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

arXiv: https://arxiv.org/abs/2212.04351 · HTML: https://mlsanity.com/paper/2212.04351/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 22 references that are in the map.
- First posted on arXiv 17 Aug 2022.

## Builds on (most cited first, 9 of 9)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Deformable Convolutional Networks](https://mlsanity.com/paper/1703.06211/) (2017)
- [Neural Architecture Optimization](https://mlsanity.com/paper/1808.07233/) (2018)
- [Liquid Time-constant Networks](https://mlsanity.com/paper/2006.04439/) (2020)
- [Evolving Deep Neural Networks](https://mlsanity.com/paper/1703.00548/) (2017)
- [FlexConv: Continuous Kernel Convolutions with Differentiable Kernel Sizes](https://mlsanity.com/paper/2110.08059/) (2021)
- [Multi-level Residual Networks from Dynamical Systems View](https://mlsanity.com/paper/1710.10348/) (2017)
- [Resolution learning in deep convolutional networks using scale-space theory](https://mlsanity.com/paper/2106.03412/) (2021)

## Abstract (arXiv)

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.