---
abstract: '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.'
author:
- |
    William H. Guss\
    Machine Learning at Berkeley\
    University of California, Berkeley\
    `wguss@ml.berkeley.edu`
bibliography:
- 'dfm.bib'
title: 'Deep Function Machines: Generalized Neural Networks for Topological Layer Expression'
---


