Artificial Intelligence: A Modern Approach
by Stuart Russell and Peter Norvig · 14 Jul 2019 · 2,466pp · 668,761 words
to preserve mutations that seemed useful. Despite thousands of hours of CPU time, almost no progress was demonstrated. Failure to come to grips with the “combinatorial explosion” was one of the main criticisms of AI contained in the Lighthill report (Lighthill, 1973), which formed the basis for the decision by the British
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limited to around a dozen, to real-world industrial applications with millions of states and thousands of actions. Planning is foremost an exercise in controlling combinatorial explosion. If there are n propositions in a domain, then there are 2n states. Against such pessimism, the identification of independent subproblems can be a powerful
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, S.P., 161, 1104 color, 995 Colossal Clean Crawled Corpus (C4), 928, 930 Colossus, 32 Colton, S., 222, 1089 column player, 596 combinatorial auction, 628 combinatorial explosion, 39 commitment epistemological, 273, 295, 404 ontological, 272, 295, 404 Common Crawl, 903, 922 common goal, 590 common sense, 426 common value, 624 communication, 595
Darwin Among the Machines
by George Dyson · 28 Mar 2012 · 463pp · 118,936 words
paths there are between the nodes of a communications net, the more resistant it is to damage from within or without. But there is a combinatorial explosion working the other way: the more you increase the connectivity, the more intelligence and memory is required to route messages efficiently through the net. In
How the Mind Works
by Steven Pinker · 1 Jan 1997 · 913pp · 265,787 words
to is that there is massive and then there is really massive. The number of combinations grows exponentially with their allowable size, setting off a combinatorial explosion whose numbers surpass even our most generous guess of the brain’s capacity. According to legend, the vizier Sissa Ben Dahir claimed a humble reward
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that the brain can store all contingencies in advance and that thought can be reduced to one-step pattern recognition. But the mathematics of a combinatorial explosion bring to mind the old slogan of MTV: Too much is never enough. Simple calculations show that the number of humanly graspable sentences, sentence meanings
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in memory when the entities are combinatorial—English sentences, chess games, all shapes in all colors and sizes at all locations—because the numbers from combinatorial explosions can exceed the number of particles in the universe and overwhelm even the most generous reckoning of the brain’s capacity. But people live for
I, Warbot: The Dawn of Artificially Intelligent Conflict
by Kenneth Payne · 16 Jun 2021 · 339pp · 92,785 words
presented all the salient information a computer might need to solve whatever conundrum you had in mind? Related to this was the problem of the ‘combinatorial explosion’. Many problems AI researchers worked with involved searching ahead through possible scenarios. Which move should you make in chess, or Go? What would the world
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actions are needed to succeed against adversaries. Even games with far fewer possible legal moves, like chess or Go, are fiendishly complicated because of the ‘combinatorial explosion’ that occurs when simple moves are combined. The fastest, most powerful computers of today certainly can’t ‘solve’ Go or chess—there are simply far
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Central Intelligence Agency (CIA) centre of gravity chaff Challenger Space Shuttle disaster (1986) Chauvet cave, France chemical weapons Chernobyl nuclear disaster (1986) chess centaur teams combinatorial explosion and creativity in Deep Blue game theory and MuZero as toy universe chicken (game) chimeras chimpanzees China aircraft carriers Baidu COVID-19 pandemic (2019–21
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War (1950–53) nuclear weapons research and SR-71 Blackbird U2 incident (1960) Vienna Summit (1961) Vietnam War (1955–75) VRYAN Cole, August combinatorial creativity combinatorial explosion combined arms common sense computers creativity cyber security games graphics processing unit (GPU) mice Moore’s Law symbolic logic viruses VRYAN confirmation bias connectionism consequentialism
Rage Inside the Machine: The Prejudice of Algorithms, and How to Stop the Internet Making Bigots of Us All
by Robert Elliott Smith · 26 Jun 2019 · 370pp · 107,983 words
that a combinatoric explosion can be averted. There is no way to find the best route that practically is better than looking through all the (combinatorially explosive number of) possible routes. This sort of hard fact isn’t unique to the TSP; there are scores of other problems that have this characteristic
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.1. Figure 4.1 An example binomial distribution, showing the probability p of k heads out of n = 50 coin flips. Gravesande’s computations involved combinatorial explosions that strained the boundaries of what could be computed, but he overcame this problem by inventing clever approximations that indicated the binomial probability of the
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a new medical treatment. To measure, understand and control mass production, mass medicine or any other mass-scale activities, one had to face down the combinatorial explosion of many unforeseen situations in the future. This compelled mathematicians to refine the estimation of the binomial distribution for large numbers, culminating in the provably
