MIQCQP reformulation of the ReLU neural networks Lipschitz constant estimation problem
It is well established that to ensure or certify the robustness of a neural network, its Lipschitz constant plays a prominent role. However, its calculation is NP-hard. In this note, by taking into account activation regions at each layer as new constraints, we propose new quadratically constrained MIP formulations for the neural network Lipschitz estimation problem. The solutions of these problems give lower bounds and upper bounds of the Lipschitz constant and we detail conditions when they coincide with the exact Lipschitz constant.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Analytical bounds on the local Lipschitz constants of ReLU networks
In this paper, we determine analytical upper bounds on the local Lipschitz constants of feedforward neural networks with ReLU activation functions. We do so by deriving Lipschitz constants and bounds for ReLU, affine-ReL…
LipBaB: Computing exact Lipschitz constant of ReLU networks
The Lipschitz constant of neural networks plays an important role in several contexts of deep learning ranging from robustness certification and regularization to stability analysis of systems with neural network control…
Exactly Computing the Local Lipschitz Constant of ReLU Networks
The local Lipschitz constant of a neural network is a useful metric with applications in robustness, generalization, and fairness evaluation. We provide novel analytic results relating the local Lipschitz constant of non…
FairnessLocal Lipschitz Constant Computation of ReLU-FNNs: Upper Bound Computation with Exactness Verification
This paper is concerned with the computation of the local Lipschitz constant of feedforward neural networks (FNNs) with activation functions being rectified linear units (ReLUs). The local Lipschitz constant of an FNN fo…
Analytical bounds on the local Lipschitz constants of affine-ReLU functions
In this paper, we determine analytical bounds on the local Lipschitz constants of of affine functions composed with rectified linear units (ReLUs). Affine-ReLU functions represent a widely used layer in deep neural netwo…