相关论文: Efficiently Computing Local Lipschitz Constants of…
Probabilistic verification problems of neural networks are concerned with formally analysing the output distribution of a neural network under a probability distribution of the inputs. Examples of probabilistic verification problems include…
In this article we present an algorithm to compute bounds on the marginals of a graphical model. For several small clusters of nodes upper and lower bounds on the marginal values are computed independently of the rest of the network. The…
We propose a new approach for propagating stable probability distributions through neural networks. Our method is based on local linearization, which we show to be an optimal approximation in terms of total variation distance for the ReLU…
The Lipschitz constant of neural networks has been established as a key quantity to enforce the robustness to adversarial examples. In this paper, we tackle the problem of building $1$-Lipschitz Neural Networks. By studying Residual…
Recent research has revealed that high compression of Deep Neural Networks (DNNs), e.g., massive pruning of the weight matrix of a DNN, leads to a severe drop in accuracy and susceptibility to adversarial attacks. Integration of network…
In this paper, we propose BPGrad, a novel approximate algorithm for deep nueral network training, based on adaptive estimates of feasible region via branch-and-bound. The method is based on the assumption of Lipschitz continuity in…
Covering numbers of (deep) ReLU networks have been used to characterize approximation-theoretic performance, to upper-bound prediction error in nonparametric regression, and to quantify classification capacity. These results rely on…
This paper introduces a new parameterization of deep neural networks (both fully-connected and convolutional) with guaranteed $\ell^2$ Lipschitz bounds, i.e. limited sensitivity to input perturbations. The Lipschitz guarantees are…
Typical adversarial-training-based unsupervised domain adaptation methods are vulnerable when the source and target datasets are highly-complex or exhibit a large discrepancy between their data distributions. Recently, several…
While neural networks can enjoy an outstanding flexibility and exhibit unprecedented performance, the mechanism behind their behavior is still not well-understood. To tackle this fundamental challenge, researchers have tried to restrict and…
Kalu\v{z}a, Kopeck\'a and the author have shown that the best Lipschitz constant for mappings taking a given $n^{d}$-element set in the integer lattice $\mathbb{Z}^{d}$, with $n\in \mathbb{N}$, surjectively to the regular $n$ times $n$ grid…
The need of fast distributed solvers for optimization problems in networked systems has motivated the recent development of the Fast-Lipschitz optimization framework. In such an optimization, problems satisfying certain qualifying…
Feature maps associated with positive definite kernels play a central role in kernel methods and learning theory, where regularity properties such as Lipschitz continuity are closely related to robustness and stability guarantees. Despite…
This paper is devoted to the proof of Lipschitz regularity, down to the microscopic scale, for solutions of an elliptic system with highly oscillating coefficients, over a highly oscillating Lipschitz boundary. The originality of this…
The trapping redundancy of a linear code is the number of rows of a smallest parity-check matrix such that no submatrix forms an $(a,b)$-trapping set. This concept was first introduced in the context of low-density parity-check (LDPC) codes…
Deep Neural Networks are vulnerable to small perturbations that can drastically alter their predictions for perceptually unchanged inputs. The literature on adversarially robust Deep Learning attempts to either enhance the robustness of…
Generative neural networks have been empirically found very promising in providing effective structural priors for compressed sensing, since they can be trained to span low-dimensional data manifolds in high-dimensional signal spaces.…
When propagating uncertainty in the data of differential equations, the probability laws describing the uncertainty are typically themselves subject to uncertainty. We present a sensitivity analysis of uncertainty propagation for…
We consider a neural network architecture designed to solve inverse problems where the degradation operator is linear and known. This architecture is constructed by unrolling a forward-backward algorithm derived from the minimization of an…
Logic-based methods for explaining neural network decisions offer formal guarantees of correctness and non-redundancy, but they often suffer from high computational costs, especially for large networks. In this work, we improve the…