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24 June 2024
 
  » arxiv » 2302.00328

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Learning Functional Transduction
Mathieu Chalvidal ; Thomas Serre ; Rufin VanRullen ;
Date 1 Feb 2023
AbstractResearch in Machine Learning has polarized into two general regression approaches: Transductive methods derive estimates directly from available data but are usually problem unspecific. Inductive methods can be much more particular, but generally require tuning and compute-intensive searches for solutions. In this work, we adopt a hybrid approach: We leverage the theory of Reproducing Kernel Banach Spaces (RKBS) and show that transductive principles can be induced through gradient descent to form efficient extit{in-context} neural approximators. We apply this approach to RKBS of function-valued operators and show that once trained, our extit{Transducer} model can capture on-the-fly relationships between infinite-dimensional input and output functions, given a few example pairs, and return new function estimates. We demonstrate the benefit of our transductive approach to model complex physical systems influenced by varying external factors with little data at a fraction of the usual deep learning training computation cost for partial differential equations and climate modeling applications.
Source arXiv, 2302.00328
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