Ricci Flow, Pruning & Convergence, Interconnectedness of Financial Systems, CytoScape

Hey Readers,

I have been superbusy lately. If some of my readers remember.. I used to write a lot about Spin Bayesian Neural Networks a decade back. Here it comes in the hardware industry in the applied way
1. All-Spin Bayesian Neural Networks - https://arxiv.org/abs/1911.05828
2. Hardware implementation of Bayesian network building blocks with stochastic spintronic devices - https://www.nature.com/articles/s41598-020-72842-6

 

Coming back to the blog... this blogpost which is divided into 2 parts -

1. Ricci Flow & Convergence
2. Amazing & brilliant article by Joseph Stiglitz on interconnectedness between banks & recovery

1. Ricci Flow & Convergence -
Gradient inequality and convergence to steady-states of the normalized Ricci flow on surfaces - This study the problem of convergence of the normalized Ricci flow evolving on compact Riemannian surfaces without boundary - https://www.sciencedirect.com/science/article/pii/S0362546X22000797

Ricci flow and a sphere theorem for Ln/2-pinched Yamabe metrics - differential sphere and Ricci flow convergence theorem for positive scalar curvature Yamabe metrics with Ln/2 -pinched curvature in general dimensions n - https://www.sciencedirect.com/science/article/pii/S000187082100493X

For more reference on EconoPhysics, you should read my earlier blog on Ricci Flow & market Fragility - https://researchcircle.blogspot.com/2022/02/job-posting-paper-ricci-flow-economics.html 

(which talks about Ricci curvature: An economic indicator for market fragility and systemicrisk - https://www.researchgate.net/publication/303600815_Ricci_curvature_An_economic_indicator_for_market_fragility_and_systemic_risk which is an analysis based on geometric feature extraction on network data of daily returns from a set of stocks & market topology comprising the Standard and Poor’s 500 (S&P 500) over a 15-year span to highlight the fact that corresponding changes in Ricci curvature, is negatively correlated to increases in network fragility)

Ricci Flow & Local Fragility 

I will talk more about Marc Cuban's DogeSphere, market fragility, Nash equilibrium of twitterSphere later along with market fragility - convergence to steady-states of the normalized Ricci flow & Yamabe Metric later. 

2. A brilliant article by Nobel Laureate Joseph Stiglitz which talks about The interconnected structure of the financial system which has been a focal point of debate among policymakers - https://voxeu.org/article/collective-moral-hazard-and-interbank-market

This column offers a theory to help explain the structure of the financial system and its consequences for risk-taking and systemic risk through network sciences & graph mining (implied through study of interconnectedness of the banks & financial institutions).

 

Gita Gopinath would agree with this brilliant article on based on her IMF blogs on asynchronous yet divergent recovery & capital flows. The Nash Equilibrium during a crisis, the government optimally bails out bank which is interconnected to prevent the inefficiencies associated with their failure (The optimum path to recovery that I have been writing about in this blog). This can be a very cool exercise for CytoScape. 

This article also talks about Channels of interconnectedness - 

The first channel through which interconnectedness alters risk-taking is represented by the top arrow in Figure. Since downside risk is implicitly insured by the government, the interbank market channels fund investment opportunities with high upside risk. As a result, the institutions which become large and interconnected (SIFIs) are those with relatively risky portfolios. 

The second channel through which interconnectedness alters risk-taking, represented by the middle arrow in Figure, is that the implicit insurance offered by a SIFI's liabilities (through the endogenously determined contracts) enables smaller, peripheral institutions to hold excessively risky assets, even though they do not directly benefit from bailouts themselves. This channel causes the resources of smaller, peripheral banks to be concentrated in excessively risky projects. Through these two channels, interconnectedness may lead to widespread excessive risk-taking, increasing the risk of crisis.

This makes me think of channel pruning (from Point 1 & Point 2) of channels through Ricci Flow - Curvature-guided Pruning of High-performance Networks Using Ricci Flow for optimum recovery. 

This is kind of inspiration from my 2017 SDSU lecture on Ricci Flow & Neural Networks Pruning (and a paper which followed that on
RicciNets: Curvature-guided Pruning of High-performance Neural Networks Using Ricci Flow) applied towards financial interconnected networks which almost behave in the similar way..

