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Chess end games using Neural Networks

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- Presented By - Kavitha S. - GH 03437 Shilpa Kendre - GH 03438 Kaustubh Kolhar - GH 03439 Priyanka Prabhu - GH 03454 Implementation of Self-Learning in Chess using Neural Networks
LEARNING ,[object Object],[object Object],[object Object],[object Object]
LEARNING AGENTS
NEED FOR LEARNING ,[object Object],[object Object],[object Object]
LEARNING APPROACHES ,[object Object],[object Object],[object Object],[object Object],[object Object],More inductive reasoning
LEARNING REPRESENTATIONS Taxonomies Procedural encodings Frames and Schemas Graphs and Networks Formal logic Production rules Formal grammars Decision Trees Parameters in algebraic expressions Data
TYPE OF FEEDBACK ,[object Object],[object Object],[object Object]
INDUCTIVE LEARNING ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
INDUCTIVE LEARNING METHOD ,[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],INDUCTIVE LEARNING METHOD
[object Object],[object Object],[object Object],INDUCTIVE LEARNING METHOD
[object Object],[object Object],[object Object],INDUCTIVE LEARNING METHOD
[object Object],[object Object],[object Object],[object Object],INDUCTIVE LEARNING METHOD
WHY USE NEURAL NETWORKS ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],WHY NEURAL NETWORKS
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],WHY NEURAL NETWORKS
LEARNING USING NEURAL NETWORKS ,[object Object]
APPLICATIONS OF NEURAL NETWORKS Problems where intelligence and induction is required Network Type Networks Use for Network Prediction ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Classification ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Data Association ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Data Conceptualization ,[object Object],[object Object],[object Object],[object Object],Data Filtering Recirculation ,[object Object],[object Object]
BENEFITS OF NEURAL NETWORKS ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
WHY CHESS? ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
WHY ENDGAMES? ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
KING-ROOK-KING ENDGAME ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
2 PRIMARY MATING PATTERNS ,[object Object],[object Object],[object Object],[object Object],[object Object]
Black King is in a corner square. White King is blocking the black King from moving to the two outer squares of the four square Anatomy of Mate mating pattern. Rook is controlling either the back rank or the file ending in the corner square 1. DIRECT KING OPPOSITION: …contd.
2. MISALIGNED KING OPPOSITION: 2.1. Kings are on squares that are not aligned parallel to each other, but separated by one square White King prevents black King from moving to the three outer squares in adjoining file for the six square rectangle Anatomy of Mate mating pattern.
PROBLEM STATEMENT ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
NEURAL NETWORK ARCHITECTURE ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
INPUT REPRESENTATION ,[object Object],[object Object],[object Object],[object Object],[object Object],Neuron Number in the I/p Layer Representation 1-3 File of Black King 4-6 Rank of Black King 7-9 File of White King 10-12 Rank of White King 13-15 File of White Rook 16-18 Rank of White Rook
Board position i/p representation for given board Thus, input representation for above board position 001101011010101110 INPUT REPRESENTATION …contd. Parameter Value Representation File of Black king b 001 Rank of Black King 6 101 File of White king d 011 Rank of White King 3 010 File of White Rook f 101 Rank of White Rook 7 110
OUTPUT REPRESENTATAION ,[object Object],[object Object],Neuron in the O/p Layer Representation 1 K/R Index 2-3 Number of squares the piece has moved 4-6 Direction of the move
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],OUTPUT REPRESENTATAION …contd.
[object Object],[object Object],[object Object],[object Object],OUTPUT REPRESENTATAION …contd. 111 101 011 100 000 001 110 010
Initial board position After White King’s move The output representation of the above move is 001001 OUTPUT REPRESENTATAION …contd. Parameter Representation K/R index 0 No. of squares 01 Direction 001
(b) White Rook to move OUTPUT REPRESENTATAION …contd. Neuron in the O/p Layer Representation 1 K/R Index 2-3 Direction of the move 4-6 Number of squares the piece has moved
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],OUTPUT REPRESENTATAION …contd.
[object Object],[object Object],[object Object],[object Object],OUTPUT REPRESENTATAION …contd. 11 00 01 01 11
Board position White rook’s move The output representation of the above move is 100101 OUTPUT REPRESENTATAION …contd. Parameter Representation K/R index 1 Direction 00 No. of squares 101
NUMBER OF HIDDEN NODES ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],NUMBER OF HIDDEN NODES …contd.
KNOWLEDGE ACQUISITION ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],KNOWLEDGE ACQUISITION …contd.
BACK PROPAGATION ,[object Object],[object Object],[object Object],[object Object],[object Object],Where, δ j = φ'( v j ) x e j φ(*) is the logistic function v j is the total input to node j i.e. Σ i w ji y i ,[object Object],Weight change learning rate local gradient input signal to node j Δ w ji = η* δ j * y i
HEURISTICS FOR MAKING THE BP ALGORITHM PERFORM BETTER ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],HEURISTICS FOR MAKING THE BP ALGORITHM PERFORM BETTER …contd.
VIRTUES OF BACK PROPAGATION ,[object Object],[object Object],[object Object],[object Object]
LIMITATIONS OF BACK PROPAGATION ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
GENERALIZATION ,[object Object],Training Data Non-Linear Mapping Generalization Properly fitted data
OVERFITTING ,[object Object],[object Object],[object Object],Training Data Non-Linear Mapping Over fitted data (poor generalization)
FACTORS AFFECTING GENERALIZATION ,[object Object],[object Object],[object Object]
Approach 1 ,[object Object],[object Object],[object Object],[object Object],[object Object],No of training samples 4900 50000 Accuracy on ideal moves 11.79% 11.79%
PERFORMANCE GRAPH
Approach 2 ,[object Object],[object Object],[object Object],[object Object],Criteria 34 hidden nodes 56 hidden nodes Valid moves 59.937% 63.071% Ideal moves 6.009% 24.917%
EFFECT OF CLUSTERING AND BIAS Clustered samples on d1 Hidden nodes=80 Total number of testing samples= 39354 Total number of training samples=???? Total number of training epochs=????? Criteria Accuracy for biased NN Accuracy for unbiased NN Valid moves 54.609% 19.822% Ideal moves 3.295% 4.200%
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],EFFECT OF CLUSTERING AND BIAS …contd.
FUTURE SCOPE ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
CONCLUSION ,[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],CONCLUSION …contd.
Thank You!

