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Deep learning has made remarkable achievement in many fields. However, learning the parameters of neural networks usually demands a large amount of labeled data. The algorithms of deep learning, therefore, encounter difficulties when…

As deep learning models continue to scale, the growing computational demands have amplified the need for effective coreset selection techniques. Coreset selection aims to accelerate training by identifying small, representative subsets of…

We study the realizability of simplicial complexes with a given pair of integer sequences, representing the node degree distribution and the facet size distribution, respectively. While the $s$-uniform variant of the problem is…

Implicit representations have been widely applied in robotics for obstacle avoidance and path planning. In this paper, we explore the problem of constructing an implicit distance representation from a single image. Past methods for implicit…

Multimodal foundation models can process several modalities. However, since the space of possible modalities is large and evolving over time, training a model from scratch to encompass all modalities is unfeasible. Moreover, integrating a…

With the rise of big data analytics, multi-layer neural networks have surfaced as one of the most powerful machine learning methods. However, their theoretical mathematical properties are still not fully understood. Training a neural…

This paper highlights how unstructured space-time meshes can be used in production engineering applications with moving domains. Unstructured space-time elements can connect different spatial meshes at the bottom and top level of the…

Neural networks can identify low-dimensional relevant structures within high-dimensional noisy data, yet our mathematical understanding of how they do so remains scarce. Here, we investigate the training dynamics of two-layer shallow neural…

In this work, we present a novel approach for general object segmentation from a monocular image, eliminating the need for manually labeled training data and enabling rapid, straightforward training and adaptation with minimal data. Our…

Synthesizing a densely sampled light field from a single image is highly beneficial for many applications. The conventional method reconstructs a depth map and relies on physical-based rendering and a secondary network to improve the…

Geo-distributed ML training can benefit many emerging ML scenarios (e.g., large model training, federated learning) with multi-regional cloud resources and wide area network. However, its efficiency is limited due to 2 challenges. First,…

Deep metric learning has yielded impressive results in tasks such as clustering and image retrieval by leveraging neural networks to obtain highly discriminative feature embeddings, which can be used to group samples into different classes.…

Many tasks in geometry processing are modeled as variational problems solved numerically using the finite element method. For solid shapes, this requires a volumetric discretization, such as a boundary conforming tetrahedral mesh.…

In this work, we propose a federated dynamical low-rank training (FeDLRT) scheme to reduce client compute and communication costs - two significant performance bottlenecks in horizontal federated learning. Our method builds upon dynamical…

Averaging neural network parameters is an intuitive method for fusing the knowledge of two independent models. It is most prominently used in federated learning. If models are averaged at the end of training, this can only lead to a good…

This paper investigates the deep learning optimization problem with softmax cross-entropy loss. We propose a layer separation strategy to alleviate the strong nonconvexity encountered during training deep networks. For cross-entropy models…

We present Submatrix-wise Vector Embedding Learner (Swivel), a method for generating low-dimensional feature embeddings from a feature co-occurrence matrix. Swivel performs approximate factorization of the point-wise mutual information…

In this article, we present an efficient deep learning method called coupled deep neural networks (CDNNs) for coupled physical problems. Our method compiles the interface conditions of the coupled PDEs into the networks properly and can be…

This work presents the application of a recently developed parametric, non-intrusive, and multi-fidelity reduced-order modeling method on high-dimensional displacement and stress fields arising from the structural analysis of geometries…

Cross-modality magnetic resonance (MR) image synthesis can be used to generate missing modalities from given ones. Existing (supervised learning) methods often require a large number of paired multi-modal data to train an effective…