Publications by Stefano Spigler

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How many training data are needed to learn a supervised task? It is often observed that the generalization error decreases as n(-beta) where n is the number of training examples and beta is an exponent that depends on both data and algorithm. In this work ...

We investigate how the training curve of isotropic kernel methods depends on the symmetry of the task to be learned, in several settings. (i) We consider a regression task, where the target function is a Gaussian random field that depends only on d(paralle ...

Deep learning has been immensely successful at a variety of tasks, ranging from classification to artificial intelligence. Learning corresponds to fitting training data, which is implemented by descending a very high-dimensional loss function. Understandin ...

Two distinct limits for deep learning have been derived as the network width h -> infinity, depending on how the weights of the last layer scale with h. In the neural tangent Kernel (NTK) limit, the dynamics becomes linear in the weights and is described b ...

We analyze numerically the training dynamics of deep neural networks (DNN) by using methods developed in statistical physics of glassy systems. The two main issues we address are (1) the complexity of the loss landscape and of the dynamics within it, and ( ...

Supervised deep learning involves the training of neural networks with a large number N of parameters. For large enough N, in the so-called over-parametrized regime, one can essentially fit the training data points. Sparsitybased arguments would suggest th ...

We analyze numerically the training dynamics of deep neural networks (DNN) by using methods developed in statistical physics of glassy systems. The two main issues we address are the complexity of the loss-landscape and of the dynamics within it, and to wh ...

Stefano Spigler

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Asymptotic learning curves of kernel methods: empirical data versus teacher-student paradigm

How isotropic kernels perform on simple invariants

Jamming transition as a paradigm to understand the loss landscape of deep neural networks

Disentangling feature and lazy training in deep neural networks

Comparing dynamics: deep neural networks versus glassy systems

Scaling description of generalization with number of parameters in deep learning

Comparing Dynamics: Deep Neural Networks versus Glassy Systems