Alokendu Mazumder

Alokendu Mazumder, Rishabh Sabharwal, Manan Tayal et al.

In neural network training, RMSProp and Adam remain widely favoured optimisation algorithms. One of the keys to their performance lies in selecting the correct step size, which can significantly influence their effectiveness. Additionally, questions about their theoretical convergence properties continue to be a subject of interest. In this paper, we theoretically analyse a constant step size version of Adam in the non-convex setting and discuss why it is important for the convergence of Adam to use a fixed step size. This work demonstrates the derivation and effective implementation of a constant step size for Adam, offering insights into its performance and efficiency in non convex optimisation scenarios. (i) First, we provide proof that these adaptive gradient algorithms are guaranteed to reach criticality for smooth non-convex objectives with constant step size, and we give bounds on the running time. Both deterministic and stochastic versions of Adam are analysed in this paper. We show sufficient conditions for the derived constant step size to achieve asymptotic convergence of the gradients to zero with minimal assumptions. Next, (ii) we design experiments to empirically study Adam's convergence with our proposed constant step size against stateof the art step size schedulers on classification tasks. Lastly, (iii) we also demonstrate that our derived constant step size has better abilities in reducing the gradient norms, and empirically, we show that despite the accumulation of a few past gradients, the key driver for convergence in Adam is the non-increasing step sizes.

Alokendu Mazumder, Tirthajit Baruah, Bhartendu Kumar et al.

The autoencoder is an unsupervised learning paradigm that aims to create a compact latent representation of data by minimizing the reconstruction loss. However, it tends to overlook the fact that most data (images) are embedded in a lower-dimensional space, which is crucial for effective data representation. To address this limitation, we propose a novel approach called Low-Rank Autoencoder (LoRAE). In LoRAE, we incorporated a low-rank regularizer to adaptively reconstruct a low-dimensional latent space while preserving the basic objective of an autoencoder. This helps embed the data in a lower-dimensional space while preserving important information. It is a simple autoencoder extension that learns low-rank latent space. Theoretically, we establish a tighter error bound for our model. Empirically, our model's superiority shines through various tasks such as image generation and downstream classification. Both theoretical and practical outcomes highlight the importance of acquiring low-dimensional embeddings.

Alokendu Mazumder, Tirthajit Baruah, Akash Kumar Singh et al.

Estimating the number of clusters and cluster structures in unlabeled, complex, and high-dimensional datasets (like images) is challenging for traditional clustering algorithms. In recent years, a matrix reordering-based algorithm called Visual Assessment of Tendency (VAT), and its variants have attracted many researchers from various domains to estimate the number of clusters and inherent cluster structure present in the data. However, these algorithms face significant challenges when dealing with image data as they fail to effectively capture the crucial features inherent in images. To overcome these limitations, we propose a deep-learning-based framework that enables the assessment of cluster structure in complex image datasets. Our approach utilizes a self-supervised deep neural network to generate representative embeddings for the data. These embeddings are then reduced to 2-dimension using t-distributed Stochastic Neighbour Embedding (t-SNE) and inputted into VAT based algorithms to estimate the underlying cluster structure. Importantly, our framework does not rely on any prior knowledge of the number of clusters. Our proposed approach demonstrates superior performance compared to state-of-the-art VAT family algorithms and two other deep clustering algorithms on four benchmark image datasets, namely MNIST, FMNIST, CIFAR-10, and INTEL.