Research fascinations

Also, I realized that the experiences equipped are the inception of my hunger for the many unsolved questions in my brain. These questions are eclectic and they eventually align to same grounding problem “how can a human brain perceive and process information (esp. visual) and can we compute the same?”

This compelling question is growing as the field of science advances. The seminal work by David Marr and his ideation of designing computational models which comprehend similar to the human brain intrigues me a lot. In Marr’s period, science has a lot of unanswered questions about the functionality of various proportions of the brain. But the current scientific research is far ahead and can pave a way to better comprehend the human brain and design more complex algorithms.

I’m highly determined to conduct research in this direction. As it’s a sophisticated question, it needs so many minute intricate questions that are to be addressed from various directions. For this reason this section looks eclectic but, in the end all the dots are connected to answer the above question (Atleast, to some extent). So, you’ll discern that these works are motivated from the field(s) of Geometry, Manifolds, Cognitive Science, Neurobiology, and Neurophysiology etc.

Stereographic Projection

A simple yet effective method to better comprehend the representations in hyperspherical and hyperbolic manifolds. It is quite easy to implement hyperspherical manifolds as they share the same topology with the Euclidean space (with both spherical and Euclidean metrics). Finding derivatives from the computational graph and backpropagating to update the weights is easy. Hence, we embedded stereographic projection as an alternative to l2-normalization.

The initial work and experiments are detailed in the paper Lalith et al. [1] where we theoretically prove that hyperspherical manifolds are convex and connected. Additionally, we conduct some experiments on standard image classification data (CIFAR-10 and 100) and prove that our method is comparatively better.

But this is not sufficient to describe the underlying significance of this method. Tons of evaluations are to be done to justify the significance. Currently this work is under progress and once we complete this work, I'll update the details accordingly (including publication details).