Field Prize Prediction 2026 - Lisa Piccirllio (comes first), Urmila Mahadev (comes 2nd), Shai Evra, W Sawin, M Weber, Kaisa Matomaki, Adam Harper, Yifeng Liu, Dr. Tang's

As a project, 3 years back, I analyzed last 50 years of papers (10 TB data) of all the field medalists & the rest of the mathematicians (a lot of unstructured text data) to predict the field medal for the 2022 event. Again, this was a graph mining & NLP (natural language processing & text mining) exercise to motivate upcoming data scientists to try something new, figure out new problems to solve, and probably unleash the power of predictive analytics & narrow AI as well. 

This required a lot of 

1. Data cleaning 

2. Defining the breakthrough of every winner  

3. Developing co-author network data 

4. look-a-like profiling based on topics, citations, embeddings, and lot of other things  

5. Developing topic models through natural language processing, the topology of networks, superimposing topology of networks with topics & changing the definition of a breakthrough with respect to the papers of the winners 

6. Deep Divergence Learning & Ricci Flow for community detection for clustering right topics with unsupervised learning 

7. Reinforcement learning & ensemble modeling 

And A Secret recipe of this predictive analytics project which came through the concept of the topology of social networks & KBGAN: Adversarial Learning for Knowledge Graph Embeddings - https://arxiv.org/abs/1711.04071 

8. Ant Colony Optimization to understand amongst research coauthors has the shortest path with innovation breakthrough yield & to win the Field..

My prediction came true for Maryana Viazovska, Hugo Duminil & J Maynard while Bhargav Bhatt won New Horizon breakthrough prize. 

I am running the algorithms this time for 2026 and the initial analysis shows Lisa Piccirllio (comes first), Urmila Mahadev (comes 2nd), Melanie Weber, Shai Evra, W Sawin, Kaisa Matomaki, Adam Harper, Yifeng Liu, Dr. Tang's name  have probability over 95% to win 2026 Field prize. 

Ricci Curvature, Yang-Mills curvature, New letter from Dr. Yau on Stable regular solution of Einstein-Yang-Mills equation

Hi Readers,

Its 3 AM in Mumbai.. I have been writing about Ricci Curvature, Yang Mills Curvature for a while. 

Some of you might like the new letter by Dr. Yau on it with Yang-Mills curvature tensor, coordinate transformation, etc. - 

https://arxiv.org/pdf/2210.09861.pdf

This is a very simple yet a genius letter. More to come on this topic. 

------------------------------

Different topic - 

I have been asked what books to read on Ricci Flow - 

The Book I recommend is Sobolev Inequalities, Heat Kernels under Ricci Flow, Poincare Conjecture by Qi S Zhang. 

Something which you might like in this book apart from my old lectures - 

 

Ricci Curvature and Field Prize prediction for 2026

Hey guys,

Here comes my new blogpost. 

1. Thank you - Thanks a lot for messages on A. my field prize prediction, B. My Ricci Flow video & C. My talk abstract which was selected for a satellite conference. 

I am building a new algorithm to predict Field Prize which is going to happen in 2026 using Graph Neural Networks, HodgeNet and Ricci Curvature. 

My Original Algorithm was - 

1. Data cleaning 

2. Defining the breakthrough of every winner  

3. Developing co-author network data 

4. look-a-like profiling based on topics, citations, embeddings, and lot of other things  

5. Developing topic models through natural language processing, the topology of networks, superimposing topology of networks with topics & changing the definition of a breakthrough with respect to the papers of the winners 

6. Deep Divergence Learning & Ricci Flow for community detection for clustering right topics with unsupervised learning 

7. Reinforcement learning & ensemble modeling 

And A Secret recipe of this predictive analytics project which came through the concept of the topology of social networks & KBGAN: Adversarial Learning for Knowledge Graph Embeddings - https://arxiv.org/abs/1711.04071 

8. Ant Colony Optimization to understand amongst research coauthors have shortest path with innovation breakthrough yield & to win field.. 

I am going to use lot of HodgeNet to analyze co-author network edges along with this original algorithm. 

More coming soon on this topic..  

Congratulations to Bhargav Bhatt and Field 2026

Hi Readers,

Congratulations to Bhargav Bhatt for winning Nemmers Prize this month.

While I have been using lot of dimensionality reduction techniques in my Field Prize Prediction algorithm (done 2 years before 2022 Field Prize which came true for which came true for - James Maynard, Hugo Duminil, Maryna Viazovska while Bhargav Bhatt winning New Horizons Breakthrough Prize and recently Northwestern University's Nemmers Prize - https://lnkd.in/dEs3E4ge ), I will be using HoroPCA for next Field Prize Prediction algorithm which is going to happen in 2026.

