def predict_mc(count, key):
key = tf_random_split(key, count)
fx_train, fx_test = vmap(predict_empirical)(key)
fx_train_mean = np.mean(fx_train, axis=0)
fx_test_mean = np.mean(fx_test, axis=0)
fx_train_centered = fx_train - fx_train_mean
fx_test_centered = fx_test - fx_test_mean
cov_train = PredictTest._cov_empirical(fx_train_centered)
cov_test = PredictTest._cov_empirical(fx_test_centered)
return fx_train_mean, fx_test_mean, cov_train, cov_test
def main(unused_argv):
# Build data pipelines.
print('Loading data.')
x_train, y_train, x_test, y_test = \
datasets.get_dataset('cifar10', FLAGS.train_size, FLAGS.test_size)
# Build the infinite network.
_, _, kernel_fn = stax.serial(
stax.Dense(1, 2., 0.05),
stax.Relu(),
stax.Dense(1, 2., 0.05)
)
# Optionally, compute the kernel in batches, in parallel.
kernel_fn = nt.batch(kernel_fn,
device_count=0,
batch_size=FLAGS.batch_size)
start = time.time()
# Bayesian and infinite-time gradient descent inference with infinite network.
predict_fn = nt.predict.gradient_descent_mse_ensemble(kernel_fn, x_train,
y_train, diag_reg=1e-3)
fx_test_nngp, fx_test_ntk = predict_fn(x_test=x_test)
duration = time.time() - start
print('Kernel construction and inference done in %s seconds.' % duration)
# Print out accuracy and loss for infinite network predictions.
loss = lambda fx, y_hat: 0.5 * np.mean((fx - y_hat) ** 2)
util.print_summary('NNGP test', y_test, fx_test_nngp, None, loss)
util.print_summary('NTK test', y_test, fx_test_ntk, None, loss)
def testMaxLearningRate(self, train_shape, network, out_logits,
fn_and_kernel):
key = stateless_uniform(shape=[2],
seed=[0, 0],
minval=None,
maxval=None,
dtype=tf.int32)
keys = tf_random_split(key)
key = keys[0]
split = keys[1]
if len(train_shape) == 2:
train_shape = (train_shape[0] * 5, train_shape[1] * 10)
else:
train_shape = (16, 8, 8, 3)
x_train = np.asarray(normal(train_shape, seed=split))
keys = tf_random_split(key)
key = keys[0]
split = keys[1]
y_train = np.asarray(
stateless_uniform(shape=(train_shape[0], out_logits),
seed=split,
minval=0,
maxval=1) < 0.5, np.float32)
# Regress to an MSE loss.
loss = lambda params, x: 0.5 * np.mean((f(params, x) - y_train)**2)
grad_loss = jit(grad(loss))
def get_loss(opt_state):
return loss(get_params(opt_state), x_train)
steps = 20
for lr_factor in [0.5, 3.]:
params, f, ntk = fn_and_kernel(key, train_shape[1:], network,
out_logits)
g_dd = ntk(x_train, None, 'ntk')
step_size = predict.max_learning_rate(
g_dd, y_train_size=y_train.size) * lr_factor
opt_init, opt_update, get_params = optimizers.sgd(step_size)
opt_state = opt_init(params)
init_loss = get_loss(opt_state)
for i in range(steps):
params = get_params(opt_state)
opt_state = opt_update(i, grad_loss(params, x_train),
opt_state)
trained_loss = get_loss(opt_state)
loss_ratio = trained_loss / (init_loss + 1e-12)
if lr_factor == 3.:
if not math.isnan(loss_ratio):
self.assertGreater(loss_ratio, 10.)
else:
self.assertLess(loss_ratio, 0.1)
def print_summary(name, labels, net_p, lin_p, loss):
"""Print summary information comparing a network with its linearization."""
