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François Serre

Publications and source records attributed to François Serre.

3 recordsLinked to original sources

Scaling Polyhedral Neural Network Verification on GPUs

Certifying the robustness of neural networks against adversarial attacks is essential to their reliable adoption in safety-critical systems such as autonomous driving and medical diagnosis. Unfortunately, state-of-the-art verifiers either do not scale to bigger networks or are too imprecise to prove robustness, limiting their practical adoption. In this work, we introduce GPUPoly, a scalable verifier that can prove the robustness of significantly larger deep neural networks than previously possible. The key technical insight behind GPUPoly is the design of custom, sound polyhedra algorithms for neural network verification on a GPU. Our algorithms leverage the available GPU parallelism and inherent sparsity of the underlying verification task. GPUPoly scales to large networks: for example, it can prove the robustness of a 1M neuron, 34-layer deep residual network in approximately 34.5 ms. We believe GPUPoly is a promising step towards practical verification of real-world neural networks.

cs.LG↗

Characterizing and Enumerating Walsh-Hadamard Transform Algorithms

We propose a way of characterizing the algorithms computing a Walsh-Hadamard transform that consist of a sequence of arrays of butterflies ($I_{2^{n-1}}\otimes \text{DFT}_2$) interleaved by linear permutations. Linear permutations are those that map linearly the binary representation of its element indices. We also propose a method to enumerate these algorithms.

cs.DS↗

A Lower-Upper-Lower Block Triangular Decomposition with Minimal Off-Diagonal Ranks

We propose a novel factorization of a non-singular matrix $P$, viewed as a $2\times 2$-blocked matrix. The factorization decomposes $P$ into a product of three matrices that are lower block-unitriangular, upper block-triangular, and lower block-unitriangular, respectively. Our goal is to make this factorization "as block-diagonal as possible" by minimizing the ranks of the off-diagonal blocks. We give lower bounds on these ranks and show that they are sharp by providing an algorithm that computes an optimal solution. The proposed decomposition can be viewed as a generalization of the well-known Block LU factorization using the Schur complement.

math.RA↗