N$ Neuron

Research on neural networks is actively exploring the phenomenon of "superposition," where individual neurons represent multiple features simultaneously, impacting computational efficiency and interpretability. Current investigations focus on mathematical models of computation in superposition, analyzing the minimal number of neurons needed for tasks like interpolation and classification using various architectures including multilayer perceptrons and neural ordinary differential equations. These studies aim to understand the relationship between network width, expressivity, and trainability, ultimately seeking to optimize network design for improved performance and reduced computational cost. This work has implications for both theoretical understanding of neural network capabilities and the practical development of more efficient and interpretable AI systems.