print('\nEvaluating Network on {} data.'.format(name))
print('---------------------------------------')
print('Network Accuracy = {}'.format(_accuracy(net_p, labels)))
print('Network Loss = {}'.format(loss(net_p, labels)))
if lin_p is not None:
print('Linearization Accuracy = {}'.format(_accuracy(lin_p, labels)))
print('Linearization Loss = {}'.format(loss(lin_p, labels)))
print('RMSE of predictions: {}'.format(
np.sqrt(np.mean((net_p - lin_p)**2))))
print('---------------------------------------')
def main(unused_argv):
# Build data pipelines.
print('Loading data.')
x_train, y_train, x_test, y_test = \
datasets.get_dataset('mnist', FLAGS.train_size, FLAGS.test_size)
# Build the network
init_fn, apply_fn, _ = stax.serial(stax.Dense(512, 1., 0.05), stax.Erf(),
stax.Dense(10, 1., 0.05))
key = random.stateless_random_uniform(shape=[2],
seed=[0, 0],
minval=None,
maxval=None,
dtype=np.int32)
_, params = init_fn(key, (1, 784))
# Create and initialize an optimizer.
opt_init, opt_apply, get_params = optimizers.sgd(FLAGS.learning_rate)
state = opt_init(params)
# Create an mse loss function and a gradient function.
loss = lambda fx, y_hat: 0.5 * np.mean((fx - y_hat)**2)
grad_loss = jit(grad(lambda params, x, y: loss(apply_fn(params, x), y)))
# Create an MSE predictor to solve the NTK equation in function space.
ntk = nt.batch(nt.empirical_ntk_fn(apply_fn), batch_size=4, device_count=0)
g_dd = ntk(x_train, None, params)
g_td = ntk(x_test, x_train, params)
predictor = nt.predict.gradient_descent_mse(g_dd, y_train)
# Get initial values of the network in function space.
fx_train = apply_fn(params, x_train)
fx_test = apply_fn(params, x_test)
# Train the network.
train_steps = int(FLAGS.train_time // FLAGS.learning_rate)
print('Training for {} steps'.format(train_steps))
for i in range(train_steps):
params = get_params(state)
state = opt_apply(i, grad_loss(params, x_train, y_train), state)
# Get predictions from analytic computation.
print('Computing analytic prediction.')
fx_train, fx_test = predictor(FLAGS.train_time, fx_train, fx_test, g_td)
# Print out summary data comparing the linear / nonlinear model.
util.print_summary('train', y_train, apply_fn(params, x_train), fx_train,
loss)
util.print_summary('test', y_test, apply_fn(params, x_test), fx_test, loss)
def run_test(*args):
num_samples = 1000
tol = 0.1 # High tolerance to keep the # of samples low else the test
# takes a long time to run.
np_random.seed(10)
outputs = [np_random.randn(*args) for _ in range(num_samples)]
# Test output shape.
for output in outputs:
self.assertEqual(output.shape, tuple(args))
default_dtype = (np.float64 if np_dtypes.is_allow_float64()
else np.float32)
self.assertEqual(output.dtype.as_numpy_dtype, default_dtype)
if np.prod(args): # Don't bother with empty arrays.
outputs = [output.tolist() for output in outputs]
# Test that the properties of normal distribution are satisfied.
mean = np.mean(outputs, axis=0)
stddev = np.std(outputs, axis=0)
self.assertAllClose(mean, np.zeros(args), atol=tol)
self.assertAllClose(stddev, np.ones(args), atol=tol)
# Test that outputs are different with different seeds.
np_random.seed(20)
diff_seed_outputs = [
np_random.randn(*args).tolist() for _ in range(num_samples)
]
self.assertNotAllClose(outputs, diff_seed_outputs)
# Test that outputs are the same with the same seed.
np_random.seed(10)
same_seed_outputs = [
np_random.randn(*args).tolist() for _ in range(num_samples)
]
self.assertAllClose(outputs, same_seed_outputs)
def main(unused_argv):
# Build data and .
print('Loading data.')
