MATRIX AS PLAN: Structured Logical Reasoning with Feedback-Driven Replanning

As knowledge and semantics on the web grow increasingly complex, enhancing Large Language Models (LLMs) comprehension and reasoning capabilities has become particularly important. Chain-of-Thought (CoT) prompting has been shown to enhance the reasoning capabilities of LLMs. However, it still falls short on logical reasoning tasks that rely on symbolic expressions and strict deductive rules. Neuro-symbolic methods address this gap by enforcing formal correctness through external solvers. Yet these solvers are highly format-sensitive, and small instabilities in model outputs can lead to frequent processing failures. LLM-driven approaches avoid parsing brittleness, but they lack structured representations and process-level error-correction mechanisms. To further enhance the logical reasoning capabilities of LLMs, we propose MatrixCoT, a structured CoT framework with a matrix-based plan. Specifically, we normalize and type natural language expressions, attach explicit citation fields, and introduce a matrix-based planning method to preserve global relations among steps. The plan becomes a verifiable artifact, making execution more stable. For verification, we also add a feedback-driven replanning mechanism. Under semantic-equivalence constraints, it identifies omissions and defects, rewrites and compresses the dependency matrix, and produces a more trustworthy final answer. Experiments on five logical-reasoning benchmarks and five LLMs show that, without relying on external solvers, MatrixCoT enhances both robustness and interpretability when tackling complex symbolic reasoning tasks, while maintaining competitive performance.

FedHL: Federated Learning for Heterogeneous Low-Rank Adaptation via Unbiased Aggregation

Federated Learning (FL) facilitates the fine-tuning of Foundation Models (FMs) using distributed data sources, with Low-Rank Adaptation (LoRA) gaining popularity due to its low communication costs and strong performance. While recent work acknowledges the benefits of heterogeneous LoRA in FL and introduces flexible algorithms to support its implementation, our theoretical analysis reveals a critical gap: existing methods lack formal convergence guarantees due to parameter truncation and biased gradient updates. Specifically, adapting client-specific LoRA ranks necessitates truncating global parameters, which introduces inherent truncation errors and leads to subsequent inaccurate gradient updates that accumulate over training rounds, ultimately degrading performance. To address the above issues, we propose \textbf{FedHL}, a simple yet effective \textbf{Fed}erated Learning framework tailored for \textbf{H}eterogeneous \textbf{L}oRA. By leveraging the full-rank global model as a calibrated aggregation basis, FedHL eliminates the direct truncation bias from initial alignment with client-specific ranks. Furthermore, we derive the theoretically optimal aggregation weights by minimizing the gradient drift term in the convergence upper bound. Our analysis shows that FedHL guarantees $\mathcal{O}(1/\sqrt{T})$ convergence rate, and experiments on multiple real-world datasets demonstrate a 1-3\% improvement over several state-of-the-art methods.

Federated Learning for Diffusion Models

Diffusion models are powerful generative models that can produce highly realistic samples for various tasks. Typically, these models are constructed using centralized, independently and identically distributed (IID) training data. However, in practical scenarios, data is often distributed across multiple clients and frequently manifests non-IID characteristics. Federated Learning (FL) can leverage this distributed data to train diffusion models, but the performance of existing FL methods is unsatisfactory in non-IID scenarios. To address this, we propose FedDDPM-Federated Learning with Denoising Diffusion Probabilistic Models, which leverages the data generative capability of diffusion models to facilitate model training. In particular, the server uses well-trained local diffusion models uploaded by each client before FL training to generate auxiliary data that can approximately represent the global data distribution. Following each round of model aggregation, the server further optimizes the global model using the auxiliary dataset to alleviate the impact of heterogeneous data on model performance. We provide a rigorous convergence analysis of FedDDPM and propose an enhanced algorithm, FedDDPM+, to reduce training overheads. FedDDPM+ detects instances of slow model learning and performs a one-shot correction using the auxiliary dataset. Experimental results validate that our proposed algorithms outperform the state-of-the-art FL algorithms on the MNIST, CIFAR10 and CIFAR100 datasets.

Neighborhood and Global Perturbations Supported SAM in Federated Learning: From Local Tweaks To Global Awareness

Federated Learning (FL) can be coordinated under the orchestration of a central server to collaboratively build a privacy-preserving model without the need for data exchange. However, participant data heterogeneity leads to local optima divergence, subsequently affecting convergence outcomes. Recent research has focused on global sharpness-aware minimization (SAM) and dynamic regularization techniques to enhance consistency between global and local generalization and optimization objectives. Nonetheless, the estimation of global SAM introduces additional computational and memory overhead, while dynamic regularization suffers from bias in the local and global dual variables due to training isolation. In this paper, we propose a novel FL algorithm, FedTOGA, designed to consider optimization and generalization objectives while maintaining minimal uplink communication overhead. By linking local perturbations to global updates, global generalization consistency is improved. Additionally, global updates are used to correct local dynamic regularizers, reducing dual variables bias and enhancing optimization consistency. Global updates are passively received by clients, reducing overhead. We also propose neighborhood perturbation to approximate local perturbation, analyzing its strengths and limitations. Theoretical analysis shows FedTOGA achieves faster convergence $O(1/T)$ under non-convex functions. Empirical studies demonstrate that FedTOGA outperforms state-of-the-art algorithms, with a 1\% accuracy increase and 30\% faster convergence, achieving state-of-the-art.