Input and output encoding (please be crazy!)

[Peter Borrmann]

The current encoding (see below for reference)  of the input and output planes are more or less replicated from Alpha Zero, which was a "quick" shot to cover go, chess, and shogi. This works obviously quite well, but there is always room for improvement ...

Questions/potential drawbacks: 

• The policy head is quite broad with 4672 outputs compared to an average of 26-27 legal moves 
• The history planes are heavily correlated as only one (or two) pieces change their position within a ply
• Aggregate planes like fields dominated etc. may help to reduce network size 

Initial thoughts on optimization (might be not compatible)

• Encode pieces not by their position, but by there legal moves (including not to move) 
• Encoding needs to be 0,1,2 in this case (rook, knight, pawn) 
• Castling planes can be removed 
• Use a delta encoding for the history planes ( 0 = no change, 1 = piece moved to the position, -1 = piece moved from position)
• Reduce history planes 
• Replace value head by - fast - evaluation of most probable among all legal moves. 
• within training one would need to replicate a position for all legal moves and the move choosen would be 1 all other 0 
• ...

I hope you have crazy good ideas! It is just to stimulate discussion. 

( With legal moves encoding a Queen could be encoded as bishop and rook, and a king as  a queen with "limited mobility". )

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Alpha Zero encoding: 

Input: 

• The position is encoded with  8x8 planes  (current + 7 history planes  = 14*8 = 112) 
  
• 6 planes:  player 1 pieces: pawn, rook, knight , bishop, queen, king
• 6 planes:  player 2 pieces: pawn, rook, knight , bishop, queen, king
• 2 planes: repetition
• Addtional planes are: 
• colour (1)
• move count (1)
• player 1 casting (2)
• player 2 castling (2)
• no progess count (1)

Output: 

• Value:  Game result (-1,0,1)
• Policy:  Vector with 4672 possible moves