mlsanityData to 7 Oct 2026

Constrained Path Reasoning: Measuring When Committed Stages Earn Their Cost

arXiv 2607.17240 ↗First posted 19 Jul 2026cs.AIcited by 0

On the map: LLM reasoning → Test-time compute and efficient thinking

Abstract (arXiv)

When does a committed intermediate stage in an LLM reasoning pipeline earn its cost? Constrained Path Reasoning (CPR) pairs a source-aware path hypothesis with stage-level accounting. Search generates provisional states; trusted or validated invariants can constrain hard, while other proposals remain soft and revisable. CPR predicts that task-compatible commitments can factor transitions, concentrate candidate mass, induce regularity, and expose feedback when their gains exceed propagated error and execution cost. The formalism covers discrete commitments and continuous flows and measures effective branching, endpoint concentration, and cost per usable output. Across 1,180 generated QCQPs and 40 engineered degenerate polynomial instances (2,140 endpoints), residual triage recovers 63.0% of repair-all's additional feasible yield with 17.7% of its attempts. Fixed-LLM accounting (270 unique calls shared across nested arms) finds usable yield of 41.1% direct, 90.0% after formalization and deterministic execution, 20.0% after one-shot convexification, and 21.1% for the full path. In 120 paired-condition calls, a two-action rollback rule reaches 90% usable yield versus 36.7% for the feedback-conditioned selector. Two endpoint probes separate source from validation: a 72-output cross-trajectory transplant reduces entropy and acceptable mass; a 24-output same-call self-proposal pilot gives unchanged two-repeat collision entropy, 25.0% versus 8.3% usable yield, and 1/8 deterministically confirmed endpoint checks. Model-generated states supply hypotheses; trusted execution earns constraint strength.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning. Builds on 26 of its 39 references that are in the map. First posted on arXiv 19 Jul 2026.

Builds on

26 of 39 references.

Closest ancestors · 7

Same direction, newest first

  1. 2025Constraints-of-Thought: A Framework for Constrained Reasoning in Language-Model-Guided Search10 Oct
  2. 2025Stop Overthinking: A Survey on Efficient Reasoning for Large Language Models20 Mar
  3. 2024Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMs30 Dec
  4. 2024Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters6 Aug
  5. 2024Stream of Search (SoS): Learning to Search in Language1 Apr
  6. 2023Tree of Thoughts: Deliberate Problem Solving with Large Language Models17 May
  7. 2023Self-Refine: Iterative Refinement with Self-Feedback30 Mar

Other references · 19

  1. 2022Chain-of-Thought Prompting Elicits Reasoning in Large Language Modelscited by 12,302
  2. 2022Self-Consistency Improves Chain of Thought Reasoning in Language Modelscited by 5,601
  3. 2022Large Language Models are Zero-Shot Reasonerscited by 4,323
  4. 2023Reflexion: Language Agents with Verbal Reinforcement Learningcited by 4,064
  5. 2023Let's Verify Step by Stepcited by 3,598
  6. 2023Graph of Thoughts: Solving Elaborate Problems with Large Language Modelscited by 873
  7. 2022Solving math word problems with process- and outcome-based feedbackcited by 871
  8. 2023Reasoning with Language Model is Planning with World Modelcited by 846
  9. 2024Training Large Language Models to Reason in a Continuous Latent Spacecited by 763
  10. 2016CVXPY: A Python-Embedded Modeling Language for Convex Optimizationcited by 633
  11. 2021PICARD: Parsing Incrementally for Constrained Auto-Regressive Decoding from Language Modelscited by 402
  12. 2024Chain of Thought Empowers Transformers to Solve Inherently Serial Problemscited by 256
7 more
  1. 2020NeuroLogic Decoding: (Un)supervised Neural Text Generation with Predicate Logic Constraintscited by 146
  2. 2023Why think step by step? Reasoning emerges from the locality of experiencecited by 103
  3. 2016Error bounds, quadratic growth, and linear convergence of proximal methodscited by 59
  4. 2024Graph-constrained Reasoning: Faithful Reasoning on Knowledge Graphs with Large Language Modelscited by 47
  5. 2015From error bounds to the complexity of first-order descent methods for convex functionscited by 42
  6. 2023OptiMUS: Optimization Modeling Using MIP Solvers and large language modelscited by 39
  7. 2026NC2C: Automated Convexification of Generic Non-Convex Optimization Problemscited by 2

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