Understanding the Distributions of Aggregation Layers in Deep Neural Networks.

Area of Science:

• Deep Learning
• Machine Learning
• Information Theory

Background:

• Aggregation layers are crucial in deep neural networks (DNNs) for feature consolidation and improving model robustness.
• Understanding the impact of aggregated features on DNN performance is vital, especially given their proximity to output layers.

Purpose of the Study:

• To develop a novel mathematical formulation for analytically modeling probability distributions of output values from deep feature aggregation layers.
• To analytically predict the Kullback-Leibler (KL)-divergence of output nodes in DNNs.

Main Methods:

• Proposing a new mathematical framework to model activation distributions in aggregation layers.
• Analytically deriving the Kullback-Leibler (KL)-divergence for output nodes.
• Empirically validating theoretical predictions across diverse classification tasks and datasets.

Main Results:

• Successfully developed an analytical model for probability distributions of aggregation layer outputs.
• Achieved accurate analytical prediction of Kullback-Leibler (KL)-divergence for DNN output nodes.
• Experimental verification confirmed the model's efficacy across various classification benchmarks.

Conclusions:

• The proposed mathematical formulation provides a powerful tool for understanding deep feature aggregation in DNNs.
• Analytical prediction of KL-divergence offers insights into model behavior and performance.
• The findings contribute to the theoretical foundation of deep learning and model interpretability.