LegalDrill: Diagnosis-Driven Synthesis for Legal Reasoning in Small Language Models

Small language models (SLMs) are promising for real-world deployment due to their efficiency and low operational cost. However, their limited capacity struggles with high-stakes legal reasoning tasks that require coherent statute interpretation and logically consistent deduction. Furthermore, training SLMs for such tasks demands high-quality, concise reasoning trajectories, which are prohibitively expensive to manually collect and difficult to curate via standard rejection sampling, lacking granularity beyond final verdicts. To address these challenges, we propose {LegalDrill}, a diagnosis-driven synthesis framework that extracts and iteratively refines reasoning trajectories from a capable teacher via fine-grained prompting, then a self-reflective verification is employed to adaptively select the most effective data for the SLM student. The resulting data empower SLM training through supervised fine-tuning and direct preference optimization. Extensive experiments on several legal benchmarks demonstrate that {LegalDrill} significantly bolsters the legal reasoning capabilities of representative SLMs while bypassing the need for scarce expert annotations, paving a scalable path toward practical legal reasoning systems.

Towards Privacy-Preserving and Heterogeneity-aware Split Federated Learning via Probabilistic Masking

Split Federated Learning (SFL) has emerged as an efficient alternative to traditional Federated Learning (FL) by reducing client-side computation through model partitioning. However, exchanging of intermediate activations and model updates introduces significant privacy risks, especially from data reconstruction attacks that recover original inputs from intermediate representations. Existing defenses using noise injection often degrade model performance. To overcome these challenges, we present PM-SFL, a scalable and privacy-preserving SFL framework that incorporates Probabilistic Mask training to add structured randomness without relying on explicit noise. This mitigates data reconstruction risks while maintaining model utility. To address data heterogeneity, PM-SFL employs personalized mask learning that tailors submodel structures to each client's local data. For system heterogeneity, we introduce a layer-wise knowledge compensation mechanism, enabling clients with varying resources to participate effectively under adaptive model splitting. Theoretical analysis confirms its privacy protection, and experiments on image and wireless sensing tasks demonstrate that PM-SFL consistently improves accuracy, communication efficiency, and robustness to privacy attacks, with particularly strong performance under data and system heterogeneity.

Structural Re-weighting Improves Graph Domain Adaptation

In many real-world applications, graph-structured data used for training and testing have differences in distribution, such as in high energy physics (HEP) where simulation data used for training may not match real experiments. Graph domain adaptation (GDA) is a method used to address these differences. However, current GDA primarily works by aligning the distributions of node representations output by a single graph neural network encoder shared across the training and testing domains, which may often yield sub-optimal solutions. This work examines different impacts of distribution shifts caused by either graph structure or node attributes and identifies a new type of shift, named conditional structure shift (CSS), which current GDA approaches are provably sub-optimal to deal with. A novel approach, called structural reweighting (StruRW), is proposed to address this issue and is tested on synthetic graphs, four benchmark datasets, and a new application in HEP. StruRW has shown significant performance improvement over the baselines in the settings with large graph structure shifts, and reasonable performance improvement when node attribute shift dominates.