Quantifying Emergence in Neural Networks: Insights from Pruning and Training Dynamics

TL;DR

This paper introduces a quantitative framework to measure emergence in neural networks, revealing how emergence influences training dynamics, pruning effects, and overall network performance.

Contribution

It provides a novel method to quantify emergence and demonstrates its predictive power for network trainability and performance improvements.

Findings

Higher emergence correlates with better trainability and performance.

Pruning enhances training efficiency but may reduce final accuracy.

Emergence relates to the complexity of the loss landscape.

Abstract

Emergence, where complex behaviors develop from the interactions of simpler components within a network, plays a crucial role in enhancing neural network capabilities. We introduce a quantitative framework to measure emergence during the training process and examine its impact on network performance, particularly in relation to pruning and training dynamics. Our hypothesis posits that the degree of emergence, defined by the connectivity between active and inactive nodes, can predict the development of emergent behaviors in the network. Through experiments with feedforward and convolutional architectures on benchmark datasets, we demonstrate that higher emergence correlates with improved trainability and performance. We further explore the relationship between network complexity and the loss landscape, suggesting that higher emergence indicates a greater concentration of local minima and a more rugged loss landscape. Pruning, which reduces network complexity by removing redundant nodes and connections, is shown to enhance training efficiency and convergence speed, though it may lead to a reduction in final accuracy. These findings provide new insights into the interplay between emergence, complexity, and performance in neural networks, offering valuable implications for the design and optimization of more efficient architectures.