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Aside on AI Will computers ever be intelligent? Really intelligent? Tasks that previously were thought to require intelligence: adding and subtracting playing chess driving a car recognizing speech or handwriting translating to a foreign language proving mathematical theorems What does it mean to say that a computer is intelligent? Is that the same as being a person? What is a person? Is a computer program a person? Is a person a computer program? Achieving “Intelligence” How do AI program achieve “intelligent” behavior? Currently, four main paradigms: Neural Nets Genetic Algorithms Symbolic knowledge representation and search Statistical machine learning Neural Nets Model behavior of neurons Each neuron has many Inputs Output is weighted sum of inputs Training: adjusting the weights to improve behavior Learning: networks improve performance with time Feedback: large networks with feedback have very complicated behavior (pondering? dreams?) Success: many (small) problems are handled well; bigger problems are problematic Genetic Algorithms Many similar simulated organisms, each with its own program governing behavior The organisms are run for a time, and their behavior is measured for fitness The more successful organisms are more likely to cross (reproduce) Random mutations can also be introduced in the programs Each generation tends to have more successful behavior than the last, on average Results: good for some optimization problems Statistical machine learning Gather much data Find patterns Symbolic AI Represent a problem as a collection of logic (symbolic) statements Characterize the initial condition symbolically Characterize goal state symbolically Characterize actions that are possible in the world as productions or changes to the initial condition Search through possible actions to find a path to the goal Google’s knowledge graph Search in Artificial Intelligence Represent your problem as a graph where nodes are states and edges are operators that go between states Define problem states (nodes) Identify start and goal states Define operators (edges) Use DFS or BFS to find goal Example: Missionaries and cannibals problem states: (3,3,1) 3 missionaries, 3 cannibals, and 1 boat on left side of river. Operators: one or two people cross the river in the boat, so that there isn’t a cannibal majority on either side. Goal: get to the other side? Moves? (331)–(220)–(321)–(210)–(221)–(020)–(031)–(010)–(021)–(000) Computer Chess How would you program a computer to play chess? Brute force or intelligence? The slow rise of computer chess Game Playing We could use DFS but…can’t search whole tree! limit depth of search and use an evaluation function We could use DFS but…how do we know which move the opponent will choose? minimax algorithm: assume the opponent does what looks best. i.e. at nodes where it is the human’s turn, pick the move that looks best for human. Where computer’s turn, pick the move that looks best for the computer DFS/BFS Resource Requirements DFS: Runtime? O(n), n=number of nodes expanded Space required? O(d), d = depth of search Can I cut off a search after 3 seconds? BFS: Runtime? O(n) Space required? O(breadth of tree) = O(bd), b=branching factor Can I cut off a search after 3 seconds? Staged DFS: do a DFS of depth 1, 2, 3, … until out of time Runtime? O(n) Space required? O(d) Mankalah An ancient gamed called Kalah or Mankalah uses stones and pits: 6 to a side and one on each end. 4 stones are initially placed in each side pit. None are in the end pits (called Kalahs – a player’s kalah is on her right). A move consists of picking up the stones in a pit and distributing them, one at a time, in successive pits. If the last stone is placed in your Kalah, you go again If the last stone is placed in an empty pit on your side, you capture the stones in that pit and the opposite one, on the opponent’s side of the board. These are put into your Kalah. The game ends when one player has no stones left; the other player puts all the remaining stones on her side into her Kalah. Whoever ends with more stones in her Kalah wins. Can you make your Kalah program smarter than Bonzo? Mankalah minimax Result minimaxVal(Board b, int d) // d is depth if (b.GameOver() or d==0) return new Result(0, evaluate(b)) if (b.whoseMove()==Board.TOP) //TOP is MAX bestVal = -infinity for (move=first; move<=last; move++) if (b.legalMove(move) [and time not expired]) Board b1 = new Board(b) //duplicate board b1.makeMove(move) //make the move val=minimaxVal(b1,d-1) //find its value if (val>bestVal) //remember if best bestVal=val; bestMove=move else // similarly for BOTTOM’s move return new Result(bestMove,bestVal); Parallelizing minimax? Algorithm- or data-parallelism? C# Task Parallel Library (TPL) Other ideas for improving play? Better evaluation function Optimize program speed Learning for feature-weight tuning Opening or closing book Alpha-beta pruning with move reordering (potentially 33% deeper