 

Nonholonomic Einstein systems, Perelman Entropy, Ricci Flow

Hi Readers,

Happy Diwali! I am in Mumbai these days.. I have been speaking about nonholonomic diffusion in Einstein Systems, Ricci Flow, Yang Mills Flow, topological game theory in social networks and neural networks since 2010 with some mathematicians.

Perelman's (Field Medalist in 2010 who rejected Field Medal first time in 150 years after solving Poincare Conjecture which was unsolved for 100 years) 2008 paper The entropy formula for the Ricci flow and its geometric applications says that he did not know enough about Blackholes & (pseudo)- Riemannian geometry, Ricci Flow, Black Hole Thermodynamics, etc https://arxiv.org/pdf/math/0211159.pdf

Hence, I thought a perfect way to apply Perelman's work was AI, Data Science (please see my Ricci Flow- https://www.youtube.com/watch?v=z_pjsJisdHQ&t=26s ) & Econophysics using black hole thermodynamics etc. 

Anyway......

Here comes a state of the art paper on Perelman Entropy and Quantum Information systems - Quantum geometric information flows and relativistic generalizations of G. Perelman thermodynamics for nonholonomic Einstein systems with black holes and stationary solitonic hierarchies - https://dl.acm.org/doi/abs/10.1007/s11128-021-03287-7

Obviously CERN has produced a great paper on application of Convolutional Neural Networks in Einstein Sasaki Vol Min. - https://arxiv.org/abs/1706.03346

But this paper Quantum Geometric Information Flows changes the way, I have analyzed GANs through Perelman Entropy and Ricci Flow in my SDSU-UCSD lecture for better convergence of GANs (the original lecture was on Image and Video Analytics/Computer Vision in Healthcare). 

This paper also gives lot of room for new research on on Ricci Flow,  Yang Mills and Social Collider articles (2 articles in KDnuggets). Twitter has recently published a blog on Ricci Curvature and Graph Neural Networks, while Univ of Cambridge has published a paper on RicciNets after my lecture.

This also changes the way I was going to apply Ricci Flow & Nash Entropy Optimized GANs to solve PDEs in Dynamical and Chaotic systems in certain way. 

More to come soon.. 

Happy Diwali again! Every Diwali brings lot of peace of mind and some good memories..    

Ricci Yamabe Flow, Neural Networks

Hi Readers,

Anyone using Ricci Yamabe flow in Neural Networks.. instead of Ricci Flow for Pruning/Optimization of neural networks.. 

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Ricci Flow, Markov Chain, Torus GAN, Yang Mills..

Hi guys,

It is 3 AM Friday Night. Few hints on Yang Mills & Calibi Yau since I have been writing a lot on these topics apart from 

1. CERN project to analyze Calabi Yau data 

2. Google project on Inception Neural Networks to analyze Calabi Yau 

3. A Julia Code on Machine learning of Vector Bundles (TBR)

4. Sobolev training of Neural Networks from Deepmind

My vision for Yang Mills was Mathematical Analogy which I developed working in the nights through 

1. Twitter and Social Collider, 

2. Use of Quantum Neural Nets - (recently published paper - Neural quantum states for supersymmetric quantum gauge theories sponsored by NTT  - https://arxiv.org/pdf/2112.05333.pdf

3. Projected Spaces, 

4. Ricci Flow and Markov chain, 

5. Vector Bundles (Gang Tian has published some awesome work in Vector Bundles and Ricci Flow in 2014), 

6. Random Vector - Salt vector (Salt vector was available in the encryption system of the banking software I was working on along with Convolutional Neural Networks etc. in 2011)... 

7. and  along with Twitter Cortex for Graph Neural Networks to analyze it Further..

.. part of which was later on published in Kdnuggets in 2013 in a very simplified format and visual way...  - https://www.kdnuggets.com/2013/11/yang-mills-million-dollar-connection-twitter-quantum-physics.html

What is yet to be seen is - 

1. Use of GraphGANs, TopologyGANs, Vector Bundles and CurvGANs for analyzing social Networks 

2. Ricci Flow to Analyze Social Networks - Available in my animation video on Ricci Flow (used to prove $1 million Poincare Conjecture) & its application in  Community detection in social networks which was an entry in Field Prize Math video Contest with your friends and colleagues 

3. Ricci Curvature and Markov Chain to Analyze social Networks along with HodgeNet for Link Prediction  

4. TorusGANs to analyze clusters in social networks further after running Ricci Flow Surgery as shown in my video of "PK - me - Prasad Kothari - giving answers to Grigori Perelman" - https://www.youtube.com/watch?v=z_pjsJisdHQ

 

Dynamical Systems, May P. Dolciani Prize etc.

