-Voting

Builds on: InftyThink chain-of-thought prompting Qwen3 thinking mode switching LIMO LIMOPro

Closest papers by meaning

• Every Rollout Counts: Optimal Resource Allocation for Efficient Test-Time Scaling (NeurIPS 2025 · similarity 0.92)
• Rethinking Fine-Tuning when Scaling Test-Time Compute: Limiting Confidence Improves Mathematical Reasoning (NeurIPS 2025 · similarity 0.91)
• Towards Thinking-Optimal Scaling of Test-Time Compute for LLM Reasoning (NeurIPS 2025 · similarity 0.91)
• Inference Scaling Laws: An Empirical Analysis of Compute-Optimal Inference for LLM Problem-Solving (ICLR 2025 · similarity 0.91)
• Test-Time Scaling in the Wild: Why Exploitation, Not Exploration, Is the Bottleneck (NeurIPS 2026 · similarity 0.90)
• OptScale: Probabilistic Optimality for Inference-time Scaling (AAAI 2026 · similarity 0.90)