DAIS: Dependency-Aware Intermediate QA Supervision for Complex Reasoning

Chain-of-thought (CoT) reasoning is widely used to improve both the performance and interpretability of large language models (LLMs), yet the generated reasoning may not faithfully support the final answer. We study this problem from a causal perspective, where a faithful CoT process should follow the chain $Z\rightarrow X\rightarrow Y$, with $Z$, $X$, and $Y$ denoting the instruction, reasoning chain, and final answer, respectively. In this process, the instruction should affect the answer only through the reasoning chain. However, conventional autoregressive LLMs condition answer generation on both the instruction and the CoT, which still allows a direct instruction-to-answer shortcut. To address this issue, we propose CASE, a framework that combines training-time causal alignment and inference-time structural enforcement. During training, CASE builds counterfactual-CoT, biased-instruction, and empty-instruction datasets, and applies selective-loss fine-tuning to strengthen CoT-to-answer dependence while suppressing instruction shortcuts. During inference, CASE masks direct attention from instruction tokens to answer tokens, preventing the model from bypassing the generated CoT. We provide an information-theoretic analysis showing how these components promote faithful chains. Experiments on three models and four benchmarks show that CASE achieves a 37% average per-setting relative improvement in overall CoT faithfulness over the strongest baselines, exhibits stronger cross-dataset faithfulness transfer, and maintains competitive average accuracy. Code is available at https://github.com/oddwang/CASE.

Large language models often improve on difficult tasks by spending inference-time compute on a reasoning trace before producing the final answer. That extra computation can be useful, but it also raises latency, token cost, and deployment complexity. We introduce \textbf{ThinkSwitch}, a low-compute procedure for co-training paired instruct and thinking checkpoints. Starting from compatible Qwen3-4B instruct and thinking models, each iteration asks the thinking checkpoint to generate answers, removes the reasoning trace, distills the answer-only pairs into the instruct checkpoint with QLoRA, and reconstructs a thinking checkpoint with spherical weight interpolation. The only human-supplied inputs are task prompts; the labels are generated by the model itself. On a 30-question AIME 2026 evaluation, ThinkSwitch improves the instruct checkpoint from 10/30 to 20/30 and the thinking checkpoint from 14/30 to 22/30. On a 30-question PubMedQA subset, it improves the instruct checkpoint from 13/30 to 18/30 and the thinking checkpoint from 18/30 to 25/30. The complete experiment uses 15 training prompts per domain and costs $2.86 on a single cloud RTX 3070. The results are small-scale, but they indicate that targeted distillation loops can move part of the benefit of explicit reasoning into weights while preserving a separate thinking mode.

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}.