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This paper proposes a proximal variant of the alternating direction method of multipliers (ADMM) for distributed optimization. Although the current versions of ADMM algorithm provide promising numerical results in producing solutions that are close to optimal for many convex and non-convex optimization problems, it remains unclear if they can converge to a stationary point for weakly convex and locally non-smooth functions. Through our analysis using the Moreau envelope function, we demonstrate that MADM can indeed converge to a stationary point under mild conditions. Our analysis also includes computing the bounds on the amount of change in the dual variable update step by relating the gradient of the Moreau envelope function to the proximal function. Furthermore, the results of our numerical experiments indicate that our method is faster and more robust than widely-used approaches.

This paper addresses the problem of localization, which is inherently non-convex and non-smooth in a federated setting where the data is distributed across a multitude of devices. Due to the decentralized nature of federated environments, distributed learning becomes essential for scalability and adaptability. Moreover, these environments are often plagued by outlier data, which presents substantial challenges to conventional methods, particularly in maintaining estimation accuracy and ensuring algorithm convergence. To mitigate these challenges, we propose a method that adopts an $L_1$-norm robust formulation within a distributed sub-gradient framework, explicitly designed to handle these obstacles. Our approach addresses the problem in its original form, without resorting to iterative simplifications or approximations, resulting in enhanced computational efficiency and improved estimation accuracy. We demonstrate that our method converges to a stationary point, highlighting its effectiveness and reliability. Through numerical simulations, we confirm the superior performance of our approach, notably in outlier-rich environments, which surpasses existing state-of-the-art localization methods.

Auditability allows to track all the read operations performed on a register. It abstracts the need of data owners to control access to their data, tracking who read which information. This work considers possible formalizations of auditing and their ramification for the possibility of providing it. The natural definition is to require a linearization of all write, read and audit operations together (atomic auditing). The paper shows that atomic auditing is a powerful tool, as it can be used to solve consensus. The number of processes that can solve consensus using atomic audit depends on the number of processes that can read or audit the register. If there is a single reader or a single auditor (the writer), then consensus can be solved among two processes. If multiple readers and auditors are possible, then consensus can be solved among the same number of processes. This means that strong synchronization primitives are needed to support atomic auditing. We give implementations of atomic audit when there are either multiple readers or multiple auditors (but not both) using primitives with consensus number 2 (swap and fetch&add). When there are multiple readers and multiple auditors, the implementation uses compare&swap. These findings motivate a weaker definition, in which audit operations are not linearized together with the write and read operations (regular auditing). We prove that regular auditing can be implemented from ordinary reads and writes on atomic registers.

In Chinese text recognition, to compensate for the insufficient local data and improve the performance of local few-shot character recognition, it is often necessary for one organization to collect a large amount of data from similar organizations. However, due to the natural presence of private information in text data, such as addresses and phone numbers, different organizations are unwilling to share private data. Therefore, it becomes increasingly important to design a privacy-preserving collaborative training framework for the Chinese text recognition task. In this paper, we introduce personalized federated learning (pFL) into the Chinese text recognition task and propose the pFedCR algorithm, which significantly improves the model performance of each client (organization) without sharing private data. Specifically, pFedCR comprises two stages: multiple rounds of global model training stage and the the local personalization stage. During stage 1, an attention mechanism is incorporated into the CRNN model to adapt to various client data distributions. Leveraging inherent character data characteristics, a balanced dataset is created on the server to mitigate character imbalance. In the personalization phase, the global model is fine-tuned for one epoch to create a local model. Parameter averaging between local and global models combines personalized and global feature extraction capabilities. Finally, we fine-tune only the attention layers to enhance its focus on local personalized features. The experimental results on three real-world industrial scenario datasets show that the pFedCR algorithm can improve the performance of local personalized models by about 20\% while also improving their generalization performance on other client data domains. Compared to other state-of-the-art personalized federated learning methods, pFedCR improves performance by 6\% $\sim$ 8\%.

