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
MyStockDNA, LLC’s Post
More Relevant Posts
-
The Traveling Salesman Problem (#TSP) has transcended beyond its mathematical origins and impacted fields such as logistics, manufacturing, and genome sequencing. Its journey through the history of AI reminds us of the power of interdisciplinary inquiry and the endless potential of human creativity. As we approach the era of quantum computing and advanced machine learning, the TSP continues to guide 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. What are your thoughts on the impact of classic problems like the TSP on the field of AI? Have you encountered any modern challenges that echo the TSP's complexity and significance? Share your insights below! #AI #optimization #interdisciplinary #quantumcomputing #machinelearning #mystockdna
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
To view or add a comment, sign in
-
Recently, CDS’ founding director Yann LeCun, Professor of Computer Science, Neural Science, Data Science, and Electrical and Computer Engineering at NYU, delivered the fifth annual Ding Shum Lecture at Harvard’s Center of Mathematical Sciences and Applications. In his insightful talk, "Objective-Driven AI: Towards AI systems that can learn, remember, reason, and plan," Professor LeCun proposed a modular cognitive architecture that could lead to machines learning as efficiently as humans and animals, understanding the world, acquiring common sense, and developing reasoning and planning abilities. The centerpiece of this architecture is a predictive world model that enables the system to predict the consequences of its actions and plan a sequence of actions to optimize its objectives, including guardrails for controllability and safety. We're proud to have Professor LeCun leading the way in AI research and shaping the future of the field. #DingShumLecture #AI #DataScience
To view or add a comment, sign in
-
🚀 Excited to share that my research paper on "Analysis of Neural Network Algorithm in comparison to Multiple Linear Regression and Random Forest Algorithm" has been published in the ASU International Conference in Emerging Technologies for Sustainability and Intelligent Systems (ICETSIS)! 📝🔍 I'm incredibly grateful to my guide, Dr visalakshi annepu, whose expertise and guidance were instrumental in navigating the complexities of my research." Generally, Regression analysis remains a cornerstone of statistical analysis, offering powerful predictive capabilities by discerning relationships between independent and dependent variables. In this study, I delved into the comparative effectiveness of Neural Network, Multiple Linear Regression, and Random Forest algorithms in predictive modeling. By leveraging historical data, these algorithms enable us to forecast outcomes and understand intricate dependencies within datasets. Through rigorous analysis and experimentation, my paper sheds light on the strengths and limitations of each method, offering valuable insights for practitioners in diverse fields. #Research #DataScience #MachineLearning #ICETSIS #Sustainability #NeuralNetworks #RandomForest #LinearRegression #EmergingTechnologies
To view or add a comment, sign in
-
I predict emergence will emerge as a huge area for investment as it limits the accuracy and usability of many predictive models. The emergent properties of systems have never been well understood, and in most cases we do not even try to understand them; we create deterministic plans and logical processes to deal with deviation from plan, and we fool ourselves into thinking the plan represents reality, and hence compliance to plan is our highest goal. A model driven world will not allow us to continue the charade. If we want better outcomes than we get today, we're going to need to rip the eye-patch off and put both eyes on the probabilistic world. #ai #predictions
The New Math of How Large-Scale Order Emerges | Quanta Magazine
quantamagazine.org
To view or add a comment, sign in
-
Emergent phenomena is when a seemingly random chaotic process leads to some kind of higher level order that was not explicitly defined in the system. If you've ever seen the murmuration's of birds in large flock that are only trying to avoid colliding with each other, seemingly produces a macro organism, then you know what I mean. One theory of AI is that it is an emergent behaviour, and as I was investigating how causality might be modelled into existing AI frameworks, I came across this article that described a new mathematical approach to modelling emergent systems. Wish I had paid more attention in more of my mathematics classes, but felt that my broader network might appreciate this. https://lnkd.in/gCfW-t9V #AI #chaostheory #emergentphenomena
The New Math of How Large-Scale Order Emerges | Quanta Magazine
quantamagazine.org
To view or add a comment, sign in
-
A Reflection: Are We Missing Something Fundamental in How We Represent Numbers? Lately, I’ve been reflecting on something we often take for granted in mathematics and science: the way we represent irrational numbers like sqrt2. For centuries, we’ve accepted that symbols like sqrt2 stand in for values we can’t precisely express in decimal form. But I can’t help but wonder—have we become too complacent with this approach? Instead of pushing for a deeper understanding, have we settled for a convention that only approximates the truth? What if there’s a more exact way to represent these numbers, one that could be directly applied without the need for approximation? Could this be the key to new breakthroughs in fields like quantum computing, AI, or advanced engineering? This isn’t just a mathematical curiosity—it’s a challenge to the way we think about the very foundations of our understanding. If we’re willing to question the tools and methods we’ve always used, what new possibilities might we uncover? Are we on the verge of a new way of thinking, one that could reshape the future of science and technology? It’s a reflection that’s been on my mind—what could we achieve if we dared to think differently? #Innovation #Mathematics #QuantumComputing #AI #Engineering #RethinkingScience #IrrationalNumbers #NewHorizons
To view or add a comment, sign in
-
