Fares B. Mehouachi

Chuhan Yang, Fares B. Mehouachi, Monica Menendez et al.

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.

Fares B. Mehouachi, Saif Eddin Jabari

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.