arXiv subjects

Arnab Paul

Publications and source records attributed to Arnab Paul.

21 records · Page 2Linked to original sources

arXiv2018

Non-thermal production of Dark Matter after Inflation

The existence of Dark Matter (DM) has been well established from various cosmological and astrophysical evidences. However, the particle properties of DM are largely undetermined and attempts to probe its interactions with the Standard Model (SM) particles have, so far, not met with any success. The stringent constraints on the DM-SM interactions, while does not exclude the standard lore of producing weakly massive interacting particle DM candidates through thermal freeze-out mechanism in its entirety, have certainly cast shadow on the same. In this work, we consider non-thermal production of DM within a simple extension of the SM including an inflaton field and a scalar DM candidate. Assuming negligible interactions between the SM particles and the DM, we study the production of the latter at the end of inflation, during the (p)reheating epoch. In this context, we explore the role of DM self-interactions and its interaction with the inflaton field, and find that DM can be over produced in a significant region of the parameter space. We further demonstrate that large self-interaction of the DM can suppress its abundance during preheating and to a certain extent helps to achieve the observed relic abundance via cannibalization.

hep-ph↗

arXiv2015

A Group Theoretic Perspective on Unsupervised Deep Learning

Why does Deep Learning work? What representations does it capture? How do higher-order representations emerge? We study these questions from the perspective of group theory, thereby opening a new approach towards a theory of Deep learning. One factor behind the recent resurgence of the subject is a key algorithmic step called {\em pretraining}: first search for a good generative model for the input samples, and repeat the process one layer at a time. We show deeper implications of this simple principle, by establishing a connection with the interplay of orbits and stabilizers of group actions. Although the neural networks themselves may not form groups, we show the existence of {\em shadow} groups whose elements serve as close approximations. Over the shadow groups, the pre-training step, originally introduced as a mechanism to better initialize a network, becomes equivalent to a search for features with minimal orbits. Intuitively, these features are in a way the {\em simplest}. Which explains why a deep learning network learns simple features first. Next, we show how the same principle, when repeated in the deeper layers, can capture higher order representations, and why representation complexity increases as the layers get deeper.

cs.LG↗

arXiv2015

Why does Deep Learning work? - A perspective from Group Theory

Why does Deep Learning work? What representations does it capture? How do higher-order representations emerge? We study these questions from the perspective of group theory, thereby opening a new approach towards a theory of Deep learning. One factor behind the recent resurgence of the subject is a key algorithmic step called pre-training: first search for a good generative model for the input samples, and repeat the process one layer at a time. We show deeper implications of this simple principle, by establishing a connection with the interplay of orbits and stabilizers of group actions. Although the neural networks themselves may not form groups, we show the existence of {\em shadow} groups whose elements serve as close approximations. Over the shadow groups, the pre-training step, originally introduced as a mechanism to better initialize a network, becomes equivalent to a search for features with minimal orbits. Intuitively, these features are in a way the {\em simplest}. Which explains why a deep learning network learns simple features first. Next, we show how the same principle, when repeated in the deeper layers, can capture higher order representations, and why representation complexity increases as the layers get deeper.

cs.LG↗