Event info

Date: 12:00~13:00 JST Monday, 22 June 2026

Zoom: Online via Zoom

Speaker: Julyan Arbel (Inria and University of Grenoble Alpes, France)

Title: Depth, Heavy Tails, and Posterior Contraction Rates: A Bayesian Nonparametric View of Bayesian Neural Networks

Abstract:
Despite their remarkable empirical success, deep neural networks remain limited in practical deployment by overconfident predictions, poor interpretability, and the absence of principled uncertainty quantification. Bayesian deep learning addresses these shortcomings by embedding neural networks within a probabilistic framework, enabling uncertainty-aware prediction, principled regularization, and more robust decision-making.
This talk begins with an overview of Bayesian neural networks, covering model formulations, prior specification, and the main approximate inference strategies used in practice, including variational inference, Monte Carlo methods, and modern scalable approximations.
We then develop a Bayesian nonparametric analysis of Gaussian-weight Bayesian neural networks, revealing a striking and practically consequential phenomenon: in deep architectures with i.i.d. Gaussian weights, the multiplicative structure across layers induces increasingly heavy-tailed function-space priors as depth grows. Leveraging a radial product-of-Gaussians representation, we show that this implicit heavy-tailed behavior generates sufficient prior mass around smooth target functions to achieve near-minimax posterior contraction rates, without any explicit heavy-tailed prior specification. Our analysis establishes prior mass conditions by exploiting depth-dependent tail amplification at the unit level, and connects these results to adaptive approximation theory and benign overfitting phenomena.
Joint work with Paul Egel and Ismaël Castillo.

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This seminar series is a valuable opportunity for graduate students to get acquainted with the work of more experienced researchers in various mathematical fields. Undergraduate students are also welcome to join, as the talks are intended for non-experts, too. Regardless of your area of research, you can attend the seminar to expand your knowledge and get in touch with the latest developments in mathematics for industry.
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