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1. Batch Normalization Preconditioning for Neural Network Training

   Lange, S.; Helfrich, K.; Ye, Q. (January 2022, Journal of machine learning research)

   Batch normalization (BN) is a popular and ubiquitous method in deep learning that has been shown to decrease training time and improve generalization performance of neural networks. Despite its success, BN is not theoretically well understood. It is not suitable for use with very small mini-batch sizes or online learning. In this paper, we propose a new method called Batch Normalization Preconditioning (BNP). Instead of applying normalization explicitly through a batch normalization layer as is done in BN, BNP applies normalization by conditioning the parameter gradients directly during training. This is designed to improve the Hessian matrix of the loss function and hence convergence during training. One benefit is that BNP is not constrained on the mini-batch size and works in the online learning setting. Furthermore, its connection to BN provides theoretical insights on how BN improves training and how BN is applied to special architectures such as convolutional neural networks. For a theoretical foundation, we also present a novel Hessian condition number based convergence theory for a locally convex but not strong-convex loss, which is applicable to networks with a scale-invariant property. 

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2. Training Faster by Separating Modes of Variation in Batch-normalized Models

   https://doi.org/10.1109/TPAMI.2019.2895781  

   Kalayeh, Mahdi M.; Shah, Mubarak (January 2019, IEEE Transactions on Pattern Analysis and Machine Intelligence)

   Batch Normalization (BN) is essential to effectively train state-of-the-art deep Convolutional Neural Networks (CNN). It normalizes the layer outputs during training using the statistics of each mini-batch. BN accelerates training procedure by allowing to safely utilize large learning rates and alleviates the need for careful initialization of the parameters. In this work, we study BN from the viewpoint of Fisher kernels that arise from generative probability models. We show that assuming samples within a mini-batch are from the same probability density function, then BN is identical to the Fisher vector of a Gaussian distribution. That means batch normalizing transform can be explained in terms of kernels that naturally emerge from the probability density function that models the generative process of the underlying data distribution. Consequently, it promises higher discrimination power for the batch-normalized mini-batch. However, given the rectifying non-linearities employed in CNN architectures, distribution of the layer outputs show an asymmetric characteristic. Therefore, in order for BN to fully benefit from the aforementioned properties, we propose approximating underlying data distribution not with one, but a mixture of Gaussian densities. Deriving Fisher vector for a Gaussian Mixture Model (GMM), reveals that batch normalization can be improved by independently normalizing with respect to the statistics of disentangled sub-populations. We refer to our proposed soft piecewise version of batch normalization as Mixture Normalization (MN). Through extensive set of experiments on CIFAR-10 and CIFAR-100, using both a 5-layers deep CNN and modern Inception-V3 architecture, we show that mixture normalization reduces required number of gradient updates to reach the maximum test accuracy of the batch normalized model by ∼31%-47% across a variety of training scenarios. Replacing even a few BN modules with MN in the 48-layers deep Inception-V3 architecture is sufficient to not only obtain considerable training acceleration but also better final test accuracy. We show that similar observations are valid for 40 and 100-layers deep DenseNet architectures as well. We complement our study by evaluating the application of mixture normalization to the Generative Adversarial Networks (GANs), where "mode collapse" hinders the training process. We solely replace a few batch normalization layers in the generator with our proposed mixture normalization. Our experiments using Deep Convolutional GAN (DCGAN) on CIFAR-10 show that mixture normalized DCGAN not only provides an acceleration of ∼58% but also reaches lower (better) "Fréchet Inception Distance" (FID) of 33.35 compared to 37.56 of its batch normalized counterpart. 

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3. Instance Enhancement Batch Normalization: An Adaptive Regulator of Batch Noise

   https://doi.org/10.1609/aaai.v34i04.5917  

   Liang, Senwei; Huang, Zhongzhan; Liang, Mingfu; Yang, Haizhao (June 2020, Proceedings of the AAAI Conference on Artificial Intelligence)

   null (Ed.)

