Riemannian approach to batch normalization
This work addresses the efficiency and analysis challenges in BN for deep learning practitioners, though it appears incremental as it builds on existing BN methods.
The paper tackled the problem of improving Batch Normalization (BN) in deep neural networks by interpreting the weight space as a Riemannian manifold, resulting in a new learning rule that consistently outperforms the original BN across various architectures and datasets.
Batch Normalization (BN) has proven to be an effective algorithm for deep neural network training by normalizing the input to each neuron and reducing the internal covariate shift. The space of weight vectors in the BN layer can be naturally interpreted as a Riemannian manifold, which is invariant to linear scaling of weights. Following the intrinsic geometry of this manifold provides a new learning rule that is more efficient and easier to analyze. We also propose intuitive and effective gradient clipping and regularization methods for the proposed algorithm by utilizing the geometry of the manifold. The resulting algorithm consistently outperforms the original BN on various types of network architectures and datasets.