mlsanityData to 14 Oct 2026

Step Potential Advantage Estimation: Harnessing Intermediate Confidence and Correctness for Efficient Mathematical Reasoning

arXiv 2601.03823 ↗First posted 7 Jan 2026cs.CLcited by 9

On the map: LLM reasoning → Reinforcement learning for reasoning

Abstract (arXiv)

Reinforcement Learning with Verifiable Rewards (RLVR) elicits long chain-of-thought reasoning in large language models (LLMs), but outcome-based rewards lead to coarse-grained advantage estimation. While existing approaches improve RLVR via token-level entropy or sequence-level length control, they lack a semantically grounded, step-level measure of reasoning progress. As a result, LLMs fail to distinguish necessary deduction from redundant verification: they may continue checking after reaching a correct solution and, in extreme cases, overturn a correct trajectory into an incorrect final answer. To remedy the lack of process supervision, we introduce a training-free probing mechanism that extracts intermediate confidence and correctness and combines them into a Step Potential signal that explicitly estimates the reasoning state at each step. Building on this signal, we propose Step Potential Advantage Estimation (SPAE), a fine-grained credit assignment method that amplifies potential gains, penalizes potential drops, and applies penalty after potential saturates to encourage timely termination. Experiments across multiple benchmarks show SPAE consistently improves accuracy while substantially reducing response length, outperforming strong RL baselines and recent efficient reasoning and token-level advantage estimation methods. The code is available at https://github.com/cii030/SPAE-RL.

Key facts. Cited by 9 papers in the map (data through 14 Oct 2026). Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning. Builds on 18 of its 31 references that are in the map. First posted on arXiv 7 Jan 2026.

Builds on

18 of 31 references.

Closest ancestors · 9

Same direction, newest first

  1. 2025No Prompt Left Behind: Exploiting Zero-Variance Prompts in LLM Reinforcement Learning via Entropy-Guided Advantage Shaping26 Sep
  2. 2025Emergent Hierarchical Reasoning in LLMs through Reinforcement Learning3 Sep
  3. 2025Part I: Tricks or Traps? A Deep Dive into RL for LLM Reasoning11 Aug
  4. 2025Reasoning with Exploration: An Entropy Perspective17 Jun
  5. 2025Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning2 Jun
  6. 2025SEED-GRPO: Semantic Entropy Enhanced GRPO for Uncertainty-Aware Policy Optimization18 May
  7. 2025DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning22 Jan
  8. 2025REINFORCE++: Stabilizing Critic-Free Policy Optimization with Global Advantage Normalization4 Jan
  9. 2017Proximal Policy Optimization Algorithms20 Jul

Other references · 9

  1. 2024DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Modelscited by 9,379
  2. 2025Qwen3 Technical Reportcited by 8,820
  3. 2025From System 1 to System 2: A Survey of Reasoning Large Language Modelscited by 320
  4. 2025AdaCoT: Pareto-Optimal Adaptive Chain-of-Thought Triggering via Reinforcement Learningcited by 87
  5. 2025Agent RL Scaling Law: Agent RL with Spontaneous Code Execution for Mathematical Problem Solvingcited by 62
  6. 2025xVerify: Efficient Answer Verifier for Reasoning Model Evaluationscited by 55
  7. 2025Harnessing Uncertainty: Entropy-Modulated Policy Gradients for Long-Horizon LLM Agentscited by 46
  8. 2025Optimizing Length Compression in Large Reasoning Modelscited by 38
  9. 2025Mixture of Reasonings: Teach Large Language Models to Reason with Adaptive Strategiescited by 3

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 9.

9 papers.

  1. 2026ATTNPO: Attention-Guided Process Supervision for Efficient Reasoningcited by 9
  2. 2026Reinforced Efficient Reasoning via Semantically Diverse Explorationcited by 8
  3. 2026One Refiner to Unlock Them All: Inference-Time Reasoning Elicitation via Reinforcement Query Refinementcited by 6
  4. 2026TSPO: Breaking the Double Homogenization Dilemma in Multi-turn Search Policy Optimizationcited by 5
  5. 2026TACO: Tool-Augmented Credit Optimization for Agentic Tool Usecited by 5
  6. 2026Dissecting Failure Dynamics in Large Language Model Reasoningcited by 2
  7. 2026KidnapRAG: A Black-Box Attack for Hijacking Reasoning in Agentic Retrieval-Augmented Generation Systemscited by 0
  8. 2026SCOUT: Self-Checking and Recovery-Aware Tool-Thought Agents for Ultra-Long Egocentric Video Reasoningcited by 0
  9. 2026VASPO: Self-Distillation with Privileged Value Estimationcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025Conditional Advantage Estimation for Reinforcement Learning in Large Reasoning Models
  2. 2025Unlocking Exploration in RLVR: Uncertainty-aware Advantage Shaping for Deeper Reasoning
  3. 2025Reinforcement Learning with Verifiable Rewards Implicitly Incentivizes Correct Reasoning in Base LLMs
  4. 2025Beyond High-Entropy Exploration: Correctness-Aware Low-Entropy Segment-Based Advantage Shaping for Reasoning LLMs
  5. 2026Back to Basics: Revisiting Exploration in Reinforcement Learning for LLM Reasoning via Generative Probabilities
  6. 2025Thinking Fast and Right: Balancing Accuracy and Reasoning Length with Adaptive Rewards
  7. 2026Stabilizing Efficient Reasoning with Step-Level Advantage Selection
  8. 2025Rethinking Reasoning Quality in Large Language Models through Enhanced Chain-of-Thought via RL