Neural Network Weight Matrix

Neural network weight matrices are the core components encoding learned information within artificial neural networks, and their properties are crucial for understanding network behavior and performance. Current research focuses on analyzing the structure and statistical properties of these matrices, particularly investigating the interplay between their singular values and eigenvectors to distinguish learned information from noise, across various architectures including convolutional neural networks, vision transformers, and recurrent neural networks. This analysis utilizes techniques from random matrix theory and numerical linear algebra to improve training stability, optimize learning algorithms, and enhance generalization capabilities, ultimately leading to more efficient and robust neural network models.