Neural MoveMap Heuristic

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Feedforward artificial neural network ¹

Depiction of a single-layer feedforward artificial neural network. Arrows originating at x2 are omitted for clairty. This network has p inputs and q outputs. Image by Mcstrother, February 17, 2010, CC BY 3.0, Wikimedia Commons, Artificial neural network from Wikipedia ↩︎

Neural MoveMap Heuristic, (NMM heuristic)
a move ordering heuristic introduced by Levente Kocsis at al., applied to the games of Lines of Action ¹ and chess ². The NMM heuristic utilizes a neural network, trained to estimate the likelihood of a move being the best one in a certain chess position. The best performing NN architecture resulted from an input layer consisting of 6 neurons per square (for each particular piece, -1 Black, 0-None, +1 White) plus one neuron for the side to move, and an butterfly output layer of 1792 neurons corresponding to valid 64x64 from- and to-squares of the moves. Although the network is very large, the move scores can be computed quickly, since one only has to propagate the activation for the pieces actually on the board, and to compute only the scores for the legal moves. An enhanced approach of the NMM heuristic used a weighted combination of the neural network and the history-heuristic scores, tested for middle-game chess positions with Crafty, yielding in encouraging results using Rprop as learning algorithm during the training phase with 4 times (from ECO A30, B84, D85 and E97) 3000 positions ³.