Deep Function Machines: Generalized Neural Networks for Topological Layer Expression

William H. Guss

Feb 15, 2018 (modified: Feb 15, 2018) ICLR 2018 Conference Blind Submission readers: everyone Show Bibtex
  • 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.
  • Keywords: deep learning theory, infinite neural networks, topology
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