Designing with Non-Finite Output Dimension via Fourier Coefficients of Neural Waveforms

TL;DR

This paper introduces a method for neural networks to produce outputs of variable, potentially infinite, dimension by learning neural waveforms and using Fourier coefficients, enabling more complex design outputs.

Contribution

It presents a novel approach for neural networks to generate non-finite dimensional outputs through Fourier series of neural waveforms, expanding design capabilities.

Findings

Neural networks can learn to produce variable-dimension outputs on toy problems.

Fourier coefficients of neural waveforms serve as flexible output representations.

Abstract

Ordinary Deep Learning models require having the dimension of their outputs determined by a human practitioner prior to training and operation. For design tasks, this places a hard limit on the maximum complexity of any designs produced by a neural network, which is disadvantageous if a greater allowance for complexity would result in better designs. In this paper, we introduce a methodology for taking outputs of non-finite dimension from neural networks, by learning a "neural waveform," and then taking as outputs the coefficients of its Fourier series representation. We then present experimental evidence that neural networks can learn in this setting on a toy problem.