Bishshoy Das

Suryaka Suresh, Bishshoy Das, Vinayak Abrol et al.

We study how the topology of feature embedding space changes as it passes through the layers of a well-trained deep neural network (DNN) through Betti numbers. Motivated by existing studies using simplicial complexes on shallow fully connected networks (FCN), we present an extended analysis using Cubical homology instead, with a variety of popular deep architectures and real image datasets. We demonstrate that as depth increases, a topologically complicated dataset is transformed into a simple one, resulting in Betti numbers attaining their lowest possible value. The rate of decay in topological complexity (as a metric) helps quantify the impact of architectural choices on the generalization ability. Interestingly from a representation learning perspective, we highlight several invariances such as topological invariance of (1) an architecture on similar datasets; (2) embedding space of a dataset for architectures of variable depth; (3) embedding space to input resolution/size, and (4) data sub-sampling. In order to further demonstrate the link between expressivity \& the generalization capability of a network, we consider the task of ranking pre-trained models for downstream classification task (transfer learning). Compared to existing approaches, the proposed metric has a better correlation to the actually achievable accuracy via fine-tuning the pre-trained model.

Bishshoy Das, Milton Mondal, Brejesh Lall et al.

In standard neural network training, the gradients in the backward pass are determined by the forward pass. As a result, the two stages are coupled. This is how most neural networks are trained currently. However, gradient modification in the backward pass has seldom been studied in the literature. In this paper we explore decoupled training, where we alter the gradients in the backward pass. We propose a simple yet powerful method called PowerGrad Transform, that alters the gradients before the weight update in the backward pass and significantly enhances the predictive performance of the neural network. PowerGrad Transform trains the network to arrive at a better optima at convergence. It is computationally extremely efficient, virtually adding no additional cost to either memory or compute, but results in improved final accuracies on both the training and test sets. PowerGrad Transform is easy to integrate into existing training routines, requiring just a few lines of code. PowerGrad Transform accelerates training and makes it possible for the network to better fit the training data. With decoupled training, PowerGrad Transform improves baseline accuracies for ResNet-50 by 0.73%, for SE-ResNet-50 by 0.66% and by more than 1.0% for the non-normalized ResNet-18 network on the ImageNet classification task.