Yang Mills, Vector bundles, Quantum Information Geometry & Fisher-Bures Adversary Graph Convolutional Networks etc.

Hello guys,


It's been a long time since my last post & its Tuesday night.. Yes.. I am still DataHulk.. When I get angry I work on Big Data... :) 

- And off course.. Maryna Viazovska (one of the researcher who might win field prize as per my first blogpost based on Graph Mining, NLP, Reinforcement Learning & Profiling along with Bhargav Bhatt etc. - Graph Mining, Network Science + Topology & Predicting Field Prize - https://researchcircle.blogspot.com/2021/12/graph-mining-network-science-topology.html) has published new paper on Hyperbolic Fourier series - https://arxiv.org/abs/2110.00148

....... while Terence Tao has published new paper on Perfectly packing a square by squares of nearly harmonic sidelength - https://arxiv.org/abs/2202.03594 (Another signal that Sphere Packing problem is flavor of the season and Maryna Viazovska might win Field Prize for her effort on Sphere Packing in N = 8 & 24) 

There are 4 papers which I suggest reading everyone who is interested in intersection of Yang Mills, Vector Bundles & Graph neural networks -

1. Fisher-Bures Adversary Graph Convolutional Networks (quantum information geometry & Fisher information of the neural network) -

http://proceedings.mlr.press/v115/sun20a.html

You can enhance this Graph Neural Network further with reconstructing Quantum geometry from Quantum Information from the following paper. 

2. Reconstructing Quantum Geometry from Quantum Information 

https://arxiv.org/pdf/gr-qc/0501075.pdf

2. The Yang-Mills α-flow in vector bundles over four manifolds and its applications (Gang Tian) - 

https://arxiv.org/abs/1303.0628

4. Vector Bundles On Algebraic Varieties (This is the most important paper by Dr. Atiyah & team from 1984 in collaboration with TIFR Mumbai & Oxford University) -

http://www.math.tifr.res.in/~publ/studies/Vector-Bundles-On-Algebraic-Varieties.pdf

One of these days, I will write in detail why Yang mills & vector bundles has potential solution while working on graph neural networks because of Quantum Information Geometry connection. It's going to be one hell of an orchestration. 

For now, look at the beauty of Sir Atiyah's 1984 paper in collaboration with TIFR. (BTW, Update 8 days after this blogpost was published.. on 17th Feb Sir Atiyah's Student George Lusztig won Wolf Prize for representation theory & Quantum Groups) 

My next blog is going to be about Spin Networks.