B-S-D Conjecture, Yang Mills, Machine Learning

Hey Readers, 

I used to write a lot about B-S-D conjecture and Yang mills (my favourite word being - SuperSymmetric Yang Mills - N = 4 -> N - 6) in this topological space called "Research Circles" (in 2010). Also, I used to write a lot on different machine learning approaches including NNs & Geoff Hionton's computer vision models.. CNNs etc.. to solve these 2 problems or rather a different way to look at these problems to generalize Ns. 

Few updates on these 2 problems -

BSD Conjecture -  

1. Machine learning invariants of arithmetic curves - https://www.sciencedirect.com/science/article/pii/S0747717122000839 

2. Ranks of elliptic curves and deep neural networks - https://arxiv.org/abs/2207.06699

Yang Mills -

1. Neural quantum states for supersymmetric quantum gauge theories - https://ml4physicalsciences.github.io/2021/files/NeurIPS_ML4PS_2021_46.pdf 

Ideally, I used to write a lot about machine learning and Q neural networks. The paper suggests that these supersymmetric matrix models could become challenging benchmark tasks for developing new neural ansatz architectures and algorithms. On such benchmark tasks one could tune the difficulty by choosing the number of bosons (and even add fermions) and the gauge group algebra, and some tasks also have exact results or analytical predictions (e.g. at very large N). At large N and strong coupling, the wave function should contain details of quantum gravity, and hence an efficient numerical method would be both powerful and exciting 

2. Preserving gauge invariance in neural networks - https://inspirehep.net/literature/1995502 

 

Congratulations to Peter Shor & Zorina Khan

 Hey guys,

A very short blog today. 

1. I have been talking about Peter Shor (Grover's algorithm, Quantum ML etc.) for a very long time including my blog on Quantum Link Prediction - https://researchcircle.blogspot.com/2022/09/quantum-link-prediction-hodge.html 

He just won breakthrough prize for his work on Quantum & heartiest congratulations to him. 

2. Economist Zorina Khan won Outstanding Book prize again - and I have been a very big fan of her book Inventing Ideas - Patents, Prizes & Knowledge Economy (something I really like apart from Amy Edmondson's book on Extreme teaming for Innovation and Francesca Gino's book on Rebel Talent)

mic drop...

Nash Embedding Theorem, Geometric Deep Learning, My field prize prediction, Predicting N-Body dynamic systems & Network Science..

Hello,

There has been lot of buzz around energy based AI models & Geometric deep learning since my comments in Forbes. I have also been speaking a lot about geometric deep learning for last few years..  

A very nice paper on it - Geometric deep learning: going beyond Euclidean data - https://arxiv.org/pdf/1611.08097.pdf 

The reasons I am mentioning this paper which includes Nash Embedding Theorem, Geodesics, Graph neural networks etc. are 

1. Field Prize Prediction - While I know my field prize prediction came true with 15 different algorithms, NLP and analyzing last 50 years of research papers, The example of Network graph across co-author & their publications in this paper could have been possibly a faster way to predict the field prize (The use of Nash Embedding Theorem, Geometric Deep Learning and Graph neural Networks is very cool way of analyzing the co-author network).. 

2. Predicting N-Body Systems & Quantum - Such Graph neural networks are currently being applied to perform event classification, energy regression, and anomaly detection in high-energy physics experiments such as the Large Hadron Collider (LHC) and neutrino detection in the IceCube Observatory. Recently, models based on graph neural networks have been applied to predict the dynamics of N-body systems  showing excellent prediction performance.

One application of GNN, Geometric Deep Learning which could have been a very cool collaboration is the new paper on Double-superradiant cathodoluminescence - Technion - Israel Institute of Technology, University of Cambridge & Harvard University - https://arxiv.org/pdf/2209.05876.pdf 

TensorStore, 2022 Field Prize, RM Machine & Ricci Flow..

Hi Readers,

I am looking for new collaborators to write a new research paper or a video on Ricci Flow.

