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Inspired by BatchNorm, there has been an explosion of normalization layers in deep learning.

Inspired by BatchNorm, there has been an explosion of normalization layers in deep learning.

We formulate the problem of neural network optimization as Bayesian filtering, where the observations are backpropagated gradients. While neural network optimization has previously been studied using natural gradient methods which are closely related to Bayesian inference, they were unable to recover standard optimizers such as Adam and RMSprop with a root-mean-square gradient normalizer, instead getting a mean-square normalizer. To recover the root-mean-square normalizer, we find it necessary to account for the temporal dynamics of all the other parameters as they are optimized. The resulting optimizer, AdaBayes, adaptively transitions between SGD-like and Adam-like behaviour, automatically recovers AdamW, a state of the art variant of Adam with decoupled weight decay, and has generalisation performance competitive with SGD.

Normalization methods are fundamental components of modern deep neural networks (DNNs). Empirically, they are known to stabilize optimization dynamics and improve generalization. However, the underlying theoretical mechanism by which normalization contributes to both optimization and generalization remains largely unexplained, especially when using many normalization layers in a DNN architecture. In this work, we develop a theoretical framework that elucidates the role of normalization through the lens of capacity control. We prove that an unnormalized DNN can exhibit exponentially large Lipschitz constants with respect to either its parameters or inputs, implying excessive functional capacity and potential overfitting. Such bad DNNs are uncountably many. In contrast, the insertion of normalization layers provably can reduce the Lipschitz constant at an exponential rate in the number of normalization operations. This exponential reduction yields two fundamental consequences: (1) it smooths the loss landscape at an exponential rate, facilitating faster and more stable optimization; and (2) it constrains the effective capacity of the network, thereby enhancing generalization guarantees on unseen data. Our results thus offer a principled explanation for the empirical success of normalization methods in deep learning.

ABSTRACT Whisper models have achieved remarkable progress in speech recognition; yet their large size remains a bottleneck for deployment on resource-constrained edge devices. This paper proposes a framework to design fine-tuned variants of Whisper which address the above problem. Structured sparsity is enforced via the Sparse Group LASSO penalty as a loss regu-larizer, to reduce the number of FLOating Point operations (FLOPs). Further, a weight statistics aware pruning algorithm is proposed. On Common V oice 11.0 Hindi dataset, we obtain, without degrading WER, (a) 35.4% reduction in model parameters, 14.25% lower memory consumption and 18.5% fewer FLOPs on Whisper-small, and (b) 31% reduction in model parameters, 15.29% lower memory consumption and 16.95% fewer FLOPs on Whisper-medium; and, (c) substantially outperform the state-of-the-art Iterative Magnitude Pruning based method by pruning 18.7% more parameters along with a 12.31 reduction in WER.

Inspired by BatchNorm, there has been an explosion of normalization layers in deep learning. Recent works have identified a multitude of beneficial properties in BatchNorm to explain its success. However, given the pursuit of alternative normalization layers, these properties need to be generalized so that any given layer's success/failure can be accurately predicted.