The Algorithmic Architecture of Mind: Structure, Learning, and Intelligence Intelligence, continues to captivate. While knowledge and processing speed are crucial, I argue that structure ultimately dictates the form of intelligence, especially when considering systems built from the same fundamental materials. Imagine two identical brains, neuron for neuron. Their cognitive abilities may still diverge wildly, highlighting the importance of architecture – the precise arrangement of neurons and synapses. These intricacies dictate how information flows and thoughts emerge. Learning sculpts structure 24 hours a day, every day. Experiences carve new pathways, strengthening some connections and pruning others. Synapses become the etchings of memory, the embodiment of acquired knowledge. In artificial neural networks, learning adjusts connection weights, refining internal representations. Memory is a structural inscription, residing in the fabric of the neuronal web or the configuration of digital circuits. Structure becomes the repository of past encounters and the foundation for future actions. This principle transcends biology. Neuromorphic computing emulates brain architecture in silicon, while unconventional computing explores novel paradigms inspired by nature. Structure emerges as the Rosetta Stone of intelligence. By deciphering its language, we can unlock the secrets of designing truly intelligent systems. This endeavor unites neuroscientists, computer scientists, physicists, and philosophers in a quest to illuminate the nature of mind. Understanding these architectural principles, we journey towards a future where minds of all kinds collaborate to solve humanity's challenges and expand our understanding. #intelligence #neuroscience #AI #structure #learning #futureofcomputing
To view or add a comment, sign in
-
🔋 Understanding Emergence: A Key to Decoding Large Language Models (#LLMs). Emergence, the process by which complex systems self-organize into large-scale patterns based on multiple micro interactions, proves essential for understanding phenomena ranging from Jupiter's Great Red Spot to human consciousness. Recent research presents an innovative methodology for identifying and analyzing emergent behavior based on computational mechanics. The methodology involves identifying and modeling key causal states, recording crucial interactions without superfluous information, and simplifying system dynamics into predictive ε-machines to show how local interactions create large-scale patterns and behaviors. This "software in the natural world" concept highlights how systems can function independently on multiple layers, comparable to how LLMs generate coherent responses from vast neural contacts. Understanding these principles can help us clarify LLM's strengths and limitations, paving the way for future AI #innovation. https://lnkd.in/dAeC8nrw
The New Math of How Large-Scale Order Emerges | Quanta Magazine
quantamagazine.org
To view or add a comment, sign in
-
We will host Yasaman Bahri from Google DeepMind at our data-driven physical simulation (#DDPS) #seminar, Lawrence Livermore National Laboratory, on November 15th, 2024, 10 AM in California time. Anyone can join us through #WebEx room: https://lnkd.in/gdjiv5Ny Please take advantage of this wonderful opportunity! #Title: A #first-#principles #approach to #understanding #deep #learning #Abstract: Recent years have seen unprecedented advancements in the development of #ML and #AI; for the #sciences, these tools offer new paradigms for combining insights developed from #theory, #computation, and #experiment towards #design and #discovery. Beyond treating them as black boxes, however, uncovering and distilling the #fundamental principles behind how systems built using neural networks work is a grand challenge, and one that can be aided by ideas, tools, and methodology from physics. I will describe some of my past work that takes a first-principles approach to deep learning through the lens of #statistical #physics, #exactly #solvable #models and #mean-#field #theories, and #nonlinear #dynamics. I will first survey connections we discovered between large-width #deep #neural #networks, #Gaussian #processes, and #kernels, which bear application to data-driven research in the #physical #sciences. I’ll then discuss our work on understanding some facets of “#scaling #laws” describing the rate of improvement of an ML model with respect to increases in the amount of training data, model size, or computational resources. #Bio: Yasaman Bahri is a Research Scientist at Google DeepMind with research interests at the interface of statistical physics, machine learning, and condensed matter physics. In recent years, she has worked on the foundations of deep learning from a physics perspective. She has been an invited lecturer at the Les Houches School of Physics and was a co-organizer of a recent program at the Kavli Institute for Theoretical Physics. Previously, she received a Ph.D. in Physics at UC Berkeley. 📚 DDPS seminar is organized by libROM team ( www.librom.net ). 🗓️ DDPS seminar schedule: https://lnkd.in/gnGsx6qq
To view or add a comment, sign in
-
Excited to Share My Latest Publication! This research is published under Elsevier - Applied Soft Computing Journal, and I am incredibly proud of this achievement. "Real-time Evaluation of Object Detection Models across Open World Scenarios," in the esteemed journal Applied Soft Computing, which boasts an impressive impact factor of 7.2 and a cite score of 15.8 Know more about Paper: https://lnkd.in/g543yKc9 This work delves into the real-time evaluation of object detection models, which have seen significant advancements thanks to deep learning techniques. We compared the performance of object detection models using DETR, Faster R-CNN, and YOLOv8s across various datasets and backbone architectures with transformers. Our findings reveal that YOLOv8s consistently emerges as the best-performing model, showcasing stable accuracy across different datasets and bounding box sizes. Thank you to everyone who supported and contributed to this work! Dr. Lakshita Aggarwal, Puneet Goswami & ARUN KUMAR #Research #DeepLearning #ObjectDetection #YOLOv8s #AppliedSoftComputing #Elsevier #AI #MachineLearning #ComputerVision
To view or add a comment, sign in
210 followers
Consultor Asociado
8moNice classical problem from operations research. It gets even more interesting when additional factors are included: sales potential for each city, city population, etc. So you may want to look at more than one objective function.