Knowledge distillation (KD) compresses large language models (LLMs), known as teacher models, into lightweight versions called student models, enabling efficient inference and downstream applications. However, prevailing approaches accomplish this by predominantly focusing on matching the final output distributions of student/teacher models. Drawing on the perspective that transformers can be viewed as discretizing ordinary differential equation (ODEs) on integer time steps (corresponding to layer indices), where intermediate features evolve across layers, we argue that effective KD requires aligning the entire feature dynamics between teacher and student models, which we call feature dynamics distillation (FDD). This alignment involves matching both the feature trajectory and its first-order derivative, rather than just the final states. Our approach extends the original KD objective with two additional loss terms: layer-wise feature KD, which matches discretized feature trajectory, and layer feature delta KD, which matches first-order changes in features across adjacent layers. Extensive experiments on various tasks validate the effectiveness of our distillation method.

Large Language Models (LLMs) have demonstrated remarkable capabilities across various tasks but their performance in complex logical reasoning tasks remains unsatisfactory. Although some prompting methods, such as Chain-of-Thought, can improve the reasoning ability of LLMs to some extent, they suffer from an unfaithful issue where derived conclusions may not align with the generated reasoning chain. To address this issue, some studies employ the approach of propositional logic to further enhance logical reasoning abilities of LLMs. However, the potential omissions in the extraction of logical expressions in these methods can cause information loss in the logical reasoning process, thereby generating incorrect results. To this end, we propose Logic-of-Thought (LoT) prompting which employs propositional logic to generate expanded logical information descriptions and utilizes them as an additional augmentation to original contexts, thereby ensuring information completeness and enhancing logical reasoning ability. LoT is orthogonal to existing prompting methods and can be seamlessly integrated with them. Extensive experiments demonstrate that LoT boosts the performance of various prompting methods with a striking margin across five logical reasoning tasks. In particular, LoT enhances Chain-of-Thought’s performance on the ReClor dataset by +4.35%, improves Chain-of-Thought with Self-Consistency’s performance on the RuleTaker dataset by +3.52%, and boosts performance of Tree-of-Thoughts on the ProofWriter dataset by +8%.

Generative retrieval (GR) has emerged as a transformative paradigm in search and recommender systems, leveraging numeric-based identifier representations to enhance efficiency and generalization. Notably, methods like TIGER, which employ Residual Quantization-based Semantic Identifiers (RQ-SID), have shown significant promise in e-commerce scenarios by effectively managing item IDs. However, a critical issue termed the "Hourglass" phenomenon, occurs in RQ-SID, where intermediate codebook tokens become overly concentrated, hindering the full utilization of generative retrieval methods. This paper analyses and addresses this problem by identifying data sparsity and long-tailed distribution as the primary causes. Through comprehensive experiments and detailed ablation studies, we analyze the impact of these factors on codebook utilization and data distribution. Our findings reveal that the “Hourglass” phenomenon substantially impacts the performance of RQ-SID in generative retrieval. We propose effective solutions to mitigate this issue, thereby significantly enhancing the effectiveness of generative retrieval in real-world E-commerce applications.