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# What Makes Effective Supervision in Latent Chain-of-Thought: An Information-Theoretic Analysis
- **arXiv**: 2606.20075v1
- **Published**: 2026-06-18
- **Authors**: Xinghao Chen, Chak Tou Leong, Wenjin Guo, Jian Wang, Wenjie Li, Xiaoyu Shen (Eastern Institute of Technology / Hong Kong Polytechnic University)
- **Categories**: cs.LG, cs.CL
- **Venue**: ICML 2026
- **Code**: https://github.com/EIT-NLP/Supervision-in-Latent-CoT
- **Source**: https://arxiv.org/abs/2606.20075
## Abstract
从信息论角度分析 Latent Chain-of-Thought 的有效监督机制。识别出 outcome supervision 的"双重崩溃"——梯度衰减和表示漂移。将过程监督分解为两个互补维度Trajectory Supervision注入密集逐步推理信号和 Space Supervision通过生成式重建保留潜空间的语义结构。提出 Unified Latent Probe (ULP) 量化潜轨迹与显式推理步骤之间的互信息。实验揭示 Information-Performance Binding推理精度严格受限于潜在链中保留的信息保真度。
## Key Contributions
1. 信息论分析框架:将 Latent CoT 监督形式化为互信息最大化问题
2. 双重崩溃诊断:梯度衰减 + 表征漂移是 outcome supervision 失败的根本原因
3. 过程监督的二维分解Trajectory Supervision × Space Supervision
4. ULP 探针:量化潜状态中的可恢复推理信息
5. Information-Performance Binding推理能力严格受限于信息保真度