x_train, y_train, x_test, y_test = datasets.get_dataset('mnist',
permute_train=True)
# Build the network
init_fn, f, _ = stax.serial(stax.Dense(512, 1., 0.05), stax.Erf(),
stax.Dense(10, 1., 0.05))
key = random.stateless_random_uniform(shape=[2],
seed=[0, 0],
minval=None,
maxval=None,
dtype=np.int32)
_, params = init_fn(key, (1, 784))
# Linearize the network about its initial parameters.
f_lin = nt.linearize(f, params)
# Create and initialize an optimizer for both f and f_lin.
opt_init, opt_apply, get_params = optimizers.momentum(
FLAGS.learning_rate, 0.9)
opt_apply = jit(opt_apply)
state = opt_init(params)
state_lin = opt_init(params)
# Create a cross-entropy loss function.
loss = lambda fx, y_hat: -np.mean(logsoftmax(fx) * y_hat)
# Specialize the loss function to compute gradients for both linearized and
# full networks.
grad_loss = jit(grad(lambda params, x, y: loss(f(params, x), y)))
grad_loss_lin = jit(grad(lambda params, x, y: loss(f_lin(params, x), y)))
# Train the network.
print('Training.')
print('Epoch\tLoss\tLinearized Loss')
print('------------------------------------------')
epoch = 0
steps_per_epoch = 50000 // FLAGS.batch_size
for i, (x, y) in enumerate(
datasets.minibatch(x_train, y_train, FLAGS.batch_size,
FLAGS.train_epochs)):
params = get_params(state)
state = opt_apply(i, grad_loss(params, x, y), state)
params_lin = get_params(state_lin)
state_lin = opt_apply(i, grad_loss_lin(params_lin, x, y), state_lin)
if i % steps_per_epoch == 0:
print('{}\t{}\t{}'.format(epoch, loss(f(params, x), y),
loss(f_lin(params_lin, x), y)))
epoch += 1
# Print out summary data comparing the linear / nonlinear model.
x, y = x_train[:10000], y_train[:10000]
util.print_summary('train', y, f(params, x), f_lin(params_lin, x), loss)
util.print_summary('test', y_test, f(params, x_test),
f_lin(params_lin, x_test), loss)
def testPredictND(self):
n_chan = 6
key = stateless_uniform(shape=[2],
seed=[1, 1],
minval=None,
maxval=None,
dtype=tf.int32)
im_shape = (5, 4, 3)
n_train = 2
n_test = 2
x_train = np.asarray(normal((n_train, ) + im_shape, seed=key))
y_train = stateless_uniform(shape=(n_train, 3, 2, n_chan), seed=key)
init_fn, apply_fn, _ = stax.Conv(n_chan, (3, 2), (1, 2))
_, params = init_fn(key, x_train.shape)
fx_train_0 = apply_fn(params, x_train)
for trace_axes in [(), (-1, ), (-2, ), (-3, ), (0, 1), (2, 3), (2, ),
(1, 3), (0, -1), (0, 0, -3), (0, 1, 2, 3),
(0, 1, -1, 2)]:
for ts in [None, np.arange(6).reshape((2, 3))]:
for x in [None, 'x_test']:
with self.subTest(trace_axes=trace_axes, ts=ts, x=x):
t_shape = ts.shape if ts is not None else ()
y_test_shape = t_shape + (n_test, ) + y_train.shape[1:]
y_train_shape = t_shape + y_train.shape
x = x if x is None else np.asarray(
normal((n_test, ) + im_shape, seed=key))
fx_test_0 = None if x is None else apply_fn(params, x)
kernel_fn = empirical.empirical_kernel_fn(
apply_fn, trace_axes=trace_axes)
# TODO(romann): investigate the SIGTERM error on CPU.
# kernel_fn = jit(kernel_fn, static_argnums=(2,))
ntk_train_train = kernel_fn(x_train, None, 'ntk',
params)
if x is not None:
ntk_test_train = kernel_fn(x, x_train, 'ntk',
params)
loss = lambda x, y: 0.5 * np.mean(