Publication

Regret Minimization in Stochastic Non-Convex Learning via a Proximal-Gradient Approach

Publications associées (30)

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While momentum-based accelerated variants of stochastic gradient descent (SGD) are widely used when training machine learning models, there is little theoretical understanding on the generalization error of such methods. In this work, we first show that th ...

Microtome Publishing2024

Understanding generalization and robustness in modern deep learning

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In this thesis, we study two closely related directions: robustness and generalization in modern deep learning. Deep learning models based on empirical risk minimization are known to be often non-robust to small, worst-case perturbations known as adversari ...

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Scalable constrained optimization

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Modern optimization is tasked with handling applications of increasingly large scale, chiefly due to the massive amounts of widely available data and the ever-growing reach of Machine Learning. Consequently, this area of research is under steady pressure t ...

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Topics in statistical physics of high-dimensional machine learning

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Leveraging Continuous Time to Understand Momentum When Training Diagonal Linear Networks

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In this work, we investigate the effect of momentum on the optimisation trajectory of gradient descent. We leverage a continuous-time approach in the analysis of momentum gradient descent with step size

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In inverse problems, the task is to reconstruct an unknown signal from its possibly noise-corrupted measurements. Penalized-likelihood-based estimation and Bayesian estimation are two powerful statistical paradigms for the resolution of such problems. They ...

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High-Dimensional Kernel Methods under Covariate Shift: Data-Dependent Implicit Regularization

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Catastrophic overfitting (CO) in single-step adversarial training (AT) results in abrupt drops in the adversarial test accuracy (even down to 0%). For models trained with multi-step AT, it has been observed that the loss function behaves locally linearly w ...

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SPACE-TIME REDUCED BASIS METHODS FOR PARAMETRIZED UNSTEADY STOKES EQUATIONS

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High-order geometric integrators for the variational Gaussian wavepacket dynamics and application to vibronic spectra at finite temperature

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Molecular quantum dynamics simulations are essential for understanding many fundamental phenomena in physics and chemistry. They often require solving the time-dependent Schrödinger equation for molecular nuclei, which is challenging even for medium-sized ...

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Error assessment of an adaptive finite elements-neural networks method for an elliptic parametric PDE

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In the rapidly evolving landscape of machine learning research, neural networks stand out with their ever-expanding number of parameters and reliance on increasingly large datasets. The financial cost and computational resources required for the training p ...

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Recent developments in neural architecture search (NAS) emphasize the significance of considering robust architectures against malicious data. However, there is a notable absence of benchmark evaluations and theoretical guarantees for searching these robus ...

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