Learning from a Computational Topology Perspective
We like to talk about and quantify things in Euclidean space, that's where our intuition works the best. However, most of the times it might be complicated trying to find the correct "metric" of understanding things in here. Under such nice and structured space, we sometimes don't know how to talk about complex, yet interesting, data. However, as a “coordinate-free” method, computational topology may provide us a new way to understand the shape of data in a more abstract but comprehensive way.
Borrowed from Prof. Wang's Computational TDA textbook: filtartion formulation
I am currently using computational topological method in Prof. Yusu Wang's DSC 214 to try to understand what's truely happening inside the weight space of neural network when they are training upon specific tasks. Particularly, I am interested in seeing how the deep reinforcement learning in the VNL system may evolve different topological characteristics across training. Hopefully, we can:
- Helping us to better understand what is truly happening inside neural network, what makes learning?
- What phenomenon is happening in the weight world when we use a topological lens?
- How does the weight tend to be represented/transformed?
- Can this phenomenon be carried from weight → intention → action?
- Providing another metric of comparing with experimental neuronal data (~homeomorphic).