Learning Proximal Operators with Gaussian Processes

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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 ...

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 ...

Distributed learning is the key for enabling training of modern large-scale machine learning models, through parallelising the learning process. Collaborative learning is essential for learning from privacy-sensitive data that is distributed across various ...

The optical domain presents potential avenues for enhancing both computing and communication due to its inherent properties of bandwidth, parallelism, and energy efficiency. This research focuses on harnessing 3-Dimensional (3D) diffractive optics for nove ...

This paper presents a novel distributed approach for solving AC power flow (PF) problems. The optimization problem is reformulated into a distributed form using a communication structure corresponding to a hypergraph, by which complex relationships between ...

Diagonal linear networks (DLNs) are a toy simplification of artificial neural networks; they consist in a quadratic reparametrization of linear regression inducing a sparse implicit regularization. In this paper, we describe the trajectory of the gradient ...

Displaced communication, whereby individuals communicate regarding a subject that is not immediately present (spatially or temporally), is one of the key features of human language. It also occurs in a few animal species, most notably the honeybee, where t ...

Deep neural networks have become ubiquitous in today's technological landscape, finding their way in a vast array of applications. Deep supervised learning, which relies on large labeled datasets, has been particularly successful in areas such as image cla ...

Recently there has been a surge of interest in understanding implicit regularization properties of iterative gradient-based optimization algorithms. In this paper, we study the statistical guarantees on the excess risk achieved by early-stopped unconstrain ...

We consider the problem of learning a target function corresponding to a deep, extensive-width, non-linear neural network with random Gaussian weights. We consider the asymptotic limit where the number of samples, the input dimension and the network width ...

In this paper, we investigate the impact of stochasticity and large stepsizes on the implicit regularisation of gradient descent (GD) and stochastic gradient descent (SGD) over diagonal linear networks. We prove the convergence of GD and SGD with macroscop ...

In this paper we fully describe the trajectory of gradient flow over diagonal linear networks in the limit of vanishing initialisation. We show that the limiting flow successively jumps from a saddle of the training loss to another until reaching the minim ...

Neural machine translation (MT) and text generation have recently reached very high levels of quality. However, both areas share a problem: in order to reach these levels, they require massive amounts of data. When this is not present, they lack generaliza ...

Environmental change is intensifying the biodiversity crisis and threatening species across the tree of life. Conservation genomics can help inform conservation actions and slow biodiversity loss. However, more training, appropriate use of novel genomic me ...

Control systems operating in real-world environments often face disturbances arising from measurement noise and model mismatch. These factors can significantly impact the perfor- mance and safety of the system. In this thesis, we aim to leverage data to de ...

This thesis is situated at the crossroads between machine learning and control engineering. Our contributions are both theoretical, through proposing a new uncertainty quantification methodology in a kernelized context; and experimental, through investigat ...

This thesis focuses on two selected learning problems: 1) statistical inference on graphs models, and, 2) gradient descent on neural networks, with the common objective of defining and analysing the measures that characterize the fundamental limits. In th ...

Spinal-cord injury interrupts communication between the brain and spinal cord, leading to paralysis. An implant that decodes the brain signals that control movements and drives electrical stimulation of the spinal cord re-establishes this communication, en ...

Linear-Quadratic-Gaussian (LQG) control is a fundamental control paradigm that is studied in various fields such as engineering, computer science, economics, and neuroscience. It involves controlling a system with linear dynamics and imperfect observations ...

The choice of the shape parameter highly effects the behaviour of radial basis function (RBF) approximations, as it needs to be selected to balance between the ill-conditioning of the interpolation matrix and high accuracy. In this paper, we demonstrate ho ...

Learning Proximal Operators with Gaussian Processes

Chattez avec Graph Search

Understanding generalization and robustness in modern deep learning

On the Generalization of Stochastic Gradient Descent with Momentum

Optimization Algorithms for Decentralized, Distributed and Collaborative Machine Learning

3D diffractive optics for linear interconnects and nonlinear processing

Hypergraph-Based Fast Distributed AC Power Flow Optimization

Incremental Learning in Diagonal Linear Networks

The evolution of behavioral cues and signaling in displaced communication

Deep Learning Generalization with Limited and Noisy Labels

The statistical complexity of early-stopped mirror descent

Bayes-optimal Learning of Deep Random Networks of Extensive-width

(S)GD over Diagonal Linear Networks: Implicit Regularisation, Large Stepsizes and Edge of Stability

Saddle-to-Saddle Dynamics in Diagonal Linear Networks

Regularization Techniques for Low-Resource Machine Translation

Genomics and conservation: Guidance from training to analyses and applications

Data-Driven Control and Optimization under Noisy and Uncertain Conditions

Machine Learning Methods for Robust Uncertainty Quantification and Controller Approximation

Fundamental Limits in Statistical Learning Problems: Block Models and Neural Networks

A digital bridge between brain and spinal cord restores walking after paralysis

Distributionally Robust Linear Quadratic Control

A new variable shape parameter strategy for RBF approximation using neural networks