Planned Test-Time Scaling with Coordinated Reasoning Paths
Abstract Overview
This paper proposes Planned Test-Time Scaling (PTTS), a framework for reasoning-time scaling that coordinates multiple inference branches instead of sampling them independently. PTTS uses a planner to jointly generate branch-specific solution outlines and an executor to produce full solutions conditioned on those outlines, aiming to cover complementary reasoning paths. The authors show theoretically that PTTS strictly generalizes repeated sampling and can improve pass@k by mitigating mode collapse and redundant attempts. They introduce both a zero-shot variant (PTTS-ZS) and a reinforcement-learning-trained planner (PTTS-RL), evaluating them on five mathematical reasoning benchmarks with Qwen3-1.7B and 4B models.
Novelty
The primary contribution is formalizing test-time scaling as a coordinated joint policy over reasoning branches via a planner-executor decomposition rather than treating branches as independent samples. The work also provides a theoretical framework explaining why joint planning improves pass@k coverage and introduces a planner trained directly on pass@k rewards using truncated execution rollouts.
Results
Across five math benchmarks, PTTS-ZS improves pass@64 over repeated sampling by up to 6.7 points, while PTTS-RL increases gains by up to 13.4 points. PTTS-RL at pass@32 surpasses repeated sampling at pass@64 across both 1.7B and 4B models, achieving equivalent or better performance with half the sampling budget. Diversity analyses confirm that PTTS increases overall solution diversity and that PTTS-RL significantly boosts useful diversity among correct reasoning paths.
Key Points
- PTTS replaces independent repeated sampling with a planner-executor decomposition that coordinates parallel branches using distinct solution outlines.
- Theoretical analysis demonstrates that PTTS strictly generalizes repeated sampling and avoids mode collapse by allocating budget across complementary reasoning modes.
- Empirical evaluations on five mathematical benchmarks show substantial pass@k and compute-efficiency gains over repeated sampling for both PTTS-ZS and PTTS-RL.