Also think about a convergence to steady states of financial systems through Ricci Flow & EconoPhysics.. 

King of AI.. Time Magazine & Arvind Krishna trying to reclaim it etc.... Also Yoshua Bengio, Yann LeCun and Geoffrey Hinton

Hey Readers, 

It's 4 AM..and I am blogging again. This article is stuck in my head by Times Magazine where Arvind Krishna mentioned about reclaiming the title of King of AI ( https://time.com/6167753/arvind-krishna-ibm-ceo-interview/ ). 

Believe me, I absolutely like Satya, Sundar & Arvind Krishna's leadership style (while Alteryx IPO has been successful, Dataiku & SAS are going for an IPO before Jan 2024, Alibaba Cloud continues to focus on AliGraph while Sundar Pichai talks about Edge computing & federated learning in his latest interview starting at 27:50 min - https://www.youtube.com/watch?v=EuF8nv53JeI&t=1997s). Very pragmatic in their approach. But, in all the honesty & humble opinion, the king of AI will be the one who is

1. Able to bring paradigm shift in the market with new AI methods.. and probably bridge the gap between Research & Industry 

2. Is able to differentiate role of Responsible AI, Narrow AI, True AI & so on...

3. Bring continuous thought leadership in use cases (e.g. Amazon's Astra) 

4. Drive adoption not only in big businesses with million $ accounts but small businesses, start-ups, local banks, local businesses, small clinics where AI & data has never been thought about.. 

5. The one that governs the data & AI world like never before with wisdom & unique ability to navigate through any domain with flawless ability to invent & reinvent new methods continuously & industrialize older methods for optimum top-line & bottom-line while seamlessly talking about other technologies including AR/VR, Blockchain, Hardware, Chip Manufacturing and so on.. 

6. Who is also able to navigate through physics, quantum, Economics, Social Sciences fledgling branches like Econophysics, SocioPhysics, Swarm Intelligence, Cobotics etc. since AI is such an interdisciplinary field which is continuous evolving. 

7. Who is also able to understand the history of AI which is put together in many books including Genius Makers and so on.. 

One guy/org to rule them all at the same time.. Pretty fancy definition right?... 

Anyway coming back to 2018 debate/discussions between Yoshua Bengio, Yann LeCun and Geoffrey Hinton which is covered in Kdnuggets - https://www.kdnuggets.com/2017/10/rework-interview-yoshua-bengio-yann-lecun-geoffrey-hinton.html  

3 highlights -

1. Bengio used to call Geoff - Probability Police :) Fancy name 

2. When asked about what advice you’d share with young people working in AI now - Bengio says 'Listen to Geoff' Pretty Fancy answer..

3. Lecun talks about Bias & partnership in AI 

Adelyn Zhou does an amazing job of conducting an interview.. 

 

 

Story of my book - Healthcare Social Media Management and Analytics,

Hey Readers,

Its 2 AM - Saturday Night & I am at it again. Most of my day time goes into work. I start my work at 5 AM in the morning & go till 4:30 PM in the evening (with a few 10 mins walks in-between).

I recently received this email from a fan in Michigan (don't want to disclose her name) - 

So, let me tell you the story behind this book... the story of my book Healthcare Social Media Management and Analytics goes long back... to the year 2000

2000 & Medical Tourism - 

It was 2000.. we just got internet at home and the first thing I saw was a video & the book from Prof. CK Prahalad about Outsourcing & Fortune at the Bottom of the Pyramid, The: Eradicating Poverty Through Profits.. (apart from Neo-Riemannian Geometry - Math in Music, Swarm intelligence, Firoozbakht's conjecture, Andrica's conjecture on prime numbers.. possible programming of it in C++ and so many more things.. Internet...especially google.. was truly amazing in terms of knowledge distribution to some small 16 year old student sitting in Thane..).. 

At the same time my dad was creating a campaign for his bank to give loans to a lot of hospitals in Mumbai & promote a lot of different services including low cost treatment for travelers coming from US & UK. So, being a curious kid I was able to send few emails to Prof. CK Prahalad about how my dad gave loans to hospitals & how few foreigners come to these hospitals to get treated while enjoying the tourism in India and asked about the possibility of outsourcing of medical services and being a great guy that Prof. Prahalad was..he was very kind to a 16 year old kid (me) and replied to me with a few articles on Medical Tourism..That's the term I was looking for.. 

