Xinghao Chen, Chak Tou Leong, Wenjin Guo +3cs.LG cs.CL
Latent Chain-of-Thought (CoT) internalizes reasoning within continuous hidden states, offering a promising alternative to verbose discrete reasoning traces. However, robust latent reasoning remains difficult because outcome supervision provides weak learning signals and leaves latent trajectories prone to semantic drift. In this work, we analyze Latent CoT from an information-theoretic perspective and identify this failure as a dual collapse: gradient attenuation along the optimization path and representational drift in the latent space. We further decompose process supervision into two complementary dimensions: Trajectory Supervision, which injects dense stepwise reasoning signals, and Space Supervision, which preserves the semantic structure of the latent manifold. Our analysis shows that rigid geometric compression can collapse the reasoning space, whereas generative reconstruction provides a more flexible semantic anchor that better preserves information capacity. To measure these effects, we introduce the Unified Latent Probe (ULP), which quantifies the mutual information between latent trajectories and explicit reasoning steps. Experiments reveal a clear Information-Performance Binding: reasoning accuracy depends on the information fidelity preserved in the latent chain. These findings provide a principled framework for latent reasoning supervision and suggest shifting from geometric imitation toward mutual information maximization. Our code is available at \href{https://github.com/EIT-NLP/Supervision-in-Latent-CoT}{this repository}.
Incomplete propagation data significantly hinders robust fake news detection. Recent approaches leverage large language models to simulate missing user interactions via role-playing, thereby enriching propagation with synthetic signals. However, such propagation data is intrinsically unreliable, and directly fusing it can lead to biased representations, leading to limited detection performance. In this paper, we alleviate the unreliability of synthetic propagation from the mutual information perspective and propose a novel information-theoretic propagation denoising and fusion (InfoPDF) framework to learn effective representations from both real and synthetic propagation. Specifically, we first generate attribute-specific synthetic propagation using large language models. Then we model each synthetic propagation graph as a probabilistic latent distribution to guide reliability-aware adaptive fusion with real propagation. During training, we design a mutual information-based objective to learn compressed and task-sufficient propagation representations. It jointly suppresses noisy signals across attribute-specific synthetic propagation, maintains consistency between real and synthetic propagation representations, and ensures task sufficiency for fake news detection and attribute prediction. Experiments on three real-world datasets show that InfoPDF consistently achieves superior performance across various fake news detection tasks. Further analysis demonstrates that InfoPDF can estimate attribute-level reliabilities and learn more discriminative propagation representations.