We use a neural network that takes a coordinate (x, y) and output the corresponding RGB value to generate an image.
With different random hyperparameters, the network generates images of large style variance.
The image is generated using a single-path feed-forward network with only fully-connected layers and batch-normalization, flavored with various nonlinearities and initialized with gaussian random weights.
The key to generate these intriguing images is the use of random nonlinearities from a large nonlinearity pool at each layer, especially those discontinuous functions (like sign) or functions with large gradient near some point (e.g, log(abs(x) + eps)).
Here are the nonlinearities we've used so far:
NONLIN_TABLE = dict(
relu=T.nnet.relu,
tanh=T.tanh,
abs_tanh=lambda x: abs(T.tanh(x)),
sigmoid=T.nnet.sigmoid,
softplus=T.nnet.softplus,
sin=T.sin,
cos=T.cos,
sgn=T.sgn,
sort=lambda x: T.sort(x, axis=1),
abs=abs,
log_abs=lambda x: T.log(abs(x) + eps), # this is awesome
log_abs_p1=lambda x: T.log(abs(x) + 1),
log_relu=lambda x: T.log(T.nnet.relu(x) + eps),
log_square=lambda x: T.log(x**2 + eps), # just a scalar
xlogx_abs=lambda x: T.xlogx.xlogx(abs(x) + eps),
xlogx_abs_p1=lambda x: T.xlogx.xlogx(abs(x) + 1),
xlogx_relu=lambda x: T.xlogx.xlogx(T.nnet.relu(x) + eps),
xlogx_relu_p1=lambda x: T.xlogx.xlogx(T.nnet.relu(x) + 1),
xlogx_square=lambda x: T.xlogx.xlogx(x**2 + eps),
softmax=T.nnet.softmax,
logsoftmax=T.nnet.logsoftmax,
hard_sigmoid=T.nnet.hard_sigmoid,
identity=lambda x: x,
square=lambda x: x**2
)See https://github.com/zxytim/neural-painter/blob/master/neural_painter.py for implementation. The code is based on theano.
./neural_painter.py --image_size 800x800 --hidden_size 100 --nr_hidden 4 --nonlin random_every_time --nr_channel 3 --output_nonlin identity --coord_bias --seed 42 --output 42.png- Wikipedia page for Compositional pattern-producing network
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