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Simple, Fast, and Flexible Framework for Matrix Completion with Infinite Width Neural Networks
TLDR
In this paper, the authors developed an infinite width neural network framework for matrix completion that is simple, fast, and flexible, which is based on the connection between the infinite width limit of neural networks and kernels known as neural tangent kernels (NTK).Abstract:
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.read more
Citations
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Journal ArticleDOI
Extrapolating missing antibody-virus measurements across serological studies.
Tal Einav,Brian Cleary +1 more
TL;DR: The authors applied matrix completion to several large-scale influenza and HIV-1 studies and explored how prediction accuracy evolves as the number of measurements changes and approximated the number required in several highly incomplete datasets (suggesting ∼250,000 measurements could be saved).
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Wide and Deep Neural Networks Achieve Optimality for Classification
TL;DR: This work identifies and constructs an explicit set of neural network classifiers that achieve optimality and creates a taxonomy of in-nitely wide and deep networks and shows that these models implement one of three well-known classi fier depending on the activation function used.
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