Main Objective Time to Gather Stones Case Studies Fuzzy Case Intelligent Computing: Neural Network Case Time to Gather Stones Quantum Computing Quantum Computing . . . (a brief preview of the Fall General Techniques General Techniques . . . class CS4365/CS5354) Home Page Title Page Vladik Kreinovich ◭◭ ◮◮ Department of Computer Science ◭ ◮ University of Texas at El Paso El Paso, Texas 79968, USA, Page 1 of 11 vladik@utep.edu Go Back Full Screen Close Quit
Main Objective Time to Gather Stones 1. Main Objective Case Studies • The main objective is to learn theoretical foundations Fuzzy Case for modern intelligent techniques. Neural Network Case Quantum Computing • The emphasis will be on: Quantum Computing . . . – foundations of fuzzy techniques, General Techniques – foundations of neural networks (in particular, deep General Techniques . . . neural networks), and Home Page – foundations of quantum computing. Title Page ◭◭ ◮◮ ◭ ◮ Page 2 of 11 Go Back Full Screen Close Quit
Main Objective Time to Gather Stones 2. Time to Gather Stones Case Studies • Many heuristic methods have been developed in intel- Fuzzy Case ligent computing. Neural Network Case Quantum Computing • Some of them work well, some don’t work so well. Quantum Computing . . . • And promising techniques – that work well – often ben- General Techniques efit from trial-and-error tuning. General Techniques . . . Home Page • It is great to know and use all these techniques. Title Page • It is also time to analyze why some technique work well and some don’t. ◭◭ ◮◮ • Following the Biblical analogy, we have gone through ◭ ◮ the time when we cast away stones in all directions. Page 3 of 11 • It is now time to gather stones, time to try to find the Go Back common patterns behind the successful ideas. Full Screen • Hopefully, in the future, this analysis will help. Close Quit
Main Objective Time to Gather Stones 3. Case Studies Case Studies • In this class, we will mainly concentrate on three classes Fuzzy Case of empirically successful semi-heuristic methods. Neural Network Case Quantum Computing • Fuzzy techniques, techniques for translating: Quantum Computing . . . – expert knowledge described in terms of imprecise General Techniques (“fuzzy”) natural-language words like “small” General Techniques . . . – into precise numerical strategies. Home Page • Neural networks (in particular, deep neural networks), Title Page techniques for learning a dependence from examples. ◭◭ ◮◮ • Quantum computing, techniques that use quantum ef- ◭ ◮ fects to make computations faster and more reliable. Page 4 of 11 Go Back Full Screen Close Quit
Main Objective Time to Gather Stones 4. Fuzzy Case Case Studies • In fuzzy case, we start with explaining, in detail, the Fuzzy Case main stages of processing fuzzy data: Neural Network Case Quantum Computing – we associate, with each imprecise word, a function Quantum Computing . . . describing the corr. degrees of uncertainty; General Techniques – then, we select “and”- and “or”-operation that best General Techniques . . . reflect the reasoning of specific experts; Home Page – these operations transform expert’s rules into a de- Title Page gree to which each action is reasonable; ◭◭ ◮◮ – if needed, finally, we transform these degrees into a single recommendation; ◭ ◮ – this selection of a single recommendation is known Page 5 of 11 as defuzzification . Go Back • We show how to select the optimal “and”- and “or”- Full Screen operations and the optimal defuzzification. Close Quit
Main Objective Time to Gather Stones 5. Neural Network Case Case Studies • We will briefly overview the main ideas behind neural Fuzzy Case networks. Neural Network Case Quantum Computing • We will then explain: Quantum Computing . . . – why deep networks are efficient, General Techniques – what is the best selection of an activation function, General Techniques . . . – what optimality criterion should we use – and why Home Page KL is better than least squares, Title Page – what is the best combination rule for combining ◭◭ ◮◮ intermediate results. ◭ ◮ • Specifically, we explain: Page 6 of 11 – the use of softmax in neural processing itself and Go Back – the use of geometric mean in dropout training. Full Screen • If time allows, we will also discuss how to avoid mis- taken recognitions. Close Quit
Main Objective Time to Gather Stones 6. Quantum Computing Case Studies • We will learn the basic ideas behind quantum comput- Fuzzy Case ing. Neural Network Case Quantum Computing • Then, we will study the main quantum algorithms: Quantum Computing . . . – Deutch-Josza’s algorithm for checking which inputs General Techniques are relevant (1-bit case in detail), General Techniques . . . – Grover’s algorithm for fast search in an unsorted Home Page array (briefly), Title Page – Shor’s algorithm for factoring large integers (briefly), ◭◭ ◮◮ – algorithms for quantum teleportation (in detail), ◭ ◮ and Page 7 of 11 – algorithms of quantum cryptography (in detail). Go Back Full Screen Close Quit
Main Objective Time to Gather Stones 7. Quantum Computing (cont-d) Case Studies • We will show: Fuzzy Case Neural Network Case – that the current teleportation algorithm is, in some Quantum Computing reasonable sense, optimal, and Quantum Computing . . . – that the current quantum cryptography algorithm General Techniques is, in some reasonable sense, optimal. General Techniques . . . • We will also discuss: Home Page – how best to represent functions in quantum com- Title Page puting, and ◭◭ ◮◮ – how best to represent input’s uncertainty in quan- ◭ ◮ tum computing. Page 8 of 11 Go Back Full Screen Close Quit
Main Objective Time to Gather Stones 8. General Techniques Case Studies • The main idea behind the theoretical results in all three Fuzzy Case application areas is the idea of symmetry. Neural Network Case Quantum Computing • Why symmetry? And what is symmetry? Quantum Computing . . . • Everyone is familiar with symmetry in geometry: General Techniques – if you rotate a ball around its center, General Techniques . . . Home Page – the shape of the ball remains the same. Title Page • Symmetries in physics are similar. ◭◭ ◮◮ • Indeed, how do we gain knowledge? ◭ ◮ • How do we know, for example, that a pen left in the Page 9 of 11 air will fall down with the acceleration of 9.81 m/sec 2 ? Go Back • We try it once, we try it again, it always falls down. Full Screen Close Quit
Main Objective Time to Gather Stones 9. General Techniques (cont-d) Case Studies • You can shift or rotate, it continues to fall down the Fuzzy Case same way; so: Neural Network Case Quantum Computing – if we have a new situation and it is similar to the Quantum Computing . . . ones in which we observed the pen falling, General Techniques – we predict that the pen will fall in a new situation General Techniques . . . as well. Home Page • At the basis of each prediction is this idea: Title Page – that we can perform some symmetry transforma- ◭◭ ◮◮ tions like shift or rotation, and ◭ ◮ – the results will not change. Page 10 of 11 • Sometimes the situation is more complex. Go Back • For example, we observe Ohm’s law in one lab, in an- other lab, etc. Full Screen • Then, we conclude that it is universally true. Close Quit
10. General Techniques (cont-d) Main Objective Time to Gather Stones Case Studies • Symmetries have been very successful in physics. Fuzzy Case Neural Network Case • We will show that they are very helpful in analyzing Quantum Computing intelligent computing as well. Quantum Computing . . . General Techniques General Techniques . . . Home Page Title Page ◭◭ ◮◮ ◭ ◮ Page 11 of 11 Go Back Full Screen Close Quit
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