One of the most common methods to train machine learning algorithms today is the stochastic gradient descent (SGD). In a distributed setting, SGD-based algorithms have been shown to converge theoretically under specific circumstances. A substantial number of works in the distributed SGD setting assume a fixed topology for the edge devices. These papers also assume that the contribution of nodes to the global model is uniform. However, experiments have shown that such assumptions are suboptimal and a non uniform aggregation strategy coupled with a dynamically shifting topology and client selection can significantly improve the performance of such models. This paper details a unified framework that covers several Local-Update SGD-based distributed algorithms with dynamic topologies and provides improved or matching theoretical guarantees on convergence compared to existing work.

Neural control variates (NCVs) have emerged as a powerful tool for variance reduction in Monte Carlo (MC) simulations, particularly in high-dimensional problems where traditional control variates are difficult to construct analytically. By training neural networks to learn auxiliary functions correlated with the target observable, NCVs can significantly reduce estimator variance while preserving unbiasedness. However, a critical but often overlooked aspect of NCV training is the role of autocorrelated samples generated by Markov Chain Monte Carlo (MCMC). While such samples are typically discarded for error estimation due to their statistical redundancy, they may contain useful information about the structure of the underlying probability distribution that can benefit the training process. In this work, we systematically examine the effect of using correlated configurations in training neural control variates. We demonstrate, both conceptually and numerically, that training on correlated data can improve control variate performance, especially in settings with limited computational resources. Our analysis includes empirical results from $U(1)$ gauge theory and scalar field theory, illustrating when and how autocorrelated samples enhance NCV construction. These findings provide practical guidance for the efficient use of MCMC data in training neural networks.

In the era of big data, data mining has become indispensable for uncovering hidden patterns and insights from vast and complex datasets. The integration of multimodal data sources further enhances its potential. Multimodal Federated Learning (MFL) is a distributed approach that enhances the efficiency and quality of multimodal learning, ensuring collaborative work and privacy protection. However, missing modalities pose a significant challenge in MFL, often due to data quality issues or privacy policies across the clients. In this work, we present MMiC, a framework for Mitigating Modality incompleteness in MFL within the Clusters. MMiC replaces partial parameters within client models inside clusters to mitigate the impact of missing modalities. Furthermore, it leverages the Banzhaf Power Index to optimize client selection under these conditions. Finally, MMiC employs an innovative approach to dynamically control global aggregation by utilizing Markovitz Portfolio Optimization. Extensive experiments demonstrate that MMiC consistently outperforms existing federated learning architectures in both global and personalized performance on multimodal datasets with missing modalities, confirming the effectiveness of our proposed solution. Our code is available at https://github.com/gotobcn8/MMiC.

We propose an efficient hybrid least squares/gradient descent method to accelerate DeepONet training. Since the output of DeepONet can be viewed as linear with respect to the last layer parameters of the branch network, these parameters can be optimized using a least squares (LS) solve, and the remaining hidden layer parameters are updated by means of gradient descent form. However, building the LS system for all possible combinations of branch and trunk inputs yields a prohibitively large linear problem that is infeasible to solve directly. To address this issue, our method decomposes the large LS system into two smaller, more manageable subproblems $\unicode{x2014}$ one for the branch network and one for the trunk network $\unicode{x2014}$ and solves them separately. This method is generalized to a broader type of $L^2$ loss with a regularization term for the last layer parameters, including the case of unsupervised learning with physics-informed loss.

In this study, we present an Evolving Fuzzy System within the context of Federated Learning, which adapts dynamically with the addition of new clusters and therefore does not require the number of clusters to be selected apriori. Unlike traditional methods, Federated Learning allows models to be trained locally on clients' devices, sharing only the model parameters with a central server instead of the data. Our method, implemented using PyTorch, was tested on clustering and classification tasks. The results show that our approach outperforms established classification methods on several well-known UCI datasets. While computationally intensive due to overlap condition calculations, the proposed method demonstrates significant advantages in decentralized data processing.

Facial landmark detection is an important task in computer vision with numerous applications, such as head pose estimation, expression analysis, face swapping, etc. Heatmap regression-based methods have been widely used to achieve state-of-the-art results in this task. These methods involve computing the argmax over the heatmaps to predict a landmark. Since argmax is not differentiable, these methods use a differentiable approximation, Soft-argmax, to enable end-to-end training on deep-nets. In this work, we revisit this long-standing choice of using Soft-argmax and demonstrate that it is not the only way to achieve strong performance. Instead, we propose an alternative training objective based on the classic structured prediction framework. Empirically, our method achieves state-of-the-art performance on three facial landmark benchmarks (WFLW, COFW, and 300W), converging 2.2x faster during training while maintaining better/competitive accuracy. Our code is available here: https://github.com/ca-joe-yang/regression-without-softarg.

Neural Information Processing Systems http://nips.cc/

Graphical models are a very useful tool to describe and understand natural phenomena, from gene expression to climate change and social interactions. The topological structure of these graphs/networks is a fundamental part of the analysis, and in many cases the main goal of the study. However, little work has been done on incorporating prior topological knowledge onto the estimation of the underlying graphical models from sample data. In this work we propose extensions to the basic joint regression model for network estimation, which explicitly incorporate graph-topological constraints into the corresponding optimization approach. The first proposed extension includes an eigenvector centrality constraint, thereby promoting this important prior topological property. The second developed extension promotes the formation of certain motifs, triangle-shaped ones in particular, which are known to exist for example in genetic regulatory networks. The presentation of the underlying formulations, which serve as examples of the introduction of topological constraints in network estimation, is complemented with examples in diverse datasets demonstrating the importance of incorporating such critical prior knowledge.