Orthogonal and Idempotent Transformations for Learning Deep Neural Networks
This work addresses training challenges in deep neural networks, particularly for researchers and practitioners, but it is incremental as it builds on existing skip-connection methods.
The paper tackled the problem of improving information flow and easing training in deep neural networks by introducing orthogonal and idempotent transformations as alternatives to identity skip-connections, resulting in similar performance in single-branch networks and superior performance in multi-branch networks compared to identity transformations.
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.