Learning Functional Transduction

• URL: http://arxiv.org/abs/2302.00328v2
• Date: Thu, 18 May 2023 14:34:02 GMT
• Title: Learning Functional Transduction
• Authors: Mathieu Chalvidal, Thomas Serre and Rufin VanRullen
• Abstract summary: We show that transductive regression principles can be meta-learned through gradient descent to form efficient in-context neural approximators. We demonstrate the benefit of our meta-learned transductive approach to model complex physical systems influenced by varying external factors with little data.
• Score: 9.926231893220063
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Research in machine learning has polarized into two general approaches for regression tasks: Transductive methods construct estimates directly from available data but are usually problem unspecific. Inductive methods can be much more specific but generally require compute-intensive solution searches. In this work, we propose a hybrid approach and show that transductive regression principles can be meta-learned through gradient descent to form efficient in-context neural approximators by leveraging the theory of vector-valued Reproducing Kernel Banach Spaces (RKBS). We apply this approach to function spaces defined over finite and infinite-dimensional spaces (function-valued operators) and show that once trained, the Transducer can almost instantaneously capture an infinity of functional relationships given a few pairs of input and output examples and return new image estimates. We demonstrate the benefit of our meta-learned transductive approach to model complex physical systems influenced by varying external factors with little data at a fraction of the usual deep learning training computational cost for partial differential equations and climate modeling applications.

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