Constraining Implicit Space with Minimum Description Length: An Unsupervised Attention Mechanism across Neural Network Layers

Inspired by the adaptation phenomenon of neuronal firing, we propose the regularity normalization (RN) as an unsupervised attention mechanism (UAM) which computes the statistical regularity in the implicit space of neural networks under the Minimum Description Length (MDL) principle. Treating the neural network optimization process as a partially observable model selection problem, UAM constrains the implicit space by a normalization factor, the universal code length. We compute this universal code incrementally across neural network layers and demonstrated the flexibility to include data priors such as top-down attention and other oracle information. Empirically, our approach outperforms existing normalization methods in tackling limited, imbalanced and non-stationary input distribution in image classification, classic control, procedurally-generated reinforcement learning, generative modeling, handwriting generation and question answering tasks with various neural network architectures. Lastly, UAM tracks dependency and critical learning stages across layers and recurrent time steps of deep networks

Optimization Theory for ReLU Neural Networks Trained with Normalization Layers

The success of deep neural networks is in part due to the use of normalization layers. Normalization layers like Batch Normalization, Layer Normalization and Weight Normalization are ubiquitous in practice, as they improve generalization performance and speed up training significantly. Nonetheless, the vast majority of current deep learning theory and non-convex optimization literature focuses on the un-normalized setting, where the functions under consideration do not exhibit the properties of commonly normalized neural networks. In this paper, we bridge this gap by giving the first global convergence result for two-layer neural networks with ReLU activations trained with a normalization layer, namely Weight Normalization. Our analysis shows how the introduction of normalization layers changes the optimization landscape and can enable faster convergence as compared with un-normalized neural networks.Comment: To be presented at ICML 202