2009 & Michelle Obama Initiative Idea - 

Years went by.. I came for my education to the US.. did some fabulous things as a research scholar for college of pharmacy, NASA Mars mission center at U of A, fraud detection for Freddie Mac, Amazing projects for Merck & Sanofi.... And then came 2009.. I was at NIH working on multiple initiatives on data science, AI and healthcare, There was the Michelle Obama Initiative for which NIH asked everyone for new ideas. The idea I submitted through an email was - 

Population health, preventative health leveraging social media, search & digital data, med devices/IoT, lab results+genome (using AI, computer vision, NLP), and online patient communities for better clinical tracking, health risk scores, patient awareness campaign/education and tracking patient outcomes/journeys (through public-private partnerships) along with Prof. Prahalad's idea of Medical Tourism. 

My then CEO & boss met President Obama that time after submitting this idea. Call it having a bigger vision thanks to Dr. Prahalad's email exchanges in 2000 (Unfortunately Prof. Prahalad passed away in 2010 without me emailing him about this idea and its roots in his emails in the year 2000)..  

There was a lot of resistance to the idea since it was too big, too advanced for 2009 & of course too many people wanted credit for it..

2013 & the book on the weekends - 

I came back to India in 2011 and went through a lot of turmoil..wrote a lot of articles.. blogs & a few books along with my full time job..(a story for another day..) But, I kept thinking how that idea changed lot of things in healthcare including lot of startups using it -

1. Qure.ai 

2. Lumiata

3. Doximity

4. Definitive Health

5. A lot of tech & AI companies entered into Healthcare & Life sciences etc.. 

Since Social Media & Healthcare was the most important part of the idea, I started writing down stories about Indian Hospitals, Payers & Pharma companies using it.. Every weekend I used to sit in front of my laptop thinking one day these stories are going to change Healthcare, AI, Life Sciences, technology forever.. 

Hence came the book - Healthcare Social Media Management and Analytics - https://www.goodreads.com/book/show/25449696-healthcare-social-media-management-and-analytics which received decent response initially and some cool pharma companies & hospitals absolutely loved it.... but then started getting good response after 9 years of publishing (after Doximity IPO)... 

And then comes the fan email.. which is today.. :) 

2 papers on Einstein Rosen Bridge, Ricci Flow and Ricci Curvature

Hello again,

Thanks for 60,000 visits on my blog in one night. Before coming to Einstein Rosenberg Bridge which got famous due to Movie Thor (which I used to write about in the space...) 

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. 

I see few papers published on this topic these days -

1. Trading networks and Hodge theory - https://iopscience.iop.org/article/10.1088/2399-6528/abd1c2/pdf

2. Semiparametric Estimates of Monetary Policy Effects: String Theory Revisited - https://economics.mit.edu/files/13030

3. Ricci Solitons & Black Holes - http://dspace.rri.res.in/bitstream/2289/3857/2/Chapter_7.pdf

4. Entropy of Reissner–Nordström 3D Black Hole in Roegenian Economics - https://www.semanticscholar.org/paper/Entropy-of-Reissner%E2%80%93Nordstr%C3%B6m-3D-Black-Hole-in-Udriste-Ferrara/fb2052f27e6700fed05ae259d63232639b465643

1. Curvature Invariants for Lorentzian Traversable Wormholes - This is based on Riemann tensor, Ricci tensor, Ricci scalar, trace free Ricci tensor, and Weyl tensor. 

A very deep paper based on Einstein Rosenberg and Ricci Tensor.

2. Ricci flows, wormholes and critical phenomena - This one talks about evolution of wormhole geometries under Ricci flow using numerical methods. Depending on values of initial data parameters, wormhole throats either pinch off or evolve to a monotonically growing state. The transition between these two behaviors exhibits a from of critical phenomena reminiscent of that observed in gravitational collapse.. 

Here comes Embedding diagrams of the Einstein Rosen Bridge.. 

