### Next seminar : Séminaire du LPTMS : Pietro Rotondo (Infn Milano)

##### Tuesday, May 17 2022 at 11:00:00

## Universal mean field upper bound for the generalisation gap of deep neural networks

### Pietro Rotondo (Infn Milano)

Hybrid seminar: onsite + zoom. https://cnrs.zoom.us/j/92485497120?pwd=c0dBZVkxT2xmUzNNZDhZbU9lM2dsQT09 Meeting ID: 924 8549 7120 Passcode: dSQ0B2 Modern deep neural networks (DNNs) represent a formidable challenge for theorists: according to the commonly accepted probabilistic framework that describes their performance, these architectures should overfit due to the huge number of parameters to train, but in practice they do not. Here we employ results from replica mean field theory to compute the generalisation gap of machine learning models with quenched features, in the teacher-student scenario and for regression problems with quadratic loss function. Notably, this framework includes the case of DNNs where the last layer is optimised given a specific realisation of the remaining weights. We show how these results – combined with ideas from statistical learning theory – provide a stringent asymptotic upper bound on the generalisation gap of fully trained DNN as a function of the size of the dataset P. In particular, in the limit of large P and Nout (where Nout is the size of the last layer) and Nout ≪ P , the generalisation gap approaches zero faster than 2Nout/P, for any choice of both architecture and teacher function. Notably, this result greatly improves existing bounds from statistical learning theory. We test our predictions on a broad range of architectures, from toy fully-connected neural networks with few hidden layers to state-of-the-art deep convolutional neural networks.### Last Highlight : Physics and Biological Systems 2022

## Physics and Biological Systems 2022

June 27 - 29, 2022

The 6th International Conference on Physics and Biological Systems will be held on Jun. 27-29 2022 at ENS Paris-Saclay in Gif-sur-Yvette, in the south of Paris. It aims to bring together a broad range of physical and life scientists working at the interface between the two disciplines around in-depth talks by first-rate international speakers. Attendance will be limited to 200 participants.

Further information: http://lptms.u-psud.fr/physbio2022/