A Gentle Introduction to Group Theory

 Group theory is kind of hard to wrap your head around.  At least for me.  But at the same time, it has a fundamental relationship to not only the theory behind neural networks, but also computational models of human visual perception.

With that thought in mind, let's check out this very simple introduction to group theory.




We have covered group theory in previous HTC posts, including a seminar by Max Weiler on gauge and group theory equivalent CNNs, as well as a post on Lie Groups and Human Visual Perception, and another post on the biophysics of visual edge detection.


Observations:

1: Note the fascinating tie in between Gabor filters, channel models of human visual perception, and notions from group theory (Lie Groups).

2: What does this whole notion of their being an absolute finite number of possible simple groups (the monster) tell us about the limits of human visual perception?

3:  How could we turn all of this around in a way that could influence the design of deep learning systems?  Especially ones for generative imaging.


Let's continue our gentle introduction to group theory via an exploration of Euler's formula.




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