Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Semialgebraic Optimization for Lipschitz Constants of ReLU Networks   The Lipschitz constant of a network plays an important role in many
applications of deep learning, such as robustness certification and Wasserstein
Generative Adversarial Network. We introduce a semidefinite programming
hierarchy to estimate the global and local Lipschitz constant of a multiple
layer deep neural network. The novelty is to combine a polynomial lifting for
ReLU functions derivatives with a weak generalization of Putinar's positivity
certificate. This idea could also apply to other, nearly sparse, polynomial
optimization problems in machine learning. We empirically demonstrate that our
method provides a trade-off with respect to state of the art linear programming
approach, and in some cases we obtain better bounds in less time.

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The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: adap-org