   Batch Normalization (BN) (Ioffe and Szegedy 2015) normalizes the features of an input image via statistics of a batch of images and hence BN will bring the noise to the gradient of training loss. Previous works indicate that the noise is important for the optimization and generalization of deep neural networks, but too much noise will harm the performance of networks. In our paper, we offer a new point of view that the self-attention mechanism can help to regulate the noise by enhancing instance-specific information to obtain a better regularization effect. Therefore, we propose an attention-based BN called Instance Enhancement Batch Normalization (IEBN) that recalibrates the information of each channel by a simple linear transformation. IEBN has a good capacity of regulating the batch noise and stabilizing network training to improve generalization even in the presence of two kinds of noise attacks during training. Finally, IEBN outperforms BN with only a light parameter increment in image classification tasks under different network structures and benchmark datasets. 

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4. Understanding Dynamics of Nonlinear Representation Learning and Its Application

   https://doi.org/10.1162/neco_a_01483  

   Kawaguchi, Kenji; Zhang, Linjun; Deng, Zhun (March 2022, Neural Computation)

   Abstract Representations of the world environment play a crucial role in artificial intelligence. It is often inefficient to conduct reasoning and inference directly in the space of raw sensory representations, such as pixel values of images. Representation learning allows us to automatically discover suitable representations from raw sensory data. For example, given raw sensory data, a deep neural network learns nonlinear representations at its hidden layers, which are subsequently used for classification (or regression) at its output layer. This happens implicitly during training through minimizing a supervised or unsupervised loss. In this letter, we study the dynamics of such implicit nonlinear representation learning. We identify a pair of a new assumption and a novel condition, called the on-model structure assumption and the data architecture alignment condition. Under the on-model structure assumption, the data architecture alignment condition is shown to be sufficient for the global convergence and necessary for global optimality. Moreover, our theory explains how and when increasing network size does and does not improve the training behaviors in the practical regime. Our results provide practical guidance for designing a model structure; for example, the on-model structure assumption can be used as a justification for using a particular model structure instead of others. As an application, we then derive a new training framework, which satisfies the data architecture alignment condition without assuming it by automatically modifying any given training algorithm dependent on data and architecture. Given a standard training algorithm, the framework running its modified version is empirically shown to maintain competitive (practical) test performances while providing global convergence guarantees for deep residual neural networks with convolutions, skip connections, and batch normalization with standard benchmark data sets, including MNIST, CIFAR-10, CIFAR-100, Semeion, KMNIST, and SVHN. 

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5. Neural sampling machine with stochastic synapse allows brain-like learning and inference

   https://doi.org/10.1038/s41467-022-30305-8  

   Dutta, Sourav; Detorakis, Georgios; Khanna, Abhishek; Grisafe, Benjamin; Neftci, Emre; Datta, Suman (May 2022, Nature Communications)

   Abstract Many real-world mission-critical applications require continual online learning from noisy data and real-time decision making with a defined confidence level. Brain-inspired probabilistic models of neural network can explicitly handle the uncertainty in data and allow adaptive learning on the fly. However, their implementation in a compact, low-power hardware remains a challenge. In this work, we introduce a novel hardware fabric that can implement a new class of stochastic neural network called Neural Sampling Machine (NSM) by exploiting the stochasticity in the synaptic connections for approximate Bayesian inference. We experimentally demonstrate an in silico hybrid stochastic synapse by pairing a ferroelectric field-effect transistor (FeFET)-based analog weight cell with a two-terminal stochastic selector element. We show that the stochastic switching characteristic of the selector between the insulator and the metallic states resembles the multiplicative synaptic noise of the NSM. We perform network-level simulations to highlight the salient features offered by the stochastic NSM such as performing autonomous weight normalization for continual online learning and Bayesian inferencing. We show that the stochastic NSM can not only perform highly accurate image classification with 98.25% accuracy on standard MNIST dataset, but also estimate the uncertainty in prediction (measured in terms of the entropy of prediction) when the digits of the MNIST dataset are rotated. Building such a probabilistic hardware platform that can support neuroscience inspired models can enhance the learning and inference capability of the current artificial intelligence (AI). 

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