Superintelligence: Paths, Dangers, Strategies
by Nick Bostrom · 3 Jun 2014 · 574pp · 164,509 words
early demonstration systems often proved difficult to extend to a wider variety of problems or to harder problem instances. One reason for this is the “combinatorial explosion” of possibilities that must be explored by methods that rely on something like exhaustive search. Such methods work well for simple instances of a problem
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uses exhaustive search, it requires combing through 550 ≈ 8.9 × 1034 possible sequences—which is computationally infeasible even with the fastest supercomputers. To overcome the combinatorial explosion, one needs algorithms that exploit structure in the target domain and take advantage of prior knowledge by using heuristic search, planning, and flexible abstract representations
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or get stuck at a local optimum. Even if a good representational format is found, evolution is computationally demanding and is often defeated by the combinatorial explosion. Neural networks and genetic algorithms are examples of methods that stimulated excitement in the 1990s by appearing to offer alternatives to the stagnating GOFAI paradigm
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a concise way of representing probabilistic and conditional independence relations that hold in some particular domain. (Exploiting such independence relations is essential for overcoming the combinatorial explosion, which is as much of a problem for probabilistic inference as it is for logical deduction.) They also provide important insight into the concept of
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is impossible to build such an agent because it is computationally intractable to perform the requisite calculations. Any attempt to do so succumbs to a combinatorial explosion just like the one described in our discussion of GOFAI. To see why this is so, consider one tiny subset of all possible worlds: those
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standards, the study leaves many challenging questions unanswered: How well does the approach scale to greater numbers of memories? How well can we control the combinatorial explosion that otherwise threatens to make learning the correct mapping infeasible as the number of input and output neurons is increased? Does the enhanced performance on
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some areas might possibly be compensated for by extra skill in others). This is far beyond the reach of contemporary AI. And because of the combinatorial explosion, which generally defeats attempts to solve complicated planning problems with brute-force methods (as we saw in Chapter 1), the shortcomings of known algorithms cannot
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–51, 52–57, 67, 72, 142, 163, 203, 259, 271, 273, 279 collective superintelligence 39, 48–49, 52–59, 83, 93, 99, 285 definition 54 combinatorial explosion 6, 9, 10, 47, 155 Common Good Principle 254–259 common sense 14 computer vision 9 computing power 7–9, 24, 25–35, 47, 53
Machine Learning Design Patterns: Solutions to Common Challenges in Data Preparation, Model Building, and MLOps
by Valliappa Lakshmanan, Sara Robinson and Michael Munn · 31 Oct 2020
values. Note We’re using the term trial here to refer to a single training run with a set of hyperparameter values. Grid search and combinatorial explosion A more structured version of the trial-and-error approach described earlier is known as grid search. When implementing hyperparameter tuning with grid search, we
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models, we’d likely want to optimize more than two hyperparameters, each with a wide range of possible values. Eventually, grid search will lead to combinatorial explosion—as we add additional hyperparameters and values to our grid of options, the number of possible combinations we need to try and the time required
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, Models and Frameworks clustering models, Models and Frameworks CNN, Images as tiled structures, Why It Works-Why It Works cold start, Problem, Cold start combinatorial explosion, Grid search and combinatorial explosion completeness, Data Quality components, definition of, Solution computer vision, Computer Vision concept drift, Problem, Estimating retraining interval confidence, Inputs with overlapping labels, When
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processes Gradient Boosting Machines, Boosting gradient descent (see SGD) graphics processing unit (see GPU) grid search, Grid search and combinatorial explosion-Grid search and combinatorial explosion, Why It Works Grid-SearchCV, Grid search and combinatorial explosion ground truth label, Data and Feature Engineering, Data Quality, Capturing ground truth-Why It Works H hash bucketscollisions, Bucket collision
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aware training, Standalone single-phase model R random forest, Decreased model interpretability, Grid search and combinatorial explosion random search, Grid search and combinatorial explosion, Why It Works random seed, Problem-Solution RandomForestRegressor, Grid search and combinatorial explosion RandomizedSearchCV, Grid search and combinatorial explosion ratings, representation of, Tabular data multiple ways ray-tracing model, Solution Rebalancing design pattern, Problem