Here comes manifold analysis of embedding diagrams, embedding diagrams after manifold & embedding diagram manifold after surgery.. 

You can watch entire video on Ricci Flow and clustering analysis which can be applied on Einstein Rosen spaces is here - 

 

Story of 3 papers - Yang Mills, Social Collider, Machine Learning, Vector Bundles, Calabi–Yau Manifolds

Hey Readers,

Thanks to 50,000 views of my last blog. Lot of my readers might remember me writing about Yang Mills, Social Collider, Social Networks and Neural Networks as well 12 years back (Remember SuperSymmetric Yang Mills N= 4 -> N= 6 and generalized solution through network sciences & neural networks??) Also, my hint in kdnuggets on Yang Mills & Social Collider - https://www.kdnuggets.com/2013/11/yang-mills-million-dollar-connection-twitter-quantum-physics.html

Here are 4 important papers which have come out of it -

1. Quantum Walk Model for Idea Propagation in Social Network and Group Decision Making - https://www.researchgate.net/publication/351631537_A_Quantum_Walk_Model_for_Idea_Propagation_in_Social_Network_and_Group_Decision_Making

2. Emergent Attention on Yang-Mills Space of Connections - https://lukepereira.github.io/notebooks/documents/2021-moduli-attention/main.pdf

3. Machine learning line bundle connections - machine learning for finding numerical hermitian Yang–Mills connections on line bundles over Calabi–Yau manifolds. Defining an appropriate loss function and focusing on the examples of an elliptic curve, a K3 surface and a quintic threefold, we show that neural networks can be trained to give a close approximation to hermitian Yang–Mills connections - https://www.sciencedirect.com/science/article/pii/S037026932200106X

4. Convergence of Hermitian-Yang-Mills Connections on Kähler Surfaces and mirror symmetry - https://arxiv.org/pdf/math/0301324.pdf

 

Also Remember my last month's Orchestration on CNNs & Swarm on Calabi–Yau & Super-Symmetric Yang Mills -

NNs & Ricci Flow, Quantum Walk, Ricci-Yamabe maps for Riemannian flows, Drone Programming using Ricci Flow

Hey Readers,

I know some people really liked my work on Yang Mills in 2011 in late nights ( https://www.kdnuggets.com/2013/11/yang-mills-million-dollar-connection-twitter-quantum-physics.html ) which has resulted in some cool work.. Emergent Attention on Yang-Mills Space of Connections - https://lukepereira.github.io/notebooks/documents/2021-moduli-attention/main.pdf

It's been some time since I spoke & gave lecture about Ricci Flow & Pruning of Neural Networks along with applications of it in CNNs & GANs at SDSU etc. University of Cambridge published a paper on it.

I also gave a very interesting lecture on Game Theory, Nash Entropy, Ricci Flow, Quantum Walk & Social Networks (shortest path across social networks) during my PwC days as a part of L&D program (2014 after ICM 2014) & at Purdue (2019). There is a paper which came up after that lecture A Quantum Walk Model for Idea Propagation in Social Network and Group Decision Making - https://www.researchgate.net/publication/351631537_A_Quantum_Walk_Model_for_Idea_Propagation_in_Social_Network_and_Group_Decision_Making

Having said that, coming back to ICM 2022 - one hope I had was to portray the importance of Ricci Flow (which was Perelman's main tool while solving Poincare Conjecture), Poincare & Perelman's work in AI. Hence, was my email to Ekaterina about possible collaboration on weekends.. (who next week gave a lecture at UCSD but no collaboration response).. talk about diversion :) :) Happens right.. I don't want justification anymore.. 

Hence, I made my own video on Ricci Flow & Community Detection - https://www.youtube.com/watch?v=z_pjsJisdHQ&t=2s which is doing great. 

Also, this blog which mainly talks about Ricci Flow etc. - https://researchcircle.blogspot.com/2022/03/maryam-mirzakhani-mirror-symmetry-swarm.html?m=1&fbclid=IwAR0uDeWBnYGxFBbH1tZ4pCLOl6yEip-w3IYp9__Fws6Dp-i7RTH5JOqkN8w 

Anyway, here comes new thing which some of my readers might like on Ricci Flow & Social Networks -

By the way, some people would absolutely love Drone programming and Ricci Flow paper - https://www.researchgate.net/publication/350736426_Topological_drone_navigation_in_uncertain_environment 

This should be used very carefully along with Swarm Intelligence is what I think.. 

