SEMINAR

Mehler’s formula, Branching process and Compositional Kernels of Deep Neural Networks

Speaker

Hai Tran-Bach

Working
University of Chicago
Timeline
Fri, Sep 18 2020 - 10:00 am (GMT + 7)
About Speaker

Hai Tran-Bach earned a Bachelor’s of Science in Mathematics and Data Science at the University of Michigan with high honors and high distinctions. Currently, he is a third year distinguished Neubauer Doctoral Fellow in the Department of Statistics at the University of Chicago. His research interest is to understand the empirical phenomena in modern machine learning and to use these insights to derive principled machine learning algorithms. He is currently working on identifying favorable properties of neural networks that lead to good generalization.

Abstract

We utilize a connection between compositional kernels and branching processes via Mehler’s formula to study deep neural networks. This new probabilistic insight provides us a novel perspective on the mathematical role of activation functions in compositional neural networks. Concretely, we

study the unscaled and rescaled limits of the compositional kernels and explore the different phases of the limiting behavior, as the compositional depth increases.
investigate the memorization capacity of the compositional kernels and neural networks by characterizing the interplay among compositional depth, sample size, dimensionality, and non-linearity of the activation.
provide explicit formulas on the eigenvalues of the compositional kernel, which quantify the complexity of the corresponding RKHS.
propose a new random features algorithm, which compresses the compositional layers by devising a new activation function.

Related seminars

Anh Nguyen

Microsoft GenAI

The Revolution of Small Language Models
Fri, Mar 8 2024 - 02:30 pm (GMT + 7)

Thang D. Bui

Australian National University (ANU)

Recent Progress on Grokking and Probabilistic Federated Learning
Fri, Jan 26 2024 - 10:00 am (GMT + 7)

Tim Baldwin

MBZUAI, The University of Melbourne

LLMs FTW
Tue, Jan 9 2024 - 10:30 am (GMT + 7)

Quan Vuong

Google DeepMind

Scaling Robot Learning
Wed, Dec 27 2023 - 10:00 am (GMT + 7)