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Features used by AlphaGo, in approximate order of importance.
Feature # Notes
Stone colour 3 Player stones; oppo. stones; empty
Ones 1 Constant plane of 1s
(Because of convolution w/ zero-padding, this is the only way the NN can know where the edge of the board is!!!)
Turns since last move 8 How many turns since a move played
Liberties 8 Number of liberties
Capture size 8 How many opponent stones would be captured
Self-atari size 8 How many own stones would be captured
Liberties after move 8 Number of liberties after this move played
ladder capture 1 Whether a move is a successful ladder cap
Ladder escape 1 Whether a move is a successful ladder escape
Sensibleness 1 Whether a move is legal + doesn't fill own eye
Zeros 1 Constant plane of 0s
All features with 8 planes are 1-hot encoded, with plane i marked with 1
only if the feature was equal to i. Any features >= 8 would be marked as 8.
import numpy as np
import go
from utils import product
# Resolution/truncation limit for one-hot features
P = 8
def make_onehot(feature, planes):
onehot_features = np.zeros(feature.shape + (planes,), dtype=np.uint8)
capped = np.minimum(feature, planes)
onehot_index_offsets = np.arange(0, product(onehot_features.shape), planes) + capped.ravel()
# A 0 is encoded as [0,0,0,0], not [1,0,0,0], so we'll
# filter out any offsets that are a multiple of $planes
# A 1 is encoded as [1,0,0,0], not [0,1,0,0], so subtract 1 from offsets
nonzero_elements = (capped != 0).ravel()
nonzero_index_offsets = onehot_index_offsets[nonzero_elements] - 1
onehot_features.ravel()[nonzero_index_offsets] = 1
return onehot_features
def planes(num_planes):
def deco(f):
f.planes = num_planes
return f
return deco
def stone_color_feature(position):
board = position.board
features = np.zeros([go.N, go.N, 3], dtype=np.uint8)
if position.to_play == go.BLACK:
features[board == go.BLACK, 0] = 1
features[board == go.WHITE, 1] = 1
features[board == go.WHITE, 0] = 1
features[board == go.BLACK, 1] = 1
features[board == go.EMPTY, 2] = 1
return features
def ones_feature(position):
return np.ones([go.N, go.N, 1], dtype=np.uint8)
def recent_move_feature(position):
onehot_features = np.zeros([go.N, go.N, P], dtype=np.uint8)
for i, move in enumerate(reversed(position.recent[-P:])):
if move is not None:
onehot_features[move[0], move[1], i] = 1
return onehot_features
def liberty_feature(position):
return make_onehot(position.get_liberties(), P)
def would_capture_feature(position):
features = np.zeros([go.N, go.N], dtype=np.uint8)
for g in position.lib_tracker.groups.values():
if g.color == position.to_play:
if len(g.liberties) == 1:
last_lib = list(g.liberties)[0]
# += because the same spot may capture more than 1 group.
features[last_lib] += len(g.stones)
return make_onehot(features, P)
class FeatureExtractor(object):
def __init__(self, features):
self.features = features
self.planes = sum(f.planes for f in features)
def extract(self, position):
return np.concatenate([feature(position) for feature in self.features], axis=2)
DEFAULT_FEATURES = FeatureExtractor([