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The potential of neural networks (NN) in engineering is rooted in their capacity to understand intricate patterns and complex systems, leveraging their universal nonlinear approximation capabilities and high expressivity. Meanwhile,…

Structured Prediction Energy Networks (SPENs) are a simple, yet expressive family of structured prediction models (Belanger and McCallum, 2016). An energy function over candidate structured outputs is given by a deep network, and…

For the past 30 years or so, machine learning has stimulated a great deal of research in the study of approximation capabilities (expressive power) of a multitude of processes, such as approximation by shallow or deep neural networks,…

Recent studies have shown that aggregating convolutional features of a pre-trained Convolutional Neural Network (CNN) can obtain impressive performance for a variety of visual tasks. The symmetric Positive Definite (SPD) matrix becomes a…

The kernel embedding algorithm is an important component for adapting kernel methods to large datasets. Since the algorithm consumes a major computation cost in the testing phase, we propose a novel teacher-learner framework of learning…

In this work, we propose a balanced multi-component and multi-layer neural network (MMNN) structure to accurately and efficiently approximate functions with complex features, in terms of both degrees of freedom and computational cost. The…

The single-hidden-layer Randomly Weighted Feature Network (RWFN) introduced by Hong and Pavlic (2021) was developed as an alternative to neural tensor network approaches for relational learning tasks. Its relatively small footprint combined…

Sum-Product Networks (SPNs) are a class of expressive yet tractable hierarchical graphical models. LearnSPN is a structure learning algorithm for SPNs that uses hierarchical co-clustering to simultaneously identifying similar entities and…

We propose a hybrid architecture composed of a fully convolutional network (FCN) and a Dempster-Shafer layer for image semantic segmentation. In the so-called evidential FCN (E-FCN), an encoder-decoder architecture first extracts pixel-wise…

Coupled multiphysics simulations for high-dimensional, large-scale problems can be prohibitively expensive due to their computational demands. This article presents a novel framework integrating a deep operator network (DeepONet) with the…

Traditional methods for tabular classification usually rely on supervised learning from scratch, which requires extensive training data to determine model parameters. However, a novel approach called Prior-Data Fitted Networks (TabPFN) has…

We present a deep layered architecture that generalizes convolutional neural networks (ConvNets). The architecture, called SimNets, is driven by two operators: (i) a similarity function that generalizes inner-product, and (ii) a…

Convolutional Neural Networks (CNNs) have been widely employed for image Super-Resolution (SR) in recent years. Various techniques enhance SR performance by altering CNN structures or incorporating improved self-attention mechanisms.…

In the intelligent communication field, deep learning (DL) has attracted much attention due to its strong fitting ability and data-driven learning capability. Compared with the typical DL feedforward network structures, an enhancement…

Federated learning is a distributed learning framework that allows a set of clients to collaboratively train a model under the orchestration of a central server, without sharing raw data samples. Although in many practical scenarios the…

We show that every piecewise linear function $f:R^d \to R$ with compact support a polyhedron $P$ has a representation as a sum of so-called `simplex functions'. Such representations arise from degree 1 triangulations of the relative…

In this paper, we address the design of lightweight deep learning-based edge detection. The deep learning technology offers a significant improvement on the edge detection accuracy. However, typical neural network designs have very high…

We present the first rigorous convergence analysis of the smoothed adaptive finite element method (S-AFEM) proposed in [Mulita, Giani, Heltai: SIAM J. Sci. Comput. 43, 2021]. S-AFEM modifies the classical adaptive finite element method…

Lightweight neural networks for single-image super-resolution (SISR) tasks have made substantial breakthroughs in recent years. Compared to low-frequency information, high-frequency detail is much more difficult to reconstruct. Most SISR…

Graph neural networks (GNNs) naturally align with sparse operators and unstructured discretizations, making them a promising paradigm for physics-informed machine learning in computational mechanics. Motivated by discrete physics losses and…