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Chess end games using Neural Networks

  • 1. - Presented By - Kavitha S. - GH 03437 Shilpa Kendre - GH 03438 Kaustubh Kolhar - GH 03439 Priyanka Prabhu - GH 03454 Implementation of Self-Learning in Chess using Neural Networks
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  • 6. LEARNING REPRESENTATIONS Taxonomies Procedural encodings Frames and Schemas Graphs and Networks Formal logic Production rules Formal grammars Decision Trees Parameters in algebraic expressions Data
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  • 24. Black King is in a corner square. White King is blocking the black King from moving to the two outer squares of the four square Anatomy of Mate mating pattern. Rook is controlling either the back rank or the file ending in the corner square 1. DIRECT KING OPPOSITION: …contd.
  • 25. 2. MISALIGNED KING OPPOSITION: 2.1. Kings are on squares that are not aligned parallel to each other, but separated by one square White King prevents black King from moving to the three outer squares in adjoining file for the six square rectangle Anatomy of Mate mating pattern.
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  • 29. Board position i/p representation for given board Thus, input representation for above board position 001101011010101110 INPUT REPRESENTATION …contd. Parameter Value Representation File of Black king b 001 Rank of Black King 6 101 File of White king d 011 Rank of White King 3 010 File of White Rook f 101 Rank of White Rook 7 110
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  • 33. Initial board position After White King’s move The output representation of the above move is 001001 OUTPUT REPRESENTATAION …contd. Parameter Representation K/R index 0 No. of squares 01 Direction 001
  • 34. (b) White Rook to move OUTPUT REPRESENTATAION …contd. Neuron in the O/p Layer Representation 1 K/R Index 2-3 Direction of the move 4-6 Number of squares the piece has moved
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  • 37. Board position White rook’s move The output representation of the above move is 100101 OUTPUT REPRESENTATAION …contd. Parameter Representation K/R index 1 Direction 00 No. of squares 101
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  • 53. EFFECT OF CLUSTERING AND BIAS Clustered samples on d1 Hidden nodes=80 Total number of testing samples= 39354 Total number of training samples=???? Total number of training epochs=????? Criteria Accuracy for biased NN Accuracy for unbiased NN Valid moves 54.609% 19.822% Ideal moves 3.295% 4.200%
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