Figure 1: An operator neural network, a discrete neural network, and a more complicated deep funciton machine with residues.
Deep funciton machines (DFMs) are a generalization of deep neural networks proposed to connect topology in data to topology in neural networks. DFMs act on vector spaces of arbitrary (possibly infinite) dimension and in fact certain 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). DFMs provide an expressive framework for designing new neural network layer types with topological considerations in mind.
Deep Function Machines: Generalized Neural Networks for Topological Layer Expression. William H. Guss. COLT 2017 (Submitting). [arXiv]
Universal Approximation of Nonlinear Operators on Banach Space. William H. Guss. Machine Learning at Berkeley Research Symposium 2016. [pdf]
Parameter Reduction using Operator Neural Networks. William H. Guss. Microsoft Research Symposium 2016. Best Poster Award. [pdf]