Simple, Fast, and Flexible Framework for Matrix Completion with Infinite Width Neural Networks
This work addresses matrix completion for applications like recommendation systems and genomics, offering a faster and more flexible method, though it is incremental as it builds on existing neural tangent kernel theory.
The authors tackled matrix completion problems, such as in drug screening and image inpainting, by developing an infinite width neural network framework based on neural tangent kernels, achieving competitive results in these applications.
Matrix completion problems arise in many applications including recommendation systems, computer vision, and genomics. Increasingly larger neural networks have been successful in many of these applications, but at considerable computational costs. Remarkably, taking the width of a neural network to infinity allows for improved computational performance. In this work, we develop an infinite width neural network framework for matrix completion that is simple, fast, and flexible. Simplicity and speed come from the connection between the infinite width limit of neural networks and kernels known as neural tangent kernels (NTK). In particular, we derive the NTK for fully connected and convolutional neural networks for matrix completion. The flexibility stems from a feature prior, which allows encoding relationships between coordinates of the target matrix, akin to semi-supervised learning. The effectiveness of our framework is demonstrated through competitive results for virtual drug screening and image inpainting/reconstruction. We also provide an implementation in Python to make our framework accessible on standard hardware to a broad audience.