In this paper, we extend the characterization of Z[x]/f , where f ∈ Z[x] to be a free Z-module to multivariate polynomial rings over any commutative Noetherian ring, A. The characterization allows us… (More)
Spectral graph partitioning methods have received significant attention from both practitioners and theorists in computer science. Some notable studies have been carried out regarding the behavior of… (More)
In a series of recent works, we have generalised the consistency results in the stochastic block model literature to the case of uniform and non-uniform hypergraphs. The present paper continues the… (More)
Kullback–Leibler relative-entropy has unique properties in cases involving distributions resulting from relative-entropy minimization. Tsallis relative-entropy is a one-parameter generalization of… (More)
Rapid learning requires flexible representations to quickly adopt to new evidence. We develop a novel class of models called Attentive Recurrent Comparators (ARCs) that form representations of… (More)
Spectral clustering, a graph partitioning technique, has gained immense popularity in machine learning in the context of unsupervised learning. This is due to convincing empirical studies, elegant… (More)
In recent years, deep architectures have gained a lot of prominence for learning complex AI tasks because of their capability to incorporate complex variations in data within the model. However,… (More)
Boltzmann selection is an important selection mechanism in evolutionary algorithms as it has theoretical properties which help in theoretical analysis. However, Boltzmann selection is not used in… (More)
In this work we use the recent advances in representation learning to propose a neural architecture for the problem of natural language inference. Our approach is aligned to mimic how a human does… (More)
Matrix spectral methods play an important role in statistics and machine learning, and most often the word ‘matrix’ is dropped as, by default, one assumes that similarities or affinities are measured… (More)