arXiv subjects

Fares B. Mehouachi

Publications and source records attributed to Fares B. Mehouachi.

4 recordsLinked to original sources

arXiv2026

Catastrophic Overfitting, Entropy Gap and Participation Ratio: A Noiseless $l^p$ Norm Solution for Fast Adversarial Training

Adversarial training is a cornerstone of robust deep learning, but fast methods like the Fast Gradient Sign Method (FGSM) often suffer from Catastrophic Overfitting (CO), where models become robust to single-step attacks but fail against multi-step variants. While existing solutions rely on noise injection, regularization, or gradient clipping, we propose a novel solution that purely controls the $l^p$ training norm to mitigate CO. Our study is motivated by the empirical observation that CO is more prevalent under the $l^{\infty}$ norm than the $l^2$ norm. Leveraging this insight, we develop a framework for generalized $l^p$ attack as a fixed point problem and craft $l^p$-FGSM attacks to understand the transition mechanics from $l^2$ to $l^{\infty}$. This leads to our core insight: CO emerges when highly concentrated gradients where information localizes in few dimensions interact with aggressive norm constraints. By quantifying gradient concentration through Participation Ratio and entropy measures, we develop an adaptive $l^p$-FGSM that automatically tunes the training norm based on gradient information. Extensive experiments demonstrate that this approach achieves strong robustness without requiring additional regularization or noise injection, providing a novel and theoretically-principled pathway to mitigate the CO problem.

cs.LG↗

arXiv2026

FlowMixer: A Depth-Agnostic Neural Architecture for Interpretable Spatiotemporal Forecasting

We introduce FlowMixer, a single-layer neural architecture that leverages constrained matrix operations to model structured spatiotemporal patterns with enhanced interpretability. FlowMixer incorporates non-negative matrix mixing layers within a reversible mapping framework - applying transforms before mixing and their inverses afterward. This shape-preserving design enables a Kronecker-Koopman eigenmodes framework that bridges statistical learning with dynamical systems theory, providing interpretable spatiotemporal patterns and facilitating direct algebraic manipulation of prediction horizons without retraining. The architecture's semi-group property enables this single layer to mathematically represent any depth through composition, eliminating depth search entirely. Extensive experiments across diverse domains demonstrate FlowMixer's long-horizon forecasting capabilities while effectively modeling physical phenomena such as chaotic attractors and turbulent flows. Our results achieve performance matching state-of-the-art methods while offering superior interpretability through directly extractable eigenmodes. This work suggests that architectural constraints can simultaneously maintain competitive performance and enhance mathematical interpretability in neural forecasting systems.

cs.LG↗

arXiv2024

Urban traffic analysis and forecasting through shared Koopman eigenmodes

Predicting traffic flow in data-scarce cities is challenging due to limited historical data. To address this, we leverage transfer learning by identifying periodic patterns common to data-rich cities using a customized variant of Dynamic Mode Decomposition (DMD): constrained Hankelized DMD (TrHDMD). This method uncovers common eigenmodes (urban heartbeats) in traffic patterns and transfers them to data-scarce cities, significantly enhancing prediction performance. TrHDMD reduces the need for extensive training datasets by utilizing prior knowledge from other cities. By applying Koopman operator theory to multi-city loop detector data, we identify stable, interpretable, and time-invariant traffic modes. Injecting ``urban heartbeats'' into forecasting tasks improves prediction accuracy and has the potential to enhance traffic management strategies for cities with varying data infrastructures. Our work introduces cross-city knowledge transfer via shared Koopman eigenmodes, offering actionable insights and reliable forecasts for data-scarce urban environments.

eess.SY↗

arXiv2021

Exact Stochastic Second Order Deep Learning

Optimization in Deep Learning is mainly dominated by first-order methods which are built around the central concept of backpropagation. Second-order optimization methods, which take into account the second-order derivatives are far less used despite superior theoretical properties. This inadequacy of second-order methods stems from its exorbitant computational cost, poor performance, and the ineluctable non-convex nature of Deep Learning. Several attempts were made to resolve the inadequacy of second-order optimization without reaching a cost-effective solution, much less an exact solution. In this work, we show that this long-standing problem in Deep Learning could be solved in the stochastic case, given a suitable regularization of the neural network. Interestingly, we provide an expression of the stochastic Hessian and its exact eigenvalues. We provide a closed-form formula for the exact stochastic second-order Newton direction, we solve the non-convexity issue and adjust our exact solution to favor flat minima through regularization and spectral adjustment. We test our exact stochastic second-order method on popular datasets and reveal its adequacy for Deep Learning.

cs.LG↗