Orthogonal and Idempotent Transformations for Learning Deep Neural Networks

TL;DR

This paper introduces orthogonal and idempotent linear transformations as alternatives to identity skip-connections in deep neural networks, enhancing information flow and training efficiency.

Contribution

It proposes novel orthogonal and idempotent transformations for skip-connections, improving information and gradient flow in deep networks.

Findings

Similar performance to identity in single-branch networks

Superior performance in multi-branch networks

Effective in easing training and maintaining information flow

Abstract

Identity transformations, used as skip-connections in residual networks, directly connect convolutional layers close to the input and those close to the output in deep neural networks, improving information flow and thus easing the training. In this paper, we introduce two alternative linear transforms, orthogonal transformation and idempotent transformation. According to the definition and property of orthogonal and idempotent matrices, the product of multiple orthogonal (same idempotent) matrices, used to form linear transformations, is equal to a single orthogonal (idempotent) matrix, resulting in that information flow is improved and the training is eased. One interesting point is that the success essentially stems from feature reuse and gradient reuse in forward and backward propagation for maintaining the information during flow and eliminating the gradient vanishing problem because of the express way through skip-connections. We empirically demonstrate the effectiveness of the proposed two transformations: similar performance in single-branch networks and even superior in multi-branch networks in comparison to identity transformations.