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In the paper Mastering the game of Go with deep neural networks and tree search, the input features of the networks of AlphaGo contains a plane of constant ones and a plane of constant zeros, as following.

Feature       #of planes Description 
Stone colour  3          Player stone/opponent stone/empty 
Ones          1          A constant plane filled with 1 
Turns since   8          How many turns since a move was played 
Liberties     8          Number of liberties (empty adjacent points) 
Capture size  8          How many opponent stones would be captured 
Self-atari size 8        How many of own stones would be captured 
Liberties after move 8   Number of liberties after this move is played 
Ladder capture 1         Whether a move at this point is a successful ladder capture 
Ladder escape 1          Whether a move at this point is a successful ladder escape 
Sensibleness  1          Whether a move is legal and does not fill its own eyes 
Zeros         1          A constant plane filled with 0 
Player color  1          Whether current player is black

I wonder why these features are necessary, because I think a constant plane contains no information and it makes the the network larger and consequently harder to train.

What's more, I don't understand the sharp sign here. Does it mean "the number"? But one number is enough to represent "the number of turns since a move was played", why eight?

Thank you very much.

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