相关论文: Simple, Fast, and Flexible Framework for Matrix Co…

The matrix completion problem aims to reconstruct a low-rank matrix based on a revealed set of possibly noisy entries. Prior works consider completing the entire matrix with generalization error guarantees. However, the completion accuracy…

Recent work by Jacot et al. (2018) has shown that training a neural network using gradient descent in parameter space is related to kernel gradient descent in function space with respect to the Neural Tangent Kernel (NTK). Lee et al. (2019)…

Model Reprogramming (MR) is a resource-efficient framework that adapts large pre-trained models to new tasks with minimal additional parameters and data, offering a promising solution to the challenges of training large models for diverse…

Code completion is one of the most widely used features of modern integrated development environments (IDEs). While deep learning has made significant progress in the statistical prediction of source code, state-of-the-art neural network…

Using tools from topology and functional analysis, we provide a framework where artificial neural networks, and their architectures, can be formally described. We define the notion of machine in a general topological context and show how…

In this paper, we study the popularly dubbed matrix completion problem, where the task is to "fill in" the unobserved entries of a matrix from a small subset of observed entries, under the assumption that the underlying matrix is of…

The Neural Tangent Kernel (NTK) framework explains optimization in over-parameterized neural networks via approximately linearized dynamics, yielding exponential convergence guarantees. However, existing results are often overly pessimistic…

We prove that a randomly initialized neural network of *any architecture* has its Tangent Kernel (NTK) converge to a deterministic limit, as the network widths tend to infinity. We demonstrate how to calculate this limit. In prior…

The universality of a quantum neural network refers to its ability to approximate arbitrary functions and is a theoretical guarantee for its effectiveness. A non-universal neural network could fail in completing the machine learning task.…

Matrix completion has received vast amount of attention and research due to its wide applications in various study fields. Existing methods of matrix completion consider only nonlinear (or linear) relations among entries in a data matrix…

Gradient descent yields zero training loss in polynomial time for deep neural networks despite non-convex nature of the objective function. The behavior of network in the infinite width limit trained by gradient descent can be described by…

It is the main goal of this paper to propose a novel method to perform matrix completion on-line. Motivated by a wide variety of applications, ranging from the design of recommender systems to sensor network localization through seismic…

It is well understood that neural networks with carefully hand-picked weights provide powerful function approximation and that they can be successfully trained in over-parametrized regimes. Since over-parametrization ensures zero training…

Despite the success of the Sylvester equation empowered methods on various graph mining applications, such as semi-supervised label learning and network alignment, there also exists several limitations. The Sylvester equation's inability of…

Larger and deeper networks generalise well despite their increased capacity to overfit. Understanding why this happens is theoretically and practically important. One recent approach looks at the infinitely wide limits of such networks and…

Matrix completion is a problem that arises in many data-analysis settings where the input consists of a partially-observed matrix (e.g., recommender systems, traffic matrix analysis etc.). Classical approaches to matrix completion assume…

Ternary Neural Networks (TNNs) have received much attention due to being potentially orders of magnitude faster in inference, as well as more power efficient, than full-precision counterparts. However, 2 bits are required to encode the…

The layered structure of deep neural networks hinders the use of numerous analysis tools and thus the development of its interpretability. Inspired by the success of functional brain networks, we propose a novel framework for…

Previous work has cast doubt on the general framework of uniform convergence and its ability to explain generalization in neural networks. By considering a specific dataset, it was observed that a neural network completely misclassifies a…

Mixed-precision Deep Neural Networks achieve the energy efficiency and throughput needed for hardware deployment, particularly when the resources are limited, without sacrificing accuracy. However, the optimal per-layer bit precision that…