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Related Experiment Video

Updated: Jul 28, 2025

Deep Neural Networks for Image-Based Dietary Assessment

Deep Neural Networks for Image-Based Dietary Assessment

Published on: March 13, 2021

Bayesian interpolation with deep linear networks.

Boris Hanin¹, Alexander Zlokapa^2,3

¹Department of Operations Research and Financial Engineering, Princeton University, Princeton, NJ 08540.

Proceedings of the National Academy of Sciences of the United States of America

|May 30, 2023

Summary

This summary is machine-generated.

Deep neural networks achieve optimal predictions at infinite depth. Increased depth aids model selection in wide networks, with effective depth determined by layers, data, and width.

Keywords:

Bayesian Inference Deep Learning Linear Networks Neural Networks

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Area of Science:

Deep learning theory
Computational neuroscience
Statistical modeling

Background:

Understanding the interplay of neural network architecture (depth, width) and dataset size on model performance is crucial.
Linear networks offer a tractable model for theoretical analysis in deep learning.

Purpose of the Study:

To provide a complete theoretical solution for linear networks regarding depth, width, and dataset size.
To derive non-asymptotic expressions for predictive posterior and Bayesian model evidence.
To elucidate the role of network depth in optimal prediction and model selection.

Main Methods:

Bayesian inference with Gaussian weight priors and mean squared error loss.
Utilizing Meijer-G functions for non-asymptotic expressions.
Applying novel asymptotic expansions of Meijer-G functions.

Main Results:

Derived non-asymptotic expressions for predictive posterior and Bayesian model evidence in linear networks.
Demonstrated that infinite-depth linear networks with data-agnostic priors yield optimal predictions.
Showcased that Bayesian model evidence in wide networks is maximized at infinite depth.

Conclusions:

Infinite depth provides a principled advantage for linear networks, especially with data-agnostic priors.
Increased network depth is beneficial for model selection in wide linear networks.
Introduced an 'effective depth' metric that governs posterior structure in the large-data limit.