# LC-ERD: Mining Latent Logic for Self-Evolving Reasoning via Consistency-Regulated Reward Decomposition

arXiv: https://arxiv.org/abs/2605.24005 · HTML: https://mlsanity.com/paper/2605.24005/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 26 of its 50 references that are in the map.
- First posted on arXiv 19 May 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)
- Synthetic data and self-improvement for LLMs / [Synthetic reasoning data and bootstrapping](https://mlsanity.com/synth/synthetic-reasoning-data-and-bootstrapping/)

## Builds on (most cited first, 26 of 26)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Safe RLHF: Safe Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2310.12773/) (2023)
- [AFlow: Automating Agentic Workflow Generation](https://mlsanity.com/paper/2410.10762/) (2024)
- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [Demystifying Long Chain-of-Thought Reasoning in LLMs](https://mlsanity.com/paper/2502.03373/) (2025)
- [Is DPO Superior to PPO for LLM Alignment? A Comprehensive Study](https://mlsanity.com/paper/2404.10719/) (2024)
- [Maximum Entropy RL (Provably) Solves Some Robust RL Problems](https://mlsanity.com/paper/2103.06257/) (2021)
- [InfiGUI-R1: Advancing Multimodal GUI Agents from Reactive Actors to Deliberative Reasoners](https://mlsanity.com/paper/2504.14239/) (2025)
- [DPO Meets PPO: Reinforced Token Optimization for RLHF](https://mlsanity.com/paper/2404.18922/) (2024)
- [A Survey of Temporal Credit Assignment in Deep Reinforcement Learning](https://mlsanity.com/paper/2312.01072/) (2023)
- [ReasonFlux-PRM: Trajectory-Aware PRMs for Long Chain-of-Thought Reasoning in LLMs](https://mlsanity.com/paper/2506.18896/) (2025)
- [Generalist Reward Models: Found Inside Large Language Models](https://mlsanity.com/paper/2506.23235/) (2025)
- [Learning to solve the credit assignment problem](https://mlsanity.com/paper/1906.00889/) (2019)
- [Optimizing Safe and Aligned Language Generation: A Multi-Objective GRPO Approach](https://mlsanity.com/paper/2503.21819/) (2025)
- [MO-GRPO: Mitigating Reward Hacking of Group Relative Policy Optimization on Multi-Objective Problems](https://mlsanity.com/paper/2509.22047/) (2025)
- [MedQA-CS: Objective Structured Clinical Examination (OSCE)-Style Benchmark for Evaluating LLM Clinical Skills](https://mlsanity.com/paper/2410.01553/) (2024)
- [On Group Relative Policy Optimization Collapse in Agent Search: The Lazy Likelihood-Displacement](https://mlsanity.com/paper/2512.04220/) (2025)
- [Offline Inverse Reinforcement Learning](https://mlsanity.com/paper/2106.05068/) (2021)
- [TIC-GRPO: Provable and Efficient Optimization for Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2508.02833/) (2025)
- [Quick on the Uptake: Eliciting Implicit Intents from Human Demonstrations for Personalized Mobile-Use Agents](https://mlsanity.com/paper/2508.08645/) (2025)
- [Why Tree-Style Branching Matters for Thought Advantage Estimation in GRPO](https://mlsanity.com/paper/2509.24494/) (2025)
- [MATH-Beyond: A Benchmark for RL to Expand Beyond the Base Model](https://mlsanity.com/paper/2510.11653/) (2025)
- [Agent-Dice: Disentangling Knowledge Updates via Geometric Consensus for Agent Continual Learning](https://mlsanity.com/paper/2601.03641/) (2026)
- [Diffusion Fine-Tuning via Reparameterized Policy Gradient of the Soft Q-Function](https://mlsanity.com/paper/2512.04559/) (2025)
- [Sub-optimality bounds for certainty equivalent policies in partially observed systems](https://mlsanity.com/paper/2602.02814/) (2026)

## Abstract (arXiv)

The evolution of Large Language Model (LLM) reasoning is bottlenecked by the scarcity of high-quality process data. While self-alignment via endogenous rewards offers a solution, mining valid supervision faces three challenges: (1) Label Noise via Mimetic Bias, where rewards prioritize statistical likelihood over logical truth, creating a "correctness illusion" that masks compounding errors; (2) Coarse-Grained Supervision, where sparse global outcomes (e.g., in GRPO) fail to provide granular guidance, treating reasoning chains as monolithic; and (3) Distributional Collapse, where signals fail to generalize without amplifying pre-training biases. To address these, we introduce LC-ERD (Logic-Consistent Endogenous Reward Decomposition), a framework framing self-alignment as latent structure mining. We derive a Variational Logic Potential by aggregating consensus from the model's Latent Logic Expertise (LLE) to denoise the reasoning manifold, and introduce a Multi-Agent Value Decomposition protocol based on the IGM principle to quantify individual step utility. Experiments show LC-ERD delivers a robust self-evolution path, uncovering trade-offs between logic consistency and accuracy while identifying high-value reasoning patterns missed by standard rewards. Our code is available at https://github.com/LC-ERD-repo/LC-ERD.