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

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.

Advancing Neural Network Performance through Emergence-Promoting Initialization Scheme

We introduce a novel yet straightforward neural network initialization scheme that modifies conventional methods like Xavier and Kaiming initialization. Inspired by the concept of emergence and leveraging the emergence measures proposed by Li (2023), our method adjusts the layer-wise weight scaling factors to achieve higher emergence values. This enhancement is easy to implement, requiring no additional optimization steps for initialization compared to GradInit. We evaluate our approach across various architectures, including MLP and convolutional architectures for image recognition, and transformers for machine translation. We demonstrate substantial improvements in both model accuracy and training speed, with and without batch normalization. The simplicity, theoretical innovation, and demonstrable empirical advantages of our method make it a potent enhancement to neural network initialization practices. These results suggest a promising direction for leveraging emergence to improve neural network training methodologies. Code is available at: https://github.com/johnnyjingzeli/EmergenceInit.