Florentin Guth

Postdoctoral Researcher in Deep Learning Theory

New York University and Flatiron Institute

Biography

I’m a Faculty Fellow in the Center for Data Science at NYU and a Research Fellow in the Center for Computational Neuroscience at the Flatiron Institute. I’m interested in improving our scientific understanding of deep learning, e.g., understand how it escapes the curse of dimensionality, particularly in the context of image generative models.

Between 2019 and 2023, I was completing my PhD at École Normale Supérieure in Paris under the supervision of Stéphane Mallat, entitled Towards a Mathematical Understanding of Deep Convolutional Neural Networks. You can find my thesis here and the defense slides here.

Interests

Science of Deep Learning
Image Generative Models

Education

Ph.D. in Applied Maths and CS, 2023
École Normale Supérieure
M.Sc. in Maths, CV and ML (MVA), 2019
École Normale Supérieure Paris-Saclay
M.Sc. and B.Sc. in Computer Science, 2019
École Normale Supérieure

News

04/24: I’m an invited speaker at the Mathematics and Machine Learning conference at ISMA in Miami!
02/24: I’m an invited speaker at the Youth in High Dimensions conference at ICTP in Trieste!
01/24: Our paper on generalization and memorization in diffusion models got an oral (top 1.2%) at ICLR 2024!
08/23: I successfully defended my PhD! Thesis and slides.
08/23: We gave a keynote and tutorial at CCN 2023 together with Mick Bonner and his lab.

Featured Publications

(see Google Scholar for a complete list)

Generalization in diffusion models arises from geometry-adaptive harmonic representations

We show that diffusion models can enter a generalization regime where the generated images are independent of the samples in the training set by relying on inductive biases towards geometric regularity in images.

A rainbow in deep network black boxes

We show how deep network weights can be compressed to a reduced set of summary statistics (the learned “features”) that (i) all networks share no matter their initialization and (ii) that allow regenerating weights with an equivalent performance.

Phase collapse in neural networks

We show that deep networks rely on phase collapses to classify images, rather than sparse coding as assumed in previous works, and introduce a simplified architecture with minimal learning while maintaining high accuracy.