
A Distributional Robustness Certificate by Randomized Smoothing
The robustness of deep neural networks against adversarial example attac...
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Regret Minimization in Partially Observable Linear Quadratic Control
We study the problem of regret minimization in partially observable line...
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Reachability Analysis of Deep Neural Networks with Provable Guarantees
Verifying correctness of deep neural networks (DNNs) is challenging. We ...
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Nonlinear TwoTimeScale Stochastic Approximation: Convergence and FiniteTime Performance
Twotimescale stochastic approximation, a generalized version of the po...
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A Dual Approach to Scalable Verification of Deep Networks
This paper addresses the problem of formally verifying desirable propert...
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Provable Worst Case Guarantees for the Detection of OutofDistribution Data
Deep neural networks are known to be overconfident when applied to outo...
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An Internal Covariate Shift Bounding Algorithm for Deep Neural Networks by Unitizing Layers' Outputs
Batch Normalization (BN) techniques have been proposed to reduce the so...
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A priori guarantees of finitetime convergence for Deep Neural Networks
In this paper, we perform Lyapunov based analysis of the loss function to derive an a priori upper bound on the settling time of deep neural networks. While previous studies have attempted to understand deep learning using control theory framework, there is limited work on a priori finite time convergence analysis. Drawing from the advances in analysis of finitetime control of nonlinear systems, we provide a priori guarantees of finitetime convergence in a deterministic control theoretic setting. We formulate the supervised learning framework as a control problem where weights of the network are control inputs and learning translates into a tracking problem. An analytical formula for finitetime upper bound on settling time is computed a priori under the assumptions of boundedness of input. Finally, we prove the robustness and sensitivity of the loss function against input perturbations.
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