Bodhi Research Group’s Post

DAY 1/30 (Exploring the History of AI) Exploring the very first calculator and how it Worked #AI #history

FactAboutAI#1 Do you know when Artificial Neural Network has been invented? In 1943, neurophysiologist Warren McCulloch and mathematician Walter Pitts laid the foundation for artificial neural networks with their groundbreaking paper "A Logical Calculus of Ideas Immanent in Nervous Activity." Springer Link for Paper:: https://lnkd.in/dsJS-S5Q #funFact #AI #ML #artificialintelligence #neuralnetworks

💥💥💥 Can LLMs do research-level mathematics? There’s a moving frontier between what can and cannot be done with LLMs. 👉 Lattice-Valued Bottleneck Duality Robert Ghrist, Julian Gould, Miguel Lopez Abstract This note reformulates certain classical combinatorial duality theorems in the context of order lattices. For source-target networks, we generalize bottleneck path-cut and flow-cut duality results to edges with capacities in a distributive lattice. For posets, we generalize a bottleneck version of Dilworth's theorem, again weighted in a distributive lattice. These results are applicable to a wide array of non-numerical network flow problems, as shown. All results, proofs, and applications were created in collaboration with AI language models. An appendix documents their role and impact. 👉 https://lnkd.in/dYbZPddc #machinelearning

Few puzzles have captured the imagination quite like the Traveling Salesman Problem (TSP). At its core, the TSP asks a seemingly simple question: "Given a list of cities and the distances between them, what is the shortest possible route that visits each city once and returns to the origin city?" Yet, this question has profound implications in the realms of optimization, logistics, and, notably, the early stages of artificial intelligence. As #AI evolved, so did approaches to the #TSP. Today, sophisticated techniques like genetic algorithms, simulated annealing, and ant colony optimization reflect our deepening understanding of both computational complexity and natural processes. These methods, inspired by biology and physics, offer scalable, often near-optimal solutions to the TSP and illuminate paths toward solving other complex problems. As we stand on the brink of quantum computing and advanced machine learning, the TSP continues to be a beacon, guiding researchers toward new horizons in optimization and beyond. Let's reflect on how far we've come and where we are headed in the pursuit of solving the unsolvable. Do you want to delve more deeply into this problem? check the work of David L. Applegate, Robert E. Bixby, Vašek Chvátal and William J. Cook. They have published an exhaustive look at this problem in their book: The Traveling Salesman Problem: A Computational Study (Princeton Series in Applied Mathematics, 17). #ArtificialIntelligence, #Optimization, #Innovation, #quantumcomputing

Nobel Committee has offered this year's Nobel prize in physics to early AI & ML research. Is the Nobel Prize for physics for contributing to physics or for being influenced by physics? Can we really say modern large AI networks today are developed from the Hopfield network and Boltzman machine as the Fb page, "Nobel Prize", claims? I doubt it. As I remember, both networks work with the Hebbian learning rule and recursive connections, which we hardly see in modern deep networks. (These recursive connections are different from RNN time steps. By the way, modern LLMs replaced RNNs.) I would rather say this research was in a different branch of AI research from the branch that grew into modern LLMs.

If anyone doubts that AI can *right now* help with your deep scientific research and understanding, I recommend this article I wrote. https://lnkd.in/gk_AtFuc

Artificial Intelligence (AI) may not be up for the Fields Medal (mathematics' Nobel Prize) any time soon, but it may act as an intermediary for mathematicians working on proofs. However, something is lacking for AI to get down to it. Terry Tao looks to the positives. Full lecture: https://lnkd.in/djJYyFDY PS: Terry won the Fields Medal in 2006. https://lnkd.in/dvP4tjAZ

The weightwatcher tool has been a passion project of mine for almost a decade. I have tried to leverage my background in theoretical chemistry, AI, and my time as a quant to invent something that can help practitioners monitor, train and/or fine-tune their AI models better, faster, and cheaper. https://weightwatcher. Behind the tool is a robust theory, based in statistical mechanics (Stat Mech), quantum chemistry, and random matrix theory (RMT). It's taken me a few years to write up all the ideas, starting with these blog posts (from way back in 2019) https://lnkd.in/gDHKvXA and 2023: https://lnkd.in/dWTUqeMx For the curious, I presented this work in my invited talk at NeurIPS 2023 last year as part of our day-long workshop on Heavy Tails in ML https://lnkd.in/gPZZX8ck The final monograph, > 100 pages , is just about ready; it just needs a little feedback (and some proofreading). If anyone has the time and is interested in nerding out on some theoretical chemistry & physics of learning, ping me and I can share the current draft. A big thanks already to those who have provided their feedback. And if you need any help using the tool, please feel free to join our Community Discord and just ask. #talkToChuck #theAIguy

New paper from Shing-Tung Yau! Distinguishing Calabi-Yau Topology using Machine Learning Yang-Hui He, Zhi-Gang Yao, Shing-Tung Yau https://lnkd.in/gMJFbTB2 "While the earliest applications of AI methodologies to pure mathematics and theoretical physics began with the study of Hodge numbers of Calabi-Yau manifolds, the topology type of such manifold also crucially depend on their intersection theory. Continuing the paradigm of machine learning algebraic geometry, we here investigate the triple intersection numbers, focusing on certain divisibility invariants constructed therefrom, using the Inception convolutional neural network. We find ∼90% accuracies in prediction in a standard fivefold cross-validation, signifying that more sophisticated tasks of identification of manifold topologies can also be performed by machine learning."