Sundar Pichai announced TensorStore for N dimensional data (including scans, image and video data), I am waiting for comments from Gunnar Carlsson - Almost a godfather of TDA (That's what i used to call Dr. Gunnar in 2018 and his company Ayasdi got acquired into Symphony AI..). I also emailed Dr. Svetha Venkatesh about TensorStore since I am a huge follower of her lectures on Biomed & Machine Learning. Her lectures are super cool in Biomed & ML e.g. - https://www.youtube.com/watch?v=YU3F_9wqX90&t=540s 

Few good snippets from this year's Field Prize (first of all my simple dialogue which I use often for Ricci Flow is Origin & End is same after going through lot of derivatives) - 

1. My movement for Ricci Flow (which Perelman used to solve Poincare Conjecture & left mathematics after that) became a very cool video which was entry into Field Prize Math Contest - https://www.youtube.com/watch?v=z_pjsJisdHQ 

2. My field prize prediction using graph Mining, Network Science, NLP, Ricci Flow, Deep Divergence Learning, Profiling + Information Topology & Predicting Field Prize ( for James Maynard, Hugo Duminil, Maryna Viazoska ) - https://researchcircle.blogspot.com/2021/12/graph-mining-network-science-topology.html

3. My contributed talk on Nash entropy optimized GANs further optimized with Ricci flow with changed discriminator function for solving PDEs in Dynamical & Chaotic systems became a hit concept for certain applied markets. More updates coming on it. 

4. Like my Researchcircles which originated in 2010 (similar to Google Circles - Google Plus - Some of my readers might remember my branding of Google Plus with Meet the Parents & Circle of Trust), ICM 2022 was going to have a wonderful conference called Math Circles.

5. Russia was going to have an exhibition on Math And Art by all ASU students (my alma mater apart from U of A), similar to my 2013 Kdnuggets article.. I am such a big fan of century old painting by 

Van Gogh called "The Starry Night" which represents perfect turbulence. - https://www.kdnuggets.com/2014/01/analytics-mathematics-art-rene-romero-schuler-van-gogh.html 

Ramanujan Machine - 

One paper which I submitted to Ramanujan Machine to change current algorithm is - 

Evolution of a geometric constant along the Ricci flow - https://journalofinequalitiesandapplications.springeropen.com/articles/10.1186/s13660-016-1003-6

Ricci Flow, Dr. Hamilton, Dr. Milind Tambe, Blockchain, Nash Equilibrium

Hi Guys,

I have been talking about Blockchain, Ricci Flow, Nash equilibrium & game theory for a while.

Few updates on it -

1. Hamilton from Columbia University joined Hawaii University as a Guest Faculty to teach Ricci Flow.

2. Evolutionary game theory, Ricci Flow & Blockchain to view Blockchain as Geometric flow & stronger cybersecurity -
Cooperation Mechanism in Blockchain by Evolutionary Game Theory
https://www.hindawi.com/journals/complexity/2021/1258730/

One update which this paper can use is using Ricci Flow, geometric flow (taking inspiration from Tracy Payne's lecture from Idaho State University which I mentioned in my earlier blogpost along with Dr. Milind Tambe's book on Game Theory & Security Systems..) as follows - 

Evolutionary game theory is a continuous model with interactions (frequency dependent selection). e.g. the classical Lotka-Volterra predator-prey system fits into this framework. Another example is an infinite population of people playing the game rock-paper-scissors in continuous time. Obviously, if almost everyone is playing rock, the trend will be for more people to play paper. Asymptotic behavior, Nash equilibria and stability of fixed points are studied.

This framework may also be used to analyze the evolution of geometric structures. The Ricci flow is exactly a “replicator equation of quadratic type” for evolutionary game theory. New evolutionary models for various types of geometric flows are put forward.

Hence application of Evolutionary game theory, the classical Lotka-Volterra predator-prey system with The Ricci flow as exactly a “replicator equation of quadratic type” for evolutionary game theory for defense strategy. 

For Example - 

Defense Strategy Selection Model Based on Multistage Evolutionary Game Theory - https://www.hindawi.com/journals/scn/2021/4773894/

The existing network attack and defense analysis methods based on evolutionary games adopt the bounded rationality hypothesis. However, the existing research ignores that both sides of the game get more information about each other with the deepening of the network attack and defense game, which may cause the attacker to crack a certain type of defense strategy, resulting in an invalid defense strategy. The failure of the defense strategy reduces the accuracy and guidance value of existing methods.

Betti Numbers, Ricci Flow, Neural Network capacity, Graph Mining $ 1 million competition

Hi guys,

I have been often speaking about Ricci Flow, Betti Numbers, Algebraic topology for a while in neural networks to optimize information flow (pruning). 2 amazing papers which have been published and one company which ran a graph mining challenge - 

1. Dive into Layers: Neural Network Capacity Bounding using Algebraic Geometry - https://arxiv.org/abs/2109.01461

2. RicciNets: Curvature-guided Pruning of High-performance Neural Networks Using Ricci Flow - https://arxiv.org/abs/2007.04216

A company which got inspired by my field prize prediction project which I performed 2 years before Field Prize ( https://researchcircle.blogspot.com/2021/12/graph-mining-network-science-topology.html - how I used definition of breakthrough, ant colony optimization, Graph Mining, NLP, Network Science, profiling, feature extraction, reinforcement learning + Information Topology to predict Field Prize - A Curious Case & motivational piece for upcoming Data Scientists) & The prediction came true for James Maynard, Hugo Duminil, Maryna Viazoska -

TigerGraphDB - 

 

And there are 15 winners - https://www.tigergraph.com/graph-for-all/

 

 

Boltzmann Prize, Dr. Dhar (TIFR India), Dr. Hopfield (Chicago), & Dr. Yau's (China) World Artificial Intelligence Congress which happened in China, JJ, Swarm Intelligence..