This paper presents efficient algorithms, designed to leverage SIMD for performing Montgomery reductions and additions on integers larger than 512 bits. The existing algorithms encounter inefficiencies when parallelized using SIMD due to extensive dependencies in both operations, particularly noticeable in costly operations like ARM's SVE. To mitigate this problem, a novel addition algorithm is introduced that simulates the addition of large integers using a smaller addition, quickly producing the same set of carries. These carries are then utilized to perform parallel additions on large integers. For Montgomery reductions, serial multiplications are replaced with precomputations that can be effectively calculated using SIMD extensions. Experimental evidence demonstrates that these proposed algorithms substantially enhance the performance of state-of-the-art implementations of several post-quantum cryptography algorithms. Notably, they deliver a 30% speed-up from the latest CTIDH implementation, an 11% speed-up from the latest CSIDH implementation in AVX-512 processors, and a 7% speed-up from Microsoft's standard PQCrypto-SIDH for SIKEp503 on A64FX.

Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation.

Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation or neither of these. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.

Relation prediction for knowledge graphs aims at predicting missing relationships between entities. Despite the importance of inductive relation prediction, most previous works are limited to a transductive setting and cannot process previously unseen entities. The recent proposed subgraph-based relation reasoning models provided alternatives to predict links from the subgraph structure surrounding a candidate triplet inductively. However, we observe that these methods often neglect the directed nature of the extracted subgraph and weaken the role of relation information in the subgraph modeling. As a result, they fail to effectively handle the asymmetric/anti-symmetric triplets and produce insufficient embeddings for the target triplets. To this end, we introduce a \textbf{C}\textbf{o}mmunicative \textbf{M}essage \textbf{P}assing neural network for \textbf{I}nductive re\textbf{L}ation r\textbf{E}asoning, \textbf{CoMPILE}, that reasons over local directed subgraph structures and has a vigorous inductive bias to process entity-independent semantic relations. In contrast to existing models, CoMPILE strengthens the message interactions between edges and entitles through a communicative kernel and enables a sufficient flow of relation information. Moreover, we demonstrate that CoMPILE can naturally handle asymmetric/anti-symmetric relations without the need for explosively increasing the number of model parameters by extracting the directed enclosing subgraphs. Extensive experiments show substantial performance gains in comparison to state-of-the-art methods on commonly used benchmark datasets with variant inductive settings.

Label Propagation (LPA) and Graph Convolutional Neural Networks (GCN) are both message passing algorithms on graphs. Both solve the task of node classification but LPA propagates node label information across the edges of the graph, while GCN propagates and transforms node feature information. However, while conceptually similar, theoretical relation between LPA and GCN has not yet been investigated. Here we study the relationship between LPA and GCN in terms of two aspects: (1) feature/label smoothing where we analyze how the feature/label of one node is spread over its neighbors; And, (2) feature/label influence of how much the initial feature/label of one node influences the final feature/label of another node. Based on our theoretical analysis, we propose an end-to-end model that unifies GCN and LPA for node classification. In our unified model, edge weights are learnable, and the LPA serves as regularization to assist the GCN in learning proper edge weights that lead to improved classification performance. Our model can also be seen as learning attention weights based on node labels, which is more task-oriented than existing feature-based attention models. In a number of experiments on real-world graphs, our model shows superiority over state-of-the-art GCN-based methods in terms of node classification accuracy.

This paper proposes a method to modify traditional convolutional neural networks (CNNs) into interpretable CNNs, in order to clarify knowledge representations in high conv-layers of CNNs. In an interpretable CNN, each filter in a high conv-layer represents a certain object part. We do not need any annotations of object parts or textures to supervise the learning process. Instead, the interpretable CNN automatically assigns each filter in a high conv-layer with an object part during the learning process. Our method can be applied to different types of CNNs with different structures. The clear knowledge representation in an interpretable CNN can help people understand the logics inside a CNN, i.e., based on which patterns the CNN makes the decision. Experiments showed that filters in an interpretable CNN were more semantically meaningful than those in traditional CNNs.