The Critical Horizon: Inspection Design Principles for Multi-Stage Operations and Deep Reasoning
On the map: LLM reasoning → Reinforcement learning for reasoning
Abstract (arXiv)
Manufacturing lines, service journeys, supply chains, and AI reasoning chains share a common challenge: attributing a terminal outcome to the intermediate stage that caused it. We establish an information-theoretic barrier to this credit assignment problem: the signal connecting early steps to final outcomes decays exponentially with depth, creating a critical horizon beyond which reliable learning from endpoint data alone requires exponentially many samples. We prove four results. First, a Signal Decay Bound: sample complexity for attributing outcomes to early stages grows exponentially in the number of intervening steps. Second, Width Limits: parallel rollouts provide only logarithmic relief, with correlation capping the effective number of independent samples. Third, an Objective Mismatch: additive reward aggregation optimizes the wrong quantity when sequential validity requires all steps to be correct. Fourth, Optimal Inspection Design: uniform checkpoint spacing is minimax-optimal under homogeneous signal attenuation, while a greedy algorithm yields optimal non-uniform schedules under heterogeneous attenuation. Together, these results provide a common analytical foundation for inspection design in operations and supervision design in AI.
Key facts. No citing papers in the map yet (data through 7 Oct 2026). Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning. Builds on 15 of its 44 references that are in the map. First posted on arXiv 10 Feb 2026.
Builds on
15 of 44 references.
Closest ancestors · 5
Same direction, newest first
- 2025Do We Need to Verify Step by Step? Rethinking Process Supervision from a Theoretical Perspective14 Feb
- 2024ReST-MCTS*: LLM Self-Training via Process Reward Guided Tree Search6 Jun
- 2023Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations14 Dec
- 2023Let's Verify Step by Step31 May
- 2022Solving math word problems with process- and outcome-based feedback25 Nov
Other references · 10
- 2024DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Modelscited by 8,851
- 2024Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameterscited by 1,928
- 2024VinePPO: Refining Credit Assignment in RL Training of LLMscited by 168
- 2019Corruption-robust exploration in episodic reinforcement learningcited by 72
- 2024Code Repair with LLMs gives an Exploration-Exploitation Tradeoffcited by 50
- 2025Reasoning Language Models: A Blueprintcited by 41
- 2023Near-Minimax-Optimal Risk-Sensitive Reinforcement Learning with CVaRcited by 32
- 2021Fast Rates for the Regret of Offline Reinforcement Learningcited by 26
- 2022Communication-constrained hypothesis testing: Optimality, robustness, and reverse data processing inequalitiescited by 11
- 2024Assouad, Fano, and Le Cam with Interaction: A Unifying Lower Bound Framework and Characterization for Bandit Learnabilitycited by 11
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- 2026Coverage, Not Targeting: A Structural Regime in Multi-Turn Agent Credit Assignment
- 2026TRACE: Turn-level Reward Assignment via Credit Estimation for Long-Horizon Agents
- 2026Trustworthy Visual Quality Inspection under Data Scarcity in Manufacturing
- 2026BiCAA: Bidirectional Credit Assignment for Search-Augmented Agent
- 2026SHAPE: Stage-aware Hierarchical Advantage via Potential Estimation for LLM Reasoning
- 2026Maintaining Benchmarks Against Increasingly Capable Agents: Detection and Remediation of Unearned Passes
- 2025Explore-Execute Chain: Towards an Efficient Structured Reasoning Paradigm
- 2026TRIM: Hybrid Inference via Targeted Stepwise Routing in Multi-Step Reasoning Tasks