Frequency Decomposition in Neural Processes

Jens Petersen, Paul F Jaeger, Gregor Koehler, David Zimmerer, Fabian Isensee, Klaus Maier-Hein

Abstract: Neural Processes are a powerful tool for learning representations of function spaces purely from examples, in a way that allows them to perform predictions at test time conditioned on so-called context observations. The learned representations are finite-dimensional, while function spaces are infinite-dimensional, and so far it has been unclear how these representations are learned and what kinds of functions can be represented. We show that deterministic Neural Processes implicitly perform a decomposition of the training signals into different frequency components, similar to a Fourier transform. In this context, we derive a theoretical upper bound on the maximum frequency Neural Processes can reproduce, depending on their representation size. This bound is confirmed empirically. Finally, we show that Neural Processes can be trained to only represent a subset of possible frequencies and suppress others, which makes them programmable band-pass or band-stop filters.

One-sentence Summary: We show that deterministic Neural Processes decompose signals into different frequency components, a behaviour that can be controlled to turn them into programmable band-pass or band-stop filters.

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