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Workshop: Mathematics of Modern Machine Learning (M3L)

Spectrum Extraction and Clipping for Implicitly Linear Layers

Ali Ebrahimpour-Boroojeny · Matus Telgarsky · Hari Sundaram


We show the effectiveness of automatic differentiation in efficiently and correctly computing and controlling the spectrum of implicitly linear operators, a rich family of layer types including all standard convolutional and dense layers. we provide the first clipping method which is correct for general convolution layers, and illuminate the representational limitation that caused correctness issues in prior work. by comparing the accuracy and performance of our methods to existing methods, using various experiments, show they lead to better generalization and adversarial robustness of the models. in addition to these advantages over the state-of-the-art methods, we show they are much faster than the alternatives.

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