Exploring the Impact of Additive Shortcuts in Neural Networks via Information Bottleneck-like Dynamics: From ResNet to Transformer.

Deep learning has made significant strides, driving advances in areas like computer vision, natural language processing, and autonomous systems. In this paper, we further investigate the implications of the role of additive shortcut connections, focusing on models such as ResNet, Vision Transformers (ViTs), and MLP-Mixers, given that they are essential in enabling efficient information flow and mitigating optimization challenges such as vanishing gradients. In particular, capitalizing on our recent information bottleneck approach, we analyze how additive shortcuts influence the fitting and compression phases of training, crucial for generalization.

On Neural Networks Fitting, Compression, and Generalization Behavior via Information-Bottleneck-like Approaches.

It is well-known that a neural network learning process-along with its connections to fitting, compression, and generalization-is not yet well understood. In this paper, we propose a novel approach to capturing such neural network dynamics using information-bottleneck-type techniques, involving the replacement of mutual information measures (which are notoriously difficult to estimate in high-dimensional spaces) by other more tractable ones, including (1) the minimum mean-squared error associated with the reconstruction of the network input data from some intermediate network representation and (2) the cross-entropy associated with a certain class label given some network representation. We then conducted an empirical study in order to ascertain how different network models, network learning algorithms, and datasets may affect the learning dynamics.