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Intrinsic training dynamics of deep neural networks
No full textA fundamental challenge in the theory of deep learning is to understand whether gradient-based training in high-dimensional parameter spaces can be captured by simpler, lower-dimensional structures, leading to so-called implicit bias. As a stepping stone, we study when a gradient flow on a high-dimensional variable implies an intrinsic gradient flow on a lower-dimensional variable , for an architecture-related function . We express a so-called intrinsic dynamic property and show how it is related to the study of conservation laws associated with the factorization . This leads to a simple criterion based on the inclusion of kernels of linear maps which yields a necessary condition for this property to hold. We then apply our theory to general ReLU networks of arbitrary depth and show that, for any initialization, it is possible to rewrite the flow as an intrinsic dynamic in a lower dimension that depends only on and the initialization, when is the so-called path-lifting. In the case of linear networks with the product of weight matrices, so-called balanced initializations are also known to enable such a dimensionality reduction; we generalize this result to a broader class of {\em relaxed balanced} initializations, showing that, in certain configurations, these are the \emph{only} initializations that ensure the intrinsic dynamic property. Finally, for the linear neural ODE associated with the limit of infinitely deep linear networks, with relaxed balanced initialization, we explicitly express the corresponding intrinsic dynamics
On Multidimensional Disjunctive Inequalities for Chance-Constrained Stochastic Problems with Finite Support
No full textWe consider mixed-integer linear chance-constrained problems for which the random vector that parameterizes the feasible region has finite support. Our key objective is to improve branch-and-bound or -cut approaches by introducing new types of valid inequalities that improve the dual bounds and, by this, the overall performance of such methods. We introduce so-called primal-dual as well as covering valid inequalities. By re-scaling the latter inequalities, we obtain so-called multi-disjunctive valid inequalities, which generalize known inequalities from the literature. We provide theoretical results regarding dominance relations, closure properties, and hardness of the separation problems. Given these insights, we propose heuristic separation procedures and present extensive numerical results showing the effectiveness of our method in comparison to state-of-the-art inequalities from the literature
A Large-Scale Study of Personalized Phishing using Large Language Models
No full textInternational audienceLarge Language Models (LLMs) can generate fluent and persuasive text, making them valuable tools for communication. However, this capability also renders them attractive for malicious purposes. While several studies have shown that LLMs can support generic phishing, their potential for personalized attacks at scale has not been explored and quantified yet. In this study, we thus evaluate the effectiveness of LLM-based spear phishing in an experiment with 7 700 participants. Using the target email addresses as queries, we collect personal information through web searches and automatically generate emails tailored to each participant. Our findings reveal a concerning situation: LLM-based spear phishing almost triples the click rate compared to generic phishing strategies. This effect is consistent, regardless of whether the generic emails are written by humans or generated by LLMs as well. Moreover, the cost of personalization is minimal, with approximately $0.03 per email. Given that phishing is still a major attack vector against IT infrastructures, we conclude that there is a pressing need to strengthen existing defenses, for example, by limiting publicly available information linkable to email addresses and incorporating personalized phishing into awareness trainings
Reconstruction of SINR Maps from Sparse Measurements using Group Equivariant Non-Expansive Operators
No full textAs sixth generation (6G) wireless networks evolve, accurate signal-to-interference-noise ratio (SINR) maps are becoming increasingly critical for effective resource management and optimization. However, acquiring such maps at high resolution is often cost-prohibitive, creating a severe data scarcity challenge. This necessitates machine learning (ML) approaches capable of robustly reconstructing the full map from extremely sparse measurements. To address this, we introduce a novel reconstruction framework based on Group Equivariant Non-Expansive Operators (GENEOs). Unlike data-hungry ML models, GENEOs are low-complexity operators that embed domain-specific geometric priors, such as translation invariance, directly into their structure. This provides a strong inductive bias, enabling effective reconstruction from very few samples. Our key insight is that for network management, preserving the topological structure of the SINR map, such as the geometry of coverage holes and interference patterns, is often more critical than minimizing pixel-wise error. We validate our approach on realistic ray-tracingbased urban scenarios, evaluating performance with both traditional statistical metrics (mean squared error (MSE)) and, crucially, a topological metric (1-Wasserstein distance). Results show that while maintaining competitive MSE, our method dramatically outperforms established ML baselines in topological fidelity. This demonstrates the practical advantage of GENEOs for creating structurally accurate SINR maps that are more reliable for downstream network optimization tasks
