Causal Distillation: Transferring Structured Explanations from Large to Compact Language Models

Large proprietary language models exhibit strong causal reasoning abilities that smaller open-source models struggle to replicate. We introduce a novel framework for distilling causal explanations that transfers causal reasoning skills from a powerful teacher model to a compact open-source model. The key idea is to train the smaller model to develop causal reasoning abilities by generating structured cause-and-effect explanations consistent with those of the teacher model. To evaluate the quality of the student-generated explanations, we introduce a new metric called Causal Explanation Coherence (CEC) to assess the structural and logical consistency of causal reasoning. This metric uses sentence-level semantic alignment to measure how well each part of the generated explanation corresponds to the teacher's reference, capturing both faithfulness and coverage of the underlying causal chain. Our framework and the CEC metric provide a principled foundation for training smaller models to perform robust causal reasoning and for systematically assessing the coherence of explanations in language model outputs.

Kuramoto-FedAvg: Using Synchronization Dynamics to Improve Federated Learning Optimization under Statistical Heterogeneity

Federated learning on heterogeneous (non-IID) client data experiences slow convergence due to client drift. To address this challenge, we propose Kuramoto-FedAvg, a federated optimization algorithm that reframes the weight aggregation step as a synchronization problem inspired by the Kuramoto model of coupled oscillators. The server dynamically weighs each client's update based on its phase alignment with the global update, amplifying contributions that align with the global gradient direction while minimizing the impact of updates that are out of phase. We theoretically prove that this synchronization mechanism reduces client drift, providing a tighter convergence bound compared to the standard FedAvg under heterogeneous data distributions. Empirical validation supports our theoretical findings, showing that Kuramoto-FedAvg significantly accelerates convergence and improves accuracy across multiple benchmark datasets. Our work highlights the potential of coordination and synchronization-based strategies for managing gradient diversity and accelerating federated optimization in realistic non-IID settings.