Simple, fast, and flexible framework for matrix completion with infinite width neural networks.

Area of Science:

• Machine Learning
• Computational Science

Background:

• Matrix completion is crucial for recommendation systems, computer vision, and genomics.
• Large neural networks offer performance but incur high computational costs.

Purpose of the Study:

• To develop a computationally efficient and flexible infinite width neural network framework for matrix completion.
• To explore the connection between infinite width neural networks and neural tangent kernels (NTK).

Main Methods:

• Derived neural tangent kernels (NTK) for fully connected and convolutional neural networks in matrix completion.
• Incorporated a feature prior for encoding relationships between matrix coordinates, similar to semisupervised learning.

Main Results:

• Demonstrated competitive results in virtual drug screening and image inpainting/reconstruction.
• Achieved improved computational performance by taking neural network width to infinity.

Conclusions:

• The infinite width neural network framework offers a simple, fast, and flexible solution for matrix completion.
• The framework is accessible via a Python implementation for broad use on standard hardware.