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Exact Visualization of Deep Neural Network Geometry and Decision Boundary
Ahmed Imtiaz Humayun · Randall Balestriero · Richard Baraniuk

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in Symmetry and Geometry in Neural Representations (NeurReps) »
Event URL: https://openreview.net/forum?id=VSLbmsoZxai »

Visualizing Deep Network (DN) geometry and decision boundaries remains a key challenge even today. In fact, despite the dire need for such methods e.g. to assess the quality of a trained model, to compare models, to interpret decisions, the community at large still relies on crude approximations and proxies. For example, computing the decision boundary of a model, say on a 2d slice of their input space, is done through gradient descent and sampling with dichotomy search. In this paper, we lean on the rich theory of Continuous Piece-Wise Linear (CPWL) DNs to provide, for the first time, a method that provably produces the exact geometry (CPWL partition) and decision boundary of any DN employing nonlinearities such as ReLU, Leaky-ReLU, and max-pooling. Using our method we are able to not only visualize the decision boundary but also obtain its spanning space, i.e., we can sample arbitrarily many inputs that provably lie on the model's decision boundary, up to numerical precision. We explore how such methods can be used to interpret architectural choices e.g. using convolutional architectures instead of fully-connected neural networks.

Keywords: Geometry · deep neural network · Visualization · Decision Boundary

Author Information

Ahmed Imtiaz Humayun (Rice University)
Randall Balestriero (Meta AI, FAIR)
Richard Baraniuk (Rice University)

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