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The Intrinsic Dimension of Neural Network Ensembles.

Francesco Tosti Guerra¹, Andrea Napoletano², Andrea Zaccaria²

¹Department of Physics, Sapienza University of Rome, 00185 Rome, Italy.

Entropy (Basel, Switzerland)

|April 26, 2025

Summary

Random network initialization significantly increases neural network ensemble variability more than data distortion or dropout. Understanding these training impacts optimizes model performance and parameter space exploration.

Keywords:

ensemble learning intrinsic dimension machine learning explainability neural network

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Area of Science:

Artificial Intelligence
Machine Learning
Computational Neuroscience

Background:

Neural networks exhibit complex collective behaviors during training.
These behaviors are often visualized on evolving mathematical structures called manifolds.
The intrinsic dimension quantifies ensemble variability and training strategy impact.

Purpose of the Study:

To analyze the collective behavior of neural network ensembles.
To quantify the impact of various training strategies on parameter space exploration.
To understand how training choices affect model accuracy.

Main Methods:

Characterizing neural network ensembles using intrinsic dimension on complex manifolds.
Quantifying parameter space coverage influenced by training choices.
Investigating the impact of random initialization, data distortion, dropout, and batch shuffle.

Main Results:

Random initialization is the primary driver of variability in neural network ensembles.
Intrinsic dimension correlates with parameter space coverage and network variability.
Combinations of training strategies and their impact on prediction accuracy were analyzed.

Conclusions:

Training choices, particularly random initialization, significantly influence neural network ensemble dynamics.
Higher intrinsic dimension indicates greater variability and parameter space exploration.
This study highlights the critical, often underestimated, role of training strategies in deep learning.