Topological Approaches to Deep Learning

Topological Approaches to Deep Learning. Carlsson, G. & Gabrielsson, R. B. Technical Report arXiv:1811.01122, arXiv, November, 2018. arXiv:1811.01122 [cs, math, stat] type: article

Paper doi abstract bibtex

We perform topological data analysis on the internal states of convolutional deep neural networks to develop an understanding of the computations that they perform. We apply this understanding to modify the computations so as to (a) speed up computations and (b) improve generalization from one data set of digits to another. One byproduct of the analysis is the production of a geometry on new sets of features on data sets of images, and use this observation to develop a methodology for constructing analogues of CNN's for many other geometries, including the graph structures constructed by topological data analysis.

@techreport{carlsson_topological_2018,
	title = {Topological {Approaches} to {Deep} {Learning}},
	url = {http://arxiv.org/abs/1811.01122},
	abstract = {We perform topological data analysis on the internal states of convolutional deep neural networks to develop an understanding of the computations that they perform. We apply this understanding to modify the computations so as to (a) speed up computations and (b) improve generalization from one data set of digits to another. One byproduct of the analysis is the production of a geometry on new sets of features on data sets of images, and use this observation to develop a methodology for constructing analogues of CNN's for many other geometries, including the graph structures constructed by topological data analysis.},
	number = {arXiv:1811.01122},
	urldate = {2022-05-28},
	institution = {arXiv},
	author = {Carlsson, Gunnar and Gabrielsson, Rickard Brüel},
	month = nov,
	year = {2018},
	doi = {10.48550/arXiv.1811.01122},
	note = {arXiv:1811.01122 [cs, math, stat]
type: article},
	keywords = {68T05, 55N35, 62-07, Computer Science - Artificial Intelligence, Computer Science - Machine Learning, Mathematics - Algebraic Topology, Statistics - Machine Learning},
}

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