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

arXiv: https://arxiv.org/abs/2409.01568 · HTML: https://mlsanity.com/paper/2409.01568/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 17 references that are in the map.
- First posted on arXiv 3 Sep 2024.

## Builds on (most cited first, 10 of 10)

- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [Network Dissection: Quantifying Interpretability of Deep Visual Representations](https://mlsanity.com/paper/1704.05796/) (2017)
- [Understanding Neural Networks Through Deep Visualization](https://mlsanity.com/paper/1506.06579/) (2015)
- [Understanding Emergent Abilities of Language Models from the Loss Perspective](https://mlsanity.com/paper/2403.15796/) (2024)
- [Robustness of Neural Networks: A Probabilistic and Practical Approach](https://mlsanity.com/paper/1902.05983/) (2019)
- [Information Flow in Deep Neural Networks](https://mlsanity.com/paper/2202.06749/) (2022)
- [Emergence and Evolution of Hierarchical Structure in Complex Systems](https://mlsanity.com/paper/1805.04924/) (2018)

## Abstract (arXiv)

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.