Related papers: Simple, Fast, and Flexible Framework for Matrix Co…

We generalize the fractional packing framework of Garg and Koenemann to the case of linear fractional packing problems over polyhedral cones. More precisely, we provide approximation algorithms for problems of the form $\max\{c^T x : Ax…

A code completion system suggests future code elements to developers given a partially-complete code snippet. Code completion is one of the most useful features in Integrated Development Environments (IDEs). Currently, most code completion…

Time cost is a major challenge in achieving high-quality pluralistic image completion. Recently, the Retentive Network (RetNet) in natural language processing offers a novel approach to this problem with its low-cost inference capabilities.…

Data with low-dimensional nonlinear structure are ubiquitous in engineering and scientific problems. We study a model problem with such structure -- a binary classification task that uses a deep fully-connected neural network to classify…

We propose a general framework for solving forward and inverse problems constrained by partial differential equations, where we interpolate neural networks onto finite element spaces to represent the (partial) unknowns. The framework…

A rising trend in theoretical deep learning is to understand why deep learning works through Neural Tangent Kernel (NTK) [jgh18], a kernel method that is equivalent to using gradient descent to train a multi-layer infinitely-wide neural…

Graph Neural Networks (GNNs) have made significant advances on several fundamental inference tasks. As a result, there is a surge of interest in using these models for making potentially important decisions in high-regret applications.…

While kernel methods and Graph Neural Networks offer complementary strengths, integrating the two has posed challenges in efficiency and scalability. The Graph Neural Tangent Kernel provides a theoretical bridge by interpreting GNNs through…

Modern neural networks are often regarded as complex black-box functions whose behavior is difficult to understand owing to their nonlinear dependence on the data and the nonconvexity in their loss landscapes. In this work, we show that…

Matrix operations (e.g., inversion and singular value decomposition (SVD)) are fundamental in science and engineering. In many emerging real-world applications (such as wireless communication and signal processing), these operations must be…

In wireless communications, estimation of channels in OFDM systems spans frequency and time, which relies on sparse collections of pilot data, posing an ill-posed inverse problem. Moreover, deep learning estimators require large amounts of…

The problem of completing a low-rank matrix from a subset of its entries is often encountered in the analysis of incomplete data sets exhibiting an underlying factor model with applications in collaborative filtering, computer vision and…

There has been significant research over the past two decades in developing new platforms for spiking neural computation. Current neural computers are primarily developed to mimick biology. They use neural networks which can be trained to…

We study training one-hidden-layer ReLU networks in the neural tangent kernel (NTK) regime, where the networks' biases are initialized to some constant rather than zero. We prove that under such initialization, the neural network will have…

Leveraging the infinite dimensional neural network architecture we proposed in arXiv:2109.13512v4 and which can process inputs from Fr\'echet spaces, and using the universal approximation property shown therein, we now largely extend the…

Catastrophic forgetting is one of the fundamental issues of continual learning because neural networks forget the tasks learned previously when trained on new tasks. The proposed framework is a new path-coordinated framework of continual…

Matrix completion is a classical problem in data science wherein one attempts to reconstruct a low-rank matrix while only observing some subset of the entries. Previous authors have phrased this problem as a nuclear norm minimization…

Neural tangent kernels (NTKs) provide a theoretical regime to analyze the learning and generalization behavior of over-parametrized neural networks. For a supervised learning task, the association between the eigenvectors of the NTK kernel…

Firms earning prediction plays a vital role in investment decisions, dividends expectation, and share price. It often involves multiple tensor-compatible datasets with non-linear multi-way relationships, spatiotemporal structures, and…

Certifying the safety or robustness of neural networks against input uncertainties and adversarial attacks is an emerging challenge in the area of safe machine learning and control. To provide such a guarantee, one must be able to bound the…