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Overview frequency principle/spectral bias in deep learning
Understanding deep learning is increasingly emergent as it penetrates more and more into
industry and science. In recent years, a research line from Fourier analysis sheds light on …
industry and science. In recent years, a research line from Fourier analysis sheds light on …
Bayes-optimal learning of deep random networks of extensive-width
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 …
width, non-linear neural network with random Gaussian weights. We consider the asymptotic …
A unifying tutorial on approximate message passing
Over the last decade or so, Approximate Message Passing (AMP) algorithms have become
extremely popular in various structured high-dimensional statistical problems. Although the …
extremely popular in various structured high-dimensional statistical problems. Although the …
Generalisation error in learning with random features and the hidden manifold model
We study generalised linear regression and classification for a synthetically generated
dataset encompassing different problems of interest, such as learning with random features …
dataset encompassing different problems of interest, such as learning with random features …
Modeling the influence of data structure on learning in neural networks: The hidden manifold model
Understanding the reasons for the success of deep neural networks trained using stochastic
gradient-based methods is a key open problem for the nascent theory of deep learning. The …
gradient-based methods is a key open problem for the nascent theory of deep learning. The …
Modern applications of machine learning in quantum sciences
In this book, we provide a comprehensive introduction to the most recent advances in the
application of machine learning methods in quantum sciences. We cover the use of deep …
application of machine learning methods in quantum sciences. We cover the use of deep …
The gaussian equivalence of generative models for learning with shallow neural networks
Understanding the impact of data structure on the computational tractability of learning is a
key challenge for the theory of neural networks. Many theoretical works do not explicitly …
key challenge for the theory of neural networks. Many theoretical works do not explicitly …
Dynamics of stochastic gradient descent for two-layer neural networks in the teacher-student setup
Deep neural networks achieve stellar generalisation even when they have enough
parameters to easily fit all their training data. We study this phenomenon by analysing the …
parameters to easily fit all their training data. We study this phenomenon by analysing the …
Continual learning in the teacher-student setup: Impact of task similarity
Continual learning {—} the ability to learn many tasks in sequence {—} is critical for artificial
learning systems. Yet standard training methods for deep networks often suffer from …
learning systems. Yet standard training methods for deep networks often suffer from …
The benefits of reusing batches for gradient descent in two-layer networks: Breaking the curse of information and leap exponents
We investigate the training dynamics of two-layer neural networks when learning multi-index
target functions. We focus on multi-pass gradient descent (GD) that reuses the batches …
target functions. We focus on multi-pass gradient descent (GD) that reuses the batches …