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Matrix completion problems arise in many applications includingrecommendation systems, computer vision, and genomics. Increasingly largerneural networks have been successful in many of these applications, but atconsiderable computational costs. Remarkably, taking the width of a neuralnetwork to infinity allows for improved computational performance. In thiswork, we develop an infinite width neural network framework for matrixcompletion that is simple, fast, and flexible. Simplicity and speed come fromthe connection between the infinite width limit of neural networks and kernelsknown as neural tangent kernels (NTK). In particular, we derive the NTK forfully connected and convolutional neural networks for matrix completion. Theflexibility stems from a feature prior, which allows encoding relationshipsbetween coordinates of the target matrix, akin to semi-supervised learning. Theeffectiveness of our framework is demonstrated through competitive results forvirtual drug screening and image inpainting/reconstruction. We also provide animplementation in Python to make our framework accessible on standard hardwareto a broad audience.

Simple, Fast, and Flexible Framework for Matrix Completion with Infinite Width Neural Networks