I have been working a lot of Nash Entropy and Ricci Flow optimized GANs to solve PDEs in Dynamical and Chaotic systems. 

One update about this topic.. Diana M. Thomas is going to receive 2023 Mary P. Dolciani Prize for excellence in research and Math. Her primary topic being Number theory and dynamical systems. 

More to come on this topic later... 

Breakthrough Prize in Mathematics, Optimizing Neural Networks through Yang Mills Flow

A very short blog for everyone who has previously read my blogposts on Ricci Flow ....  

I am looking for a co-author to publish a new Neural Network architecture on Yang Mills Flow, Vector Bundles, GANs (Torus GANs), Nash Flow, DeepWalk & Markov Chains

A hint - When we pass from holomorphic vector bundles to complex manifolds, the Yang-Mills flow is replaced by the Ricci flow. Reverse is true as well. 

If I ever write my next book, it is going to cover Maryam Mirzakhani,
Firoozbakht, Einstein, Godel, Bernoulli, Jacob Jacobi, Levi Civita and lot of other mathematicians..

Mathematics, data & AI makes history.. something to remember since my Field prize prediction came true..

Also, heartiest congratulations to Daniel Spielman for $3 million Breakthrough Prize in Mathematics. His graph theory principles were used in my field prize prediction.

My old book on GANs, DCGANs, QGANs, InfoGANs, GANs & RNNs, DGANs+CNNs+RNNs, GraphGANs, Reinforcement Learning, Deepfake detection using CNNs including self driving cars which I never published..

This was the book I was going to write on GANs in 2017... I was looking for coauthor... but, my readers would like the index, business use cases and the syllabus...  

Ricci-Yang-Mills flow, DeepWalk, GANs, Markov Chains

Hi Readers, 

Those who have been following my articles & blog on Ricci flow, Ricci Curavture on applications which Perelman used to solve Poincaré conjecture including 'my field prize math contest video' - https://www.youtube.com/watch?v=z_pjsJisdHQ on Ricci Flow & community detection, my accepted lecture in satellite conference on solving PDEs through Nash entropy & Ricci Flow optimized GANs in dynamical systems apart from my field prize prediction which came true (Hugo, Maynard, Maryana.. Bhargav Bhatt missing it out of millions of mathematicians but winning Clay Award..), my special congratulations email to Nikolai 1 year back... Here comes Twitter talking about Ricci Curvature - https://blog.twitter.com/engineering/en_us/topics/insights/2022/over-squashing--bottlenecks--and-graph-ricci-curvature

I am looking for a co-author to write a new Network Science paper on 

1. Ricci-Yang-Mills flow, 

2. GANs (Torus GANs), Nash Flow

3. DeepWalk & 

4. Markov Chains

Here is a wonderful blog on DeepWalk by IIT Roorkee  - https://dsgiitr.com/blogs/deepwalk/ 

Congratulations to 2022 physics Nobel Laureates for Quantum Entanglement & Quantum Information Processing

Hi Readers,

I have been writing a ton on Quantum Information Processing, Quantum entanglement, Quantum Game Theory, Ricci Flow etc. including my poster/talk at Purdue University few years back. Here is an abstract of the talk -

Complex networks including social networks, protein-protein networks, etc. have always alluded to us for a very long time. Quantum computers hold key to the evolving problem of community detection. Obviously, D-wave has been used with superconducting flux qubits while Universal quantum computer leverages the limited number of qubits with still exponential speed available. The further algorithms used on quantum computers have been mainly modularity graph clustering or modules available in tools such as Gurobi with graph optimization. This talk intends to stir the conversation towards a new method of community detection on quantum computers. quantum machine learning has been used to analyze Weyl spaces, Banach spaces, and Hilbert spaces. Using geometric decomposition if we apply discrete Ricci flow, the evolution of communities in the network can be analyzed and community detection becomes more accurate. Ricci flow has been known as a leading tool for smooth manifold decomposition. Many of the times, Communities detected Lie groups on Riemannian manifolds. Using Perelman entropy functional or Nash entropy functional, along with Weyl vector and quantum mass density function, Ricci flow can be further expressed in terms of entanglement. Using Ricci flow and quantum game theory, the study of communities, the way they are entangled with key players, and the payoffs of entanglement prove to be a significant breakthrough in network analysis. 