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scikit-learn, Reproducibility, Why scaling is desirable, Text data multiple ways, Increased training and design time, Choosing a model architecture, Grid search and combinatorial explosion, Grid search and combinatorial explosion sentence embeddings, Embeddings of words versus sentences Sequential API, Images as pixel values, Images as tiled structures serverless, Data and Model Tooling, Trade-Offs
Bounce: Mozart, Federer, Picasso, Beckham, and the Science of Success
by Matthew Syed · 19 Apr 2010 · 304pp · 84,396 words
relate to each other in such complex ways that it would take forever to codify them in their mind-boggling totality. This is known as combinatorial explosion, a concept that will help to nail down many of the insights of this chapter. The best way to get a sense of the strange
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power of combinatorial explosion is to imagine folding a piece of paper in two, making the paper twice as thick. Now repeat the process a hundred times. How thick
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, top athletes, and other experts. By now it should be obvious why Deep Blue’s gigantic advantage in processing speed was not sufficient to win—combinatorial explosion. Even in a game as simple as chess, the variables rapidly escalate beyond the capacity of any machine to compute. There are around thirty ways
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20,000 words. American psychologist Herbert Simon has estimated that chess masters command a comparable vocabulary of patterns, or chunks. Now consider the scope of combinatorial explosion in games like ice hockey, American football, rugby, tennis, soccer, and the like. Even when scientists have invented simplified representations of these sports, they have
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dart ahead to a spot where, an instant later, the puck turns up. This is a perfect example of expert decision making in practice: circumventing combinatorial explosion via advanced pattern recognition. It is precisely the same skill wielded by Kasparov, but on an ice hockey pitch rather than a chessboard. How was
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ten-thousand-hour rule was said to apply to any complex task. What is meant by complexity? In effect, it describes those tasks characterized by combinatorial explosion; tasks where success is determined, first and foremost, by superiority in software (pattern recognition and sophisticated motor programs) rather than hardware (simple speed or strength
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). Most sports are characterized by combinatorial explosion: tennis, table tennis, soccer, hockey, and so on. Just try to imagine, for a moment, designing a robot capable of solving the real-time spatial
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be sure how an opponent might have reacted to an alternative move, and how you would have responded in turn, and so on (this is combinatorial explosion, to use the jargon of chapter 1). So, how to gain useful feedback? Quite early in the development of chess it was realized that a
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the shot is likely to be catastrophic because there are too many interconnecting variables for the conscious mind to handle (this is another example of combinatorial explosion). Choking, then, is a kind of neural glitch that occurs when the brain switches to a system of explicit monitoring in circumstances when it ought
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3020 (Berlin: Springer, 2004). “Gretzky doesn’t look like a hockey player”: Charles McGrath, “Elders on Ice,” New York Times Magazine, March 23, 1997. circumventing combinatorial explosion via advanced pattern recognition: This idea does not imply that humans do not rely on sophisticated processing. It is just that the processing takes a
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, 31–32 Clifford, Simon, 87, 88 Cohen, Geoffrey, 117–18, 119 Collier, Sue, 7 Colvin, Geoff, 56, 85–86 Talent Is Overrated, 21–22, 44 combinatorial explosion, 45, 47, 49–50 complexity, 50, 97–100 concentration, 78, 83, 92 Conte, Victor, 240 Courier, Jim, 134 Coyle, Daniel, 118, 121 The Talent Code
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, Charles, 10, 278 Davis, Randall, 44 Davis, Steve, 200 Dawkins, Richard, 151 decision making: in chess, 47–48, 49, 51 by chunking patterns, 48, 49 combinatorial explosion, 47, 50 by computer, 44 and experience, 51 by firefighters, 40–43, 44–45, 47, 51 by hospital nurses, 41, 43, 78 independent, 63 and
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emotions, 212–13 mutations in, 106 and race, 278 and superstition, 207 Ewald, Manfred, 238, 239, 251 excellence: capacity for, 111 citadels of, 133–38 combinatorial explosion in attainment of, 45 in competition, 154 in complex tasks, 94 and experience, 45–46 long-term process to, 15–16, 122, 129 and practice
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, Nicholas, 173–74 Hussain, Nasser, 206 IBM, and Deep Blue, 37–39, 52–53 iceberg illusion, 22 ice hockey: birthdays of players, 17–18, 20 combinatorial explosion in, 49, 50 Gretzky’s genius in, 49–50, 224 Immelt, Jeff, 44, 53 innovation, 96–100 instinct, for sports, 27–28, 31 intelligence: and