Umesh & Vijay Vazrani, Urmila Mahadev, Information Economics, EconoPhysics, Market equilibrium, Fisher Markets, Vijay Vazirani, NP Hard, Ricci Flow..

Hi Readers, 

3 important topics in information economics (Yes, It was topic of discussion between me and my younger brother Pratik in 2009 - market forces & Nash equilibrium & Vijay Vazirani's paper - Combinatorial Algorithms for Matching Markets via Nash Bargaining: One-Sided, Two-Sided and Non-Bipartite - https://arxiv.org/pdf/2106.02024.pdf ) - 

1. Off course the genius Job Postings and Aggregate Stock Returns by Pratik Kothari PhD - https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3223141 

1. Ricci Curavature, Ricci Curvature & Economics - 

How information Flow impacts the stock markets & impacts Ricci curvature resulting into dynamic market topology and impacting the stock networks including Bitcoin Flow.. (you should check out my blog on how I predicted that the Google stock will go down by 278 points ( https://researchcircle.blogspot.com/2022/03/ricci-flow-market-fragility-market.html in 1.5 days with Hodge Decomposition of information flow over complex networks) 

Also, please check out Vijay Vazirani's paper on market equilibrium, NP Hard & fisher information - Market equilibrium under separable, piecewise-linear, concave utilities   - https://www.ics.uci.edu/~vazirani/market.pdf ) 

  

3. Umesh Vazirani & his student (Urmila Mahadev) are pretty famous for Quantum Verification Proof & ICM 2022 (field prize lecture).... & Sir Atiyah's student George Lusztig winning Wolf Prize for Quantum groups & representation theory ...That's what my next blog post is going to be about... 

 

Maryam Mirzakhani & Forbes, Teichmüller Space, WeChat - Fully Hyperbolic Neural Networks

Hi Readers,

I had a super-busy day at work yesterday and wrote a blog at 1 AM. But, today I have taken a leave to spend some time to chill out.  

--- One of the reasons I speak about Mirror Symmetry and Maryam Mirzakhani is this Forbes article- https://www.forbes.com/sites/startswithabang/2017/08/01/maryam-mirzakhani-a-candle-illuminating-the-dark/?sh=5aa7449836c1 

Sometimes Forbes writes really cool articles right.. I hope they get right influencers to spread awareness of such brilliant articles through influencer marketing while understanding stubborn & non-stubborn players in social networks with opinion mining - Ref - https://arxiv.org/abs/1609.03465 (it would be cool & optimum to spread awareness of math articles through math based influencer marketing right?)  

--- One of the brilliant papers by Maryam Mirzakhani is Volume Growth on Teichmuller Space which speaks about topological entropy of the geodesic flow. (September 20, 2011- Lattice point asymptotics and volume growth on Teichmüller space Jayadev Athreya, Alexander Bufetov, Alex Eskin, Maryam Mirzakhani) Kind of cool paper to study Geodesic CNNs (Geodesic Convolutional Neural Networks bit more)...  

--- The paper Hyperbolic spaces in Teichmüller Space by Christopher J. Leininger and Saul Schleimer explains the way hyperbolic space almost-isometrically embeds into the Teichmüller Space (  https://arxiv.org/abs/1110.6526 ) kind of very smart inspiration from Mirzakhani's paper.. 

--- which is further adopted in Hyperbolic Neural Networks by Octavian-Eugen Ganea ( https://arxiv.org/abs/1805.09112 )which focuses on hyperbolic embeddings - Möbius gyrovector spaces with the Riemannian geometry of the Poincaré model of hyperbolic spaces which helps to embed sequential data and perform classification in the hyperbolic space (for further Poincare Glove as well - HyperE at Stanford)  

While this paper cites Sanja Fidler's paper on Order Embeddings, One of the best papers which has recently come out is by WeChat - Fully Hyperbolic Neural Networks .. one of the smartest point in the design being.. Fully Hyperbolic Attention Layer - https://arxiv.org/pdf/2105.14686.pdf