Antoine Gonon

Antoine Gonon, Nicolas Brisebarre, Elisa Riccietti et al.

This work introduces the first toolkit around path-norms that fully encompasses general DAG ReLU networks with biases, skip connections and any operation based on the extraction of order statistics: max pooling, GroupSort etc. This toolkit notably allows us to establish generalization bounds for modern neural networks that are not only the most widely applicable path-norm based ones, but also recover or beat the sharpest known bounds of this type. These extended path-norms further enjoy the usual benefits of path-norms: ease of computation, invariance under the symmetries of the network, and improved sharpness on layered fully-connected networks compared to the product of operator norms, another complexity measure most commonly used. The versatility of the toolkit and its ease of implementation allow us to challenge the concrete promises of path-norm-based generalization bounds, by numerically evaluating the sharpest known bounds for ResNets on ImageNet.

Antoine Gonon, Léon Zheng, Pascal Carrivain et al.

Kronecker-sparse (KS) matrices -- whose supports are Kronecker products of identity and all-ones blocks -- underpin the structure of Butterfly and Monarch matrices and offer the promise of more efficient models. However, existing GPU kernels for KS matrix multiplication suffer from high data movement costs, with up to 50% of time spent on memory-bound tensor permutations. We propose a fused, output-stationary GPU kernel that eliminates these overheads, reducing global memory traffic threefold. Across 600 KS patterns, our kernel achieves in FP32 a median speedup of x1.4 and lowers energy consumption by 15%. A simple heuristic based on KS pattern parameters predicts when our method outperforms existing ones. We release all code at github.com/PascalCarrivain/ksmm, including a PyTorch-compatible KSLinear layer, and demonstrate in FP32 end-to-end latency reductions of up to 22% in ViT-S/16 and 16% in GPT-2 medium.

Antoine Gonon, Léon Zheng, Clément Lalanne et al.

This article measures how sparsity can make neural networks more robust to membership inference attacks. The obtained empirical results show that sparsity improves the privacy of the network, while preserving comparable performances on the task at hand. This empirical study completes and extends existing literature.

Antoine Gonon, Léon Zheng, Clément Lalanne et al.

Sparse neural networks are mainly motivated by ressource efficiency since they use fewer parameters than their dense counterparts but still reach comparable accuracies. This article empirically investigates whether sparsity could also improve the privacy of the data used to train the networks. The experiments show positive correlations between the sparsity of the model, its privacy, and its classification error. Simply comparing the privacy of two models with different sparsity levels can yield misleading conclusions on the role of sparsity, because of the additional correlation with the classification error. From this perspective, some caveats are raised about previous works that investigate sparsity and privacy.

Antoine Gonon, Nicolas Brisebarre, Elisa Riccietti et al.

Robustness with respect to weight perturbations underpins guarantees for generalization, pruning and quantization. Existing guarantees rely on Lipschitz bounds in parameter space, cover only plain feed-forward MLPs, and break under the ubiquitous neuron-wise rescaling symmetry of ReLU networks. We prove a new Lipschitz inequality expressed through the $\ell^1$-path-metric of the weights. The bound is (i) rescaling-invariant by construction and (ii) applies to any ReLU-DAG architecture with any combination of convolutions, skip connections, pooling, and frozen (inference-time) batch-normalization -- thus encompassing ResNets, U-Nets, VGG-style CNNs, and more. By respecting the network's natural symmetries, the new bound strictly sharpens prior parameter-space bounds and can be computed in two forward passes. To illustrate its utility, we derive from it a symmetry-aware pruning criterion and show -- through a proof-of-concept experiment on a ResNet-18 trained on ImageNet -- that its pruning performance matches that of classical magnitude pruning, while becoming totally immune to arbitrary neuron-wise rescalings.

Damien Rouchouse, Antoine Gonon, Rémi Gribonval et al.

A central challenge in understanding generalization is to obtain non-vacuous guarantees that go beyond worst-case complexity over data or weight space. Among existing approaches, PAC-Bayes bounds stand out as they can provide tight, data-dependent guarantees even for large networks. However, in ReLU networks, rescaling invariances mean that different weight distributions can represent the same function while leading to arbitrarily different PAC-Bayes complexities. We propose to study PAC-Bayes bounds in an invariant, lifted representation that resolves this discrepancy. This paper explores both the guarantees provided by this approach (invariance, tighter bounds via data processing) and the algorithmic aspects of KL-based rescaling-invariant PAC-Bayes bounds.

Michael P. Sheehan, Antoine Gonon, Mike E. Davies

In the compressive learning theory, instead of solving a statistical learning problem from the input data, a so-called sketch is computed from the data prior to learning. The sketch has to capture enough information to solve the problem directly from it, allowing to discard the dataset from the memory. This is useful when dealing with large datasets as the size of the sketch does not scale with the size of the database. In this paper, we reformulate the original compressive learning framework to explicitly cater for the class of semi-parametric models. The reformulation takes account of the inherent topology and structure of semi-parametric models, creating an intuitive pathway to the development of compressive learning algorithms. We apply our developed framework to both the semi-parametric models of independent component analysis and subspace clustering, demonstrating the robustness of the framework to explicitly show when a compression in complexity can be achieved.