# Deep Networks Provably Classify Data on Curves

@inproceedings{Wang2021DeepNP, title={Deep Networks Provably Classify Data on Curves}, author={Tingran Wang and Sam Buchanan and Dar Gilboa and John N. Wright}, booktitle={NeurIPS}, year={2021} }

Data with low-dimensional nonlinear structure are ubiquitous in engineering and scientific problems. We study a model problem with such structure—a binary classification task that uses a deep fully-connected neural network to classify data drawn from two disjoint smooth curves on the unit sphere. Aside from mild regularity conditions, we place no restrictions on the configuration of the curves. We prove that when (i) the network depth is large relative to certain geometric properties that set…

## One Citation

### On the principles of Parsimony and Self-consistency for the emergence of intelligence

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A theoretical framework is proposed that sheds light on understanding deep networks within a bigger picture of intelligence in general and introduces two fundamental principles, Parsimony and Self-consistency, which address two fundamental questions regarding intelligence: what to learn and how to learn, respectively.

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