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

The prevailing thinking is that orthogonal weights are crucial to enforcing dynamical isometry and speeding up training. The increase in learning speed that results from orthogonal initialization in linear networks has been well-proven.…

Conventional matrix completion methods approximate the missing values by assuming the matrix to be low-rank, which leads to a linear approximation of missing values. It has been shown that enhanced performance could be attained by using…

The neural tangent kernel (NTK) has garnered significant attention as a theoretical framework for describing the behavior of large-scale neural networks. Kernel methods are theoretically well-understood and as a result enjoy algorithmic…

A convergence analysis is developed for the regularized Newton method for training neural networks (NNs) in the overparameterized limit. As the number of hidden units tends to infinity, the NN training dynamics converge in probability to…

The inductive biases of trained neural networks are difficult to understand and, consequently, to adapt to new settings. We study the inductive biases of linearizations of neural networks, which we show to be surprisingly good summaries of…

We propose a totally functional view of geometric matrix completion problem. Differently from existing work, we propose a novel regularization inspired from the functional map literature that is more interpretable and theoretically sound.…

Recent theoretical work has established connections between over-parametrized neural networks and linearized models governed by he Neural Tangent Kernels (NTKs). NTK theory leads to concrete convergence and generalization results, yet the…

Matrix completion is the problem of recovering a low rank matrix by observing a small fraction of its entries. A series of recent works [KOM12,JNS13,HW14] have proposed fast non-convex optimization based iterative algorithms to solve this…

Given the complexity of genetic risk prediction, there is a critical need for the development of novel methodologies that can effectively capture intricate genotype--phenotype relationships (e.g., nonlinear) while remaining statistically…

Recent works have examined theoretical and empirical properties of wide neural networks trained in the Neural Tangent Kernel (NTK) regime. Given that biological neural networks are much wider than their artificial counterparts, we consider…

The Neural Tangent Kernel (NTK) has discovered connections between deep neural networks and kernel methods with insights of optimization and generalization. Motivated by this, recent works report that NTK can achieve better performances…

A primary advantage of neural networks lies in their feature learning characteristics, which is challenging to theoretically analyze due to the complexity of their training dynamics. We propose a new paradigm for studying feature learning…

The ``Neural Tangent Kernel'' (NTK) (Jacot et al 2018), and its empirical variants have been proposed as a proxy to capture certain behaviors of real neural networks. In this work, we study NTKs through the lens of scaling laws, and…

This work analyzes Graph Neural Networks, a generalization of Fully-Connected Deep Neural Nets on Graph structured data, when their width, that is the number of nodes in each fullyconnected layer is increasing to infinity. Infinite Width…

Sparse neural networks promise efficiency, yet training them effectively remains a fundamental challenge. Despite advances in pruning methods that create sparse architectures, understanding why some sparse structures are better trainable…

Matrix Completion is the problem of recovering an unknown real-valued low-rank matrix from a subsample of its entries. Important recent results show that the problem can be solved efficiently under the assumption that the unknown matrix is…

This work studies the neural tangent kernel (NTK) of the deep equilibrium (DEQ) model, a practical ``infinite-depth'' architecture which directly computes the infinite-depth limit of a weight-tied network via root-finding. Even though the…

Matrix completion is a fundamental problem that comes up in a variety of applications like the Netflix problem, collaborative filtering, computer vision, and crowdsourcing. The goal of the problem is to recover a k-by-n unknown matrix from…

The study of deep neural networks (DNNs) in the infinite-width limit, via the so-called neural tangent kernel (NTK) approach, has provided new insights into the dynamics of learning, generalization, and the impact of initialization. One key…

The inherent diversity of computation types within the deep neural network (DNN) models often requires a variety of specialized units in hardware processors, which limits computational efficiency, increasing both inference latency and power…