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Spartak club, Moscow, 7–8 speed, in sports, 32, 34 speed skating, 197–99 spontaneous influence events, 115 sports: age-based selection in, 18–19 combinatorial explosion in, 49, 50 decision making in, 45, 47 gene doping in, 246–48 genetic factors in, 52n instincts in, 27–28, 31 as meritocracy, 9
The Road to Conscious Machines
by Michael Wooldridge · 2 Nov 2018 · 346pp · 97,890 words
technology is ever going to be able to cope with search trees this large. Search trees grow fast. Ludicrously, unimaginably fast. This problem is called combinatorial explosion, and it is the single most important practical problem in AI, because search is such a ubiquitous requirement in AI problems.12 If you could
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are currently very difficult for AI would suddenly become easy. But you won’t, I’m afraid. We can’t get around combinatorial explosion: we need to work with it. Combinatorial explosion was recognized as a fundamental problem from the earliest days of AI – it was identified by McCarthy as one of the topics
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yield a machine that could check all these alternatives in any reasonable amount of time. The phenomenon we are witnessing here is another example of combinatorial explosion. We were introduced to combinatorial explosion when looking at search trees, where each successive layer in the search tree multiplies the size of the tree
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. Combinatorial explosion occurs in situations where you must make a series of successive choices: each choice multiplies the total number of possible outcomes. In our team-building
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checking all the alternatives? No! You might find a technique that improves things marginally, but, ultimately, you won’t be able to get around that combinatorial explosion. Any recipe you find that is guaranteed to solve this problem is not going to be feasible for most cases of interest. The reason for
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3.6 million possible tours; for 11 cities, you would have to consider up to 40 million. So, the travelling salesman problem suffers from the combinatorial explosion problem, just like the team-building problem. But apart from this, they don’t seem to have anything in common. And why should they? After
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don’t yet know for certain that NP-complete problems cannot be solved efficiently. But by the late 1970s the spectre of NP-completeness and combinatorial explosion began to loom large over the AI landscape. The field had hit a barrier, in the form of computational complexity, and progress ground to a
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suggest themselves based on machine intelligence exceeding human intelligence by the year 2000. Lighthill’s report was fiercely dismissive of mainstream AI – he specifically identified combinatorial explosion as a key problem that the AI community had failed to tackle. His report immediately led to severe funding cuts to AI research across the
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possible outcomes, and all that we know, for every possible choice we might make, is the probability that each outcome will occur. See expected utility. combinatorial explosion Where we must make a succession of choices, and each successive choice multiplies the number of possibilities we need to consider. A fundamental problem in
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paribus preferences 262 chain reactions 242–3 chatbots 36 checkers 75–7 chess 163–4, 199 Chinese room 311–14 choice under uncertainty 152–3 combinatorial explosion 74, 80–1 common values and norms 260 common-sense reasoning 121–3 see also reasoning COMPAS 280 complexity barrier 77–85 comprehension 38–41
Data Mining: Concepts, Models, Methods, and Algorithms
by Mehmed Kantardzić · 2 Jan 2003 · 721pp · 197,134 words
with one of the possible feature values of a given domain. Although this interpretation may look more natural, the problem with this approach is the combinatorial explosion of artificial samples. For example, if one 3-D sample X is given as X = {1, ?, 3}, where the second feature’s value is missing
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of finding the smallest decision tree consistent with a training data set is NP-complete. Enumeration and analysis of all possible trees will cause a combinatorial explosion for any real-world problem. For example, for a small database with five attributes and only 20 training examples, the possible number of decision trees
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poses many new challenges. In addition to the one-scan nature, the unbounded memory requirement and the high data arrival rate of data streams, the combinatorial explosion of itemsets exacerbates the mining task. The high complexity of the frequent itemset mining problem hinders the application of the stream-mining techniques. We recognize
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rather generic way. Achieving focus is important in data mining because there are too many attributes and values to be considered and can result in combinatorial explosion. Most unsupervised data-mining approaches try to achieve focus by recognizing the most interesting structures and their features even if there is still some level
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