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This paper proposes a general machine learning framework called the localization method, which is fundamentally built on two core concepts: localization kernels and local means -- key components that underpin the self-attention mechanism. To establish a rigorous theoretical foundation, the framework is formally defined through two essential pillars: the formulation of the local(-ized) model and the localization trick. We systematically investigate the connections between the localization method and a wide range of existing machine learning models/methods, including (but not limited to) kernel methods, lazy learning, the MeanShift algorithm, relaxation labeling, Hopfield networks, local linear embedding (LLE), fuzzy inference, and denoising autoencoders (DAEs). By dissecting these relationships, we clarify the broader theoretical significance of the localization method and demonstrate its practical applicability across diverse machine learning tasks. Furthermore, we explore advanced extensions of the framework, such as adaptive kernels, hierarchical local models, and non-local models. Notably, we show that the Transformer -- a cornerstone of modern sequence modeling -- can be constructed using hierarchical local models, revealing the ability of the localization method to unify and generalize state-of-the-art architectures. This work not only provides a unified theoretical lens to reinterpret existing models but also offers new methodological tools for designing flexible, data-adaptive learning systems.

Out-of-distribution (OOD) detection and lossless compression constitute two problems that can be solved by the training of probabilistic models on a first dataset with subsequent likelihood evaluation on a second dataset, where data distributions differ. By defining the generalization of probabilistic models in terms of likelihood we show that, in the case of image models, the OOD generalization ability is dominated by local features.

Federated Learning (FL) is a prevalent machine learning paradigm designed to address challenges posed by heterogeneous client data while preserving data privacy. Unlike distributed training, it typically orchestrates resource-constrained edge devices to communicate via a low-bandwidth communication network with a central server. This urges the development of more computation and communication efficient training algorithms. In this paper, we propose an efficient FL paradigm, where the local models in the clients are trained with low-precision operations and communicated with the server in low precision format, while only the model aggregation in the server is performed with high-precision computation. We surprisingly find that high precision models can be recovered from the low precision local models with proper aggregation in the server.

Efficiently aggregating trained neural networks from local clients into a global model on a server is a widely researched topic in federated learning. Recently, motivated by diminishing privacy concerns, mitigating potential attacks, and reducing communication overhead, one-shot federated learning (i.e., limiting client-server communication into a single round) has gained popularity among researchers. However, the one-shot aggregation performances are sensitively affected by the non-identical training data distribution, which exhibits high statistical heterogeneity in some real-world scenarios. To address this issue, we propose a novel one-shot aggregation method with layer-wise posterior aggregation, named FedLPA. FedLPA aggregates local models to obtain a more accurate global model without requiring extra auxiliary datasets or exposing any private label information, e.g., label distributions. To effectively capture the statistics maintained in the biased local datasets in the practical non-IID scenario, we efficiently infer the posteriors of each layer in each local model using layer-wise Laplace approximation and aggregate them to train the global parameters. Extensive experimental results demonstrate that FedLPA significantly improves learning performance over state-of-the-art methods across several metrics.

Federated learning (FL) has emerged as a prominent machine learning paradigm in edge computing environments, enabling edge devices to collaboratively optimize a global model without sharing their private data. However, existing FL frameworks suffer from efficacy deterioration due to the system heterogeneity inherent in edge computing, especially in the presence of domain shifts across local data. In this paper, we propose a heterogeneous FL framework DapperFL, to enhance model performance across multiple domains. In DapperFL, we introduce a dedicated Model Fusion Pruning (MFP) module to produce personalized compact local models for clients to address the system heterogeneity challenges. The MFP module prunes local models with fused knowledge obtained from both local and remaining domains, ensuring robustness to domain shifts.