This year's Physics Nobel has been given to Aspect, Clauser and Zeilinger for Quantum Entanglement, Quantum Information Processing etc. Heartiest congratulations to all 3 for their wonderful research. 

Few papers which I really liked from Dr. Aspect (since I am a huge fan of Einstein - Niels Bohr Debates .. Einsten - God plays a Dice..Niel's Bohr - Don't tell god what to do with his dice! etc.. randomness etc.) - 

1. From the Einstein-Bohr debate to quantum information: the second quantum revolution (Orale) - https://hal.archives-ouvertes.fr/hal-01724593/
2. 14 From Einstein, Bohr, Schrödinger to Bell and Feynman: a New Quantum Revolution? -  https://www.degruyter.com/document/doi/10.1051/978-2-7598-2265-2.c021/html

Also, my movie submission to Harvard Math Department - Copenhagen - A BBC documentary and a dialogue between Niels Bohr and Werner Heisenberg    https://people.math.harvard.edu/~knill/various/copenhagen/index.html

I think it's a win for entire Quantum Computing community including me. 

Poincare, Perelman & Ricci Flow - Business to Blackholes

Hey guys,

In a rare interview, Perelman mentioned - The Poincare conjecture also gives an answer to the question about the shape of the Universe ( https://www.maa.org/news/math-news/perelman-calls-poincare-conjecture-formula-of-the-universe ). 

Not really. But, this blog has made sure that Ricci Flow, Ricci Curvature & Poincare conjecture have lot of applications in this business world & Black hole stability. 

1. NNs & Ricci Flow, Quantum Walk, Ricci-Yamabe maps for Riemannian flows, Drone Programming using Ricci Flow - https://researchcircle.blogspot.com/2022/04/nns-ricci-flow-quantum-walk-ricci.html?m=1 .

2. Ricci Flow, Market Fragility, Market Topology, Influencers & Game Theory, Ramanujan graph+Block Sparse Neural Networks, Hodge decomposition of information flow, RNNs - https://researchcircle.blogspot.com/2022/03/ricci-flow-market-fragility-market.html?m=1 .

3. Ricci Flow, Nash Entropy, Cigar Soliton, Lie groups, Sobolev inequality -  https://researchcircle.blogspot.com/2022/03/ricci-flow-nash-entropy-cigar-soliton.html?m=1 .

4. Ricci Flow, Economics, COVID outbreak prediction and Drug Design - https://researchcircle.blogspot.com/2022/02/ricci-flow-economics-covid-outbreak.html?m=1 .

5. Ricci Flow, Neural Networks, Nash Entropy, Ricci Yang-Mills flow - https://researchcircle.blogspot.com/2022/02/ricci-flow-neural-networks-nash-entropy.html?m=1 .

6. Security, Topological Game Theory & Ricci Flow - https://researchcircle.blogspot.com/2022/02/security-topological-game-theory-ricci.html?m=1 .

7. Ricci Flow, Geomstats, Lie Groups on Julia & EconoPhysics - https://researchcircle.blogspot.com/2022/02/security-topological-game-theory-ricci.html?m=1 .

8. Ricci Flow, Economics & a brilliant blog by Gita Gopinath - https://researchcircle.blogspot.com/2022/02/job-posting-paper-ricci-flow-economics.html?m=1 .

9. 4 interesting papers on Ricci Flow & Deep Learning - https://researchcircle.blogspot.com/2022/01/4-interesting-papers-on-ricci-flow-deep.html?m=1 . 

10. Ricci Curvature, Hawking's Vector and BlackHole Stability - https://researchcircle.blogspot.com/2022/08/stable-blackholes-perelman-ricci.html

11. Betti Numbers, Ricci Flow, Neural Network capacity, Graph Mining $ 1 million competition - https://researchcircle.blogspot.com/2022/09/betti-numbers-ricci-flow-neural-network.html 

12. Thank you, IBM-DeepRing, Neural Networks & Ricci Flow Pruning, New way of solving Yang Mills - https://researchcircle.blogspot.com/2022/08/thank-you-ibm-deepring-neural-networks.html 

13. Ollivier persistent Ricci curvature, Molecular design, CurvGAN - https://researchcircle.blogspot.com/2022/08/ollivier-persistent-ricci-curvature.html 

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...