Linear Neural Network

Linear neural networks, despite their apparent simplicity, are a crucial area of research in deep learning, serving as a tractable model for investigating fundamental optimization and generalization properties. Current research focuses on understanding the dynamics of gradient descent in these networks, particularly in overparameterized settings and across various architectures including fully-connected and convolutional models, analyzing phenomena like double descent and the impact of regularization techniques such as batch normalization and L2 regularization. These studies provide valuable insights into the behavior of more complex nonlinear networks and contribute to a deeper theoretical understanding of deep learning's success, impacting both algorithm design and the interpretation of model behavior.