Modal analysis of a domain decomposition method for Maxwell's equations in a waveguide
No full textTime-harmonic wave propagation problems, especially those governed by Maxwell's equations, pose significant computational challenges due to the non-self-adjoint nature of the operators and the large, non-Hermitian linear systems resulting from discretization. Domain decomposition methods, particularly one-level Schwarz methods, offer a promising framework to tackle these challenges, with recent advancements showing the potential for weak scalability under certain conditions. In this paper, we analyze the weak scalability of one-level Schwarz methods for Maxwell's equations in strip-wise domain decompositions, focusing on waveguides with general cross sections and different types of transmission conditions such as impedance or perfectly matched layers (PMLs). By combining techniques from the limiting spectrum analysis of Toeplitz matrices and the modal decomposition of Maxwell's solutions, we provide a novel theoretical framework that extends previous work to more complex geometries and transmission conditions. Numerical experiments confirm that the limiting spectrum effectively predicts practical behavior even with a modest number of subdomains. Furthermore, we demonstrate that the one-level Schwarz method can achieve robustness with respect to the wave number under specific domain decomposition parameters, offering new insights into its applicability for large-scale electromagnetic wave problems
Early-Reverberation Imaging Functions for Bounded Elastic Domains
No full textInternational audienceFor the ultrasonic inspection of bounded elastic structures, finite-duration imaging functions are derived in the Fourier-Laplace domain.The signals involved are exponentially windowed, so that early reflections are taken into account more strongly than later ones in the imaging methodology.Applying classical approaches to the general case of anisotropic elasticity, we express the Fréchet derivatives of the relevant data-misfit functional with respect to arbitrary perturbations of the mass density and stiffnesses in terms of forward and adjoint solutions.Their definitions incorporate the exponentially decaying weighting. The proposed finite-duration imaging functions are then defined on that basis.As some areas of the structure are less insonified than others, it is necessary to define normalized imaging functions to compensate for these variations.Our approach in particular aims to overcome the difficulty of dealing with bounded domains containing defects not located in direct line of sight from the transducers and measured signals of long duration.For this initiation work, we demonstate the potential of the proposed method on a two-dimensional test case featuring the imaging of mass and elastic stiffness variations in a region of a bounded isotropic medium that is not directly visible from the transducers
The Tensor-Plus Calculus
No full textWe propose a graphical language that accommodates two monoidal structures: a multiplicative one for pairing and an additional one for branching. In this colored PROP, whether wires in parallel are linked through the multiplicative structure or the additive structure is implicit and determined contextually rather than explicitly through tapes, world annotations, or other techniques, as is usually the case in the literature. The diagrams are used as parameter elements of a commutative semiring, whose choice is determined by the kind of computation we want to model, such as non-deterministic, probabilistic, or quantum. Given such a semiring, we provide a categorical semantics of diagrams and show the language as universal for it. We also provide an equational theory to identify diagrams that share the same semantics and show that the theory is sound and complete and captures semantical equivalence. In categorical terms, we design an internal language for semiadditive categories (C,+,0) with a symmetric monoidal structure (C,x,1) distributive over it, and such that the homset C(1,1) is isomorphic to a given commutative semiring, e.g., the semiring of non-negative real numbers for the probabilistic case
Geometric characterisation of structural and regular equivalences in undirected (hyper)graphs
No full textSimilarity notions between vertices in a graph, such as structural and regular equivalence, are one of the main ingredients in clustering tools in complex network science. We generalise structural and regular equivalences for undirected hypergraphs and provide a characterisation of structural and regular equivalences of undirected graphs and hypergraphs through neighbourhood graphs and Ollivier-Ricci curvature. Our characterisation sheds new light on these similarity notions opening a new avenue for their exploration. These characterisations also enable the construction of a possibly wide family of regular partitions, thereby offering a new route to a task that has so far been computationally challenging
ROAD-AI : un projet au service de l’amélioration de la résilience des infrastructures et réseaux de transport
No full textInternational audienceLe projet Road-AI, né de la collaboration entre le Cerema et Inria, marque une avancée majeure dans la modernisation de la gestion des infrastructures routières. En combinant expertise métier et excellence scientifique, cette initiative vise à améliorer la durabilité, la sécurité et la résilience des routes, ponts et tunnels grâce à des outils innovants