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hf_examples.py
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hf_examples.py
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import numpy, sys
import theano
import theano.tensor as T
from hf import hf_optimizer, SequenceDataset
def test_cg(n=500):
'''Attempt to solve a linear system using the CG function in hf_optimizer.'''
A = numpy.random.uniform(-1, 1, (n, n))
A = numpy.dot(A.T, A)
val, vec = numpy.linalg.eig(A)
val = numpy.random.uniform(1, 5000, (n, 1))
A = numpy.dot(vec.T, val*vec)
# hack into a fake hf_optimizer object
x = theano.shared(0.0)
s = 2.0*x
hf = hf_optimizer([x], [], s, [s**2])
hf.quick_cost = lambda *args, **kwargs: 0.0
hf.global_backtracking = False
hf.preconditioner = False
hf.max_cg_iterations = 300
hf.batch_Gv = lambda v: numpy.dot(A, v)
b = numpy.random.random(n)
c, x, j, i = hf.cg(b)
print
print 'error on b =', abs(numpy.dot(A, x) - b).mean()
print 'error on x =', abs(numpy.linalg.solve(A, b) - x).mean()
def sgd_optimizer(p, inputs, costs, train_set, lr=1e-4):
'''SGD optimizer with a similar interface to hf_optimizer.'''
g = [T.grad(costs[0], i) for i in p]
updates = dict((i, i - lr*j) for i, j in zip(p, g))
f = theano.function(inputs, costs, updates=updates)
try:
for u in xrange(1000):
cost = []
for i in train_set.iterate(True):
cost.append(f(*i))
print 'update %i, cost=' %u, numpy.mean(cost, axis=0)
sys.stdout.flush()
except KeyboardInterrupt:
print 'Training interrupted.'
# feed-forward neural network with sigmoidal output
def simple_NN(sizes=(784, 100, 10)):
x = T.matrix()
t = T.matrix()
p = []
y = x
for i in xrange(len(sizes)-1):
a, b = sizes[i:i+2]
Wi = theano.shared((10./numpy.sqrt(a+b) * numpy.random.uniform(-1, 1, size=(a, b))).astype(theano.config.floatX))
bi = theano.shared(numpy.zeros(b, dtype=theano.config.floatX))
p += [Wi, bi]
s = T.dot(y,Wi) + bi
y = T.nnet.sigmoid(s)
c = (-t* T.log(y) - (1-t)* T.log(1-y)).mean()
acc = T.neq(T.round(y), t).mean()
return p, [x, t], s, [c, acc]
def example_NN(hf=True):
p, inputs, s, costs = simple_NN((2, 50, 40, 30, 1))
xor_dataset = [[], []]
for i in xrange(50000):
x = numpy.random.randint(0, 2, (50, 2))
t = (x[:, 0:1] ^ x[:, 1:2]).astype(theano.config.floatX)
x = x.astype(theano.config.floatX)
xor_dataset[0].append(x)
xor_dataset[1].append(t)
training_examples = len(xor_dataset[0]) * 3/4
train = [xor_dataset[0][:training_examples], xor_dataset[1][:training_examples]]
valid = [xor_dataset[0][training_examples:], xor_dataset[1][training_examples:]]
gradient_dataset = SequenceDataset(train, batch_size=None, number_batches=10000)
cg_dataset = SequenceDataset(train, batch_size=None, number_batches=5000)
valid_dataset = SequenceDataset(valid, batch_size=None, number_batches=5000)
if hf:
hf_optimizer(p, inputs, s, costs).train(gradient_dataset, cg_dataset, initial_lambda=1.0, preconditioner=True, validation=valid_dataset)
else:
sgd_optimizer(p, inputs, costs, gradient_dataset, lr=1e-3)
# single-layer recurrent neural network with sigmoid output, only last time-step output is significant
def simple_RNN(nh):
Wx = theano.shared(0.2 * numpy.random.uniform(-1.0, 1.0, (1, nh)).astype(theano.config.floatX))
Wh = theano.shared(0.2 * numpy.random.uniform(-1.0, 1.0, (nh, nh)).astype(theano.config.floatX))
Wy = theano.shared(0.2 * numpy.random.uniform(-1.0, 1.0, (nh, 1)).astype(theano.config.floatX))
bh = theano.shared(numpy.zeros(nh, dtype=theano.config.floatX))
by = theano.shared(numpy.zeros(1, dtype=theano.config.floatX))
h0 = theano.shared(numpy.zeros(nh, dtype=theano.config.floatX))
p = [Wx, Wh, Wy, bh, by, h0]
x = T.matrix()
def recurrence(x_t, h_tm1):
h_t = T.tanh(T.dot(x_t, Wx) + T.dot(h_tm1, Wh) + bh)
s_t = T.dot(h_t, Wy) + by
return [h_t, s_t]
([h, activations], updates) = theano.scan(fn=recurrence, sequences=x, outputs_info=[h0, dict()])
t = x[0, 0]
s = activations[-1, 0]
y = T.nnet.sigmoid(s)
loss = -t*T.log(y + 1e-14) - (1-t)*T.log((1-y) + 1e-14)
acc = T.neq(T.round(y), t)
return p, [x], s, [loss, acc], h
def example_RNN(hf=True):
p, inputs, s, costs, h = simple_RNN(100)
memorization_dataset = [[]] # memorize the first unit for 100 time-steps with binary noise
for i in xrange(100000):
memorization_dataset[0].append(numpy.random.randint(2, size=(100, 1)).astype(theano.config.floatX))
train = [memorization_dataset[0][:-1000]]
valid = [memorization_dataset[0][-1000:]]
gradient_dataset = SequenceDataset(train, batch_size=None, number_batches=5000)
cg_dataset = SequenceDataset(train, batch_size=None, number_batches=1000)
valid_dataset = SequenceDataset(valid, batch_size=None, number_batches=1000)
if hf:
hf_optimizer(p, inputs, s, costs, h).train(gradient_dataset, cg_dataset, initial_lambda=0.5, mu=1.0, preconditioner=False, validation=valid_dataset)
else:
sgd_optimizer(p, inputs, costs, gradient_dataset, lr=5e-5)