scale-selective-test-time

name	scale-selective-test-time
title	SCALE: Selective Resource Allocation for Mathematical Test-Time Scaling
version	0.0.2
engine	skillxiv-v0.0.2-claude-opus-4.6
license	MIT
url	https://arxiv.org/abs/2512.00466
keywords	["test-time-scaling","resource-allocation","mathematical-reasoning","system-1-2","adaptive-compute"]
description	Decomposes math problems into sequential sub-problems, assesses difficulty, and allocates simple ones to fast System 1 reasoning while directing complex ones to deliberate System 2. Save 33-53% tokens while improving accuracy by up to 13.75 points on AIME.

Summary

SCALE addresses inefficient resource allocation in test-time scaling by implementing selective resource allocation based on sub-problem difficulty. Rather than uniformly distributing computational resources across all steps, the approach decomposes mathematical problems into sequential sub-problems, assesses difficulty, and dynamically assigns simple problems to fast processing while directing complex ones to deliberate reasoning.

Core Technique

Problem Decomposition: Break mathematical problems into smaller steps or sub-problems. For math:

• Step 1: Parse and identify key quantities
• Step 2: Determine solution strategy
• Step 3: Execute calculations
• Step 4: Verify answer

Difficulty Assessment: For each sub-problem, estimate complexity via:

• Token count of problem statement
• Number of dependencies on previous steps
• Complexity of mathematical operations involved
• Uncertainty in model confidence

Dual-System Allocation:

• System 1 (Fast): Single-shot generation with minimal reasoning, optimal for straightforward calculations
• System 2 (Deliberate): Multiple sampling, majority voting, extended reasoning for complex steps

Implementation

Difficulty scorer: Train a lightweight classifier:

difficulty = mlp(encode(subproblem))  # 0 (easy) to 1 (hard)

Dynamic allocation:

if difficulty < 0.3:
    # System 1: single pass
    answer = model.generate(subproblem, max_tokens=50)
else:
    # System 2: deliberate reasoning
    answers = [model.generate(subproblem, max_tokens=500) for _ in range(5)]
    answer = majority_vote(answers)

Token counting: Track token usage:

total_tokens = sum(difficulty_threshold * tokens_system1 + (1 - difficulty_threshold) * tokens_system2)