Hi Guys,

Statistical physics pioneer Dr. Dhar & Neural Nets Pioneer Dr. Hopfield won Boltzmann Prize this year. 

1. One of the most interesting 1983 paper by Dr. Dhar is Directed diffusion in a percolation network - https://iopscience.iop.org/article/10.1088/0022-3719/16/8/014/meta

2. Tank DW, Hopfield JJ. 1987 - ANALOG NEURAL NETWORKS WITH APPLICATIONS TO SPEECH RECOGNITION PROBLEMS - https://collaborate.princeton.edu/en/publications/concentration-information-in-time-analog-neural-networks-with-app

Recent Speech mining models & Diffusion models which Nvidia (Tutorial on Denoising Diffusion-based Generative Modeling: Foundations and Applications - https://www.youtube.com/watch?v=cS6JQpEY9cs&t=3471s )

 & other are publishing... the basic mathematics behind ML comes from these legends. 

Dr. Yau mentioned similar comments about explainable ML.. in 2022 World Artificial Intelligence Congress which happened in China on AI & Math - https://www.yicaiglobal.com/news/exclusive-math-offers-deeper-understanding-of-ai-uses-chinese-fields-medalist-says 

Yau mentioned Prof. Andrew Yao, a Turing Prize winner at Tsinghua University, who has done a lot of work to prove that some algorithms are unlikely to work, and although his efforts have no direct benefit for developing industrial applications, it can give us a deeper understanding of computing...

Lot of applications of Dr. Dhar's paper are also depicted in swarm intelligence...

Dr. Yau & AI at 2022 World Artificial Intelligence Congress

Hi Readers,

I have been talking about Dr. Yau and lot of mathematics around Calabi Yau, Yang Mills and lot of Physics informed AI, GANs etc. while building the AI gangs for years.. Please check out end credits of my Ricci Flow video - 

Here comes Dr. Yau's response in 2022 World Artificial Intelligence Congress on AI & Math - https://www.yicaiglobal.com/news/exclusive-math-offers-deeper-understanding-of-ai-uses-chinese-fields-medalist-says 

Hint - If you read my 24th March blog on SYZ conjecture (Dr. Yau famed), Maryam Mirzakhani - AI, Geodesics, Riemannian surfaces, Dennis Sullivan) and GANs - Generative Adversarial Networks (with optimum convergence while leveraging Nash entropy) to solve PDEs in Dynamical & Chaotic systems..

....Zhiren Wang, associate professor of mathematics at Penn State, has been given an award the 11th Brin Prize in Dynamical Systems MAY 24, 2022..  

Mechanical Engineering Assistant Professor Aditya Nair won DOE Early Career Award - His research project, “Network-based simulations of coupled multi-physics systems,” seeks to establish a computational framework that models how physical systems “talk” to each other on a graph dynamical system. The graph dynamical system considers nodes, or basic units of data structure, and how they are connected to each other by weighted graphs (graphs in which each edge has an associated value). The research insights, Nair wrote in the project abstract, “will facilitate an accurate characterization of cross-physics sensitivities, automate the algorithmic selection process for high-performance computing, and enable energy-efficient functioning of multi-physics systems.”

Quantum Link Prediction, Hodge Decomposition of Information Flow on Complex Networks, Complex networks..

Hi Guys,

A short blog on what complex networks.. 

Umesh Vazirani & Peter Shor are gurus of quantum computing. Hence, applying a bit of quantum walk in complex networks across regular economy & crypto economy..  

1. Quantum Link Prediction in Complex Networks (instead of topological link prediction) - https://arxiv.org/pdf/2112.04768.pdf 

2. Hodge Decomposition of Information Flow on Complex Networks - https://www.researchgate.net/publication/301439563_Hodge_Decomposition_of_Information_Flow_on_Complex_Networks

Pretty accurate link prediction of Market Topology referring to my old blog on..

Instead of Topological link prediction, Using Quantum Link Prediction using AWS Braket.. 

Chainlinks, Google, Tesla & Twitter is my new small market topology.