search) Heuristic Search Techniques What do you do when the search space is very large or infinite? We’ll study three more AI search algorithms: Backtracking search Greedy search (Best-first) A* Example: the 8-puzzle How would you use AI techniques to solve the 8-puzzle problem? Symbolic AI solution Start state: 5 4 0 6 1 8 7 3 2 (e.g.) Goal state: 1 2 3 8 0 4 7 6 5 Edges: sliding a tile. From start state: 548610732 504618732 What search algorithm should I use? Backtracking search Start at the start state Search in any direction Backtrack when stuck This is really the same as Used very frequently Depth-first search E.g. Perl regular expression matching E.g. finding a traveling salesman’s circuit E.g. graph coloring Is there any way I can be smarter than a blind search? 09-08-04 How to get from Arad to Bucharest? How to get from Isai to Fagaras? Greedy Search (Best-first) Best-first search: like DFS, but pick the path that gets you closest to the goal first Need a measure of distance from the goal h(n) = estimated cost of cheapest path from n to goal h(n) is a heuristic Analysis Greed tends to work quite well (despite being one of the seven deadly sins) But, it doesn’t always find the shortest path Susceptible to false starts May go down an infinite path with no way to reach goal How to ensure you’ll find the best solution? A* Can we apply the ideas of Dijkstra’s algorithm? Pay attention to total path length, not just distance to the goal f(n) = g(n) + h(n) g(n) = distance traveled so far h(n) = estimated remaining distance (heuristic) A*: do a DFS-like search with lowest f(n) first Does this guarantee an optimal solution? Optimality of A* Suppose h(n) never overestimates (such heuristics are called admissible) Note that f(n) always increases as search progresses A* is complete and optimal (though often slower than best-first search) The first limitation you are likely to run into with A* search: not enough RAM in your computer… Heuristics for the 8-puzzle What would a good, admissible heuristic be for the 8-puzzle? h1: number of tiles out of place h2: total distance of squares from destinations Results of A* Consider solving the 8-puzzle by search, using the following algorithms DFS BFS IDS (iterative deepening search): like staged DFS. A* with heuristic h1 A* with heuristic h2 Will each be able to find the shortest solution? Which one will find it most quickly? Which ones will use lots of memory? Search Cost IDS A*(h1) Effective Branching Factor A*(h2) IDS A*(h1) A*(h2) 2 10 6 6 2.45 1.79 1.79 4 112 13 12 2.87 1.48 1.45 6 680 20 18 2.73 1.34 1.30 8 6384 39 25 2.80 1.33 1.24 10 47127 93 39 2.79 1.38 1.22 12 364404 227 73 2.78 1.42 1.24 14 3473941 539 113 2.83 1.44 1.23 16 1301 211 1.45 1.25 18 3056 363 1.46 1.26 20 7276 676 1.47 1.27 22 18094 1219 1.48 1.28 24 39135 1641 1.48 1.26 AI and Personhood AI proponents: a machine as complex as a brain would be as intelligent as a person maybe it would be a person. Hidden assumptions: intelligence: I/O, storage, and processing capabilities the brain: a machine whose function can be duplicated by other machines (and function is what matters) a person: an intelligent hunk of meat What makes a person? Is there anything to being a person besides “intelligence”? Consciousness: is it an ‘epiphenomenon’ – or can it affect the body? Will: do we make real choices, or are they determined by the laws of physics? Affections: is there a ‘love’ algorithm? Spirit: is there a human capability to know God beyond the five sense? Moral responsibility: what are you doing when you kick your computer – punishment? What are these views called? “all the world (including the brain and mind) operate according to physical laws” “There is a part of the mind (or soul or spirit) that is outside of nature, exempt from physical laws” Materialism [or metaphysical materialism] Dualism [or Cartesian dualism] “The mind is the program running on the ‘wet-ware’ of the brain” Functionalism [or non-reductive materialism] Non-Reductive Materialism Characteristics there is no non-physical part of a person mental processes can be localized in the brain consciousness, will, etc. are real, but they are an ‘emergent property’ of brain function Questions How could there be a real will or moral responsibility? Where is the intensionality or meaning? What then can a verse like Matt. 10:28 mean? [Do not be afraid of those who kill the body but cannot kill the soul.] What about the existence of angels, God if there is no second substance? What of church history and doctrine? Cartesian Dualism Characteristics The soul is a second substance, created by God, like the Angels The mind is a faculty of the soul, and it can affect the body Whatever the brain does, it is not the mind Questions A second substance is messy… Where does this soul come from? How does it affect the body without breaking the laws of nature? It seems that current research is localizing more and more mental processes in the brain… What does this do to the science of AI?