# Deep Function Machines: Generalized Neural Networks for Topological Layer Expression

arXiv: https://arxiv.org/abs/1612.04799 · HTML: https://mlsanity.com/paper/1612.04799/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Dec 2016.

## Built on by (most cited first, 4 of 4)

- [Neural Operator: Learning Maps Between Function Spaces](https://mlsanity.com/paper/2108.08481/) (2021)
- [Deep Learning for Functional Data Analysis with Adaptive Basis Layers](https://mlsanity.com/paper/2106.10414/) (2021)
- [Infinite-dimensional Folded-in-time Deep Neural Networks](https://mlsanity.com/paper/2101.02966/) (2021)
- [A Functional Extension of Semi-Structured Networks](https://mlsanity.com/paper/2410.05430/) (2024)

## Abstract (arXiv)

In this paper we propose a generalization of deep neural networks called deep function machines (DFMs). DFMs act on vector spaces of arbitrary (possibly infinite) dimension and we show that a family of DFMs are invariant to the dimension of input data; that is, the parameterization of the model does not directly hinge on the quality of the input (eg. high resolution images). Using this generalization we provide a new theory of universal approximation of bounded non-linear operators between function spaces. We then suggest that DFMs provide an expressive framework for designing new neural network layer types with topological considerations in mind. Finally, we introduce a novel architecture, RippLeNet, for resolution invariant computer vision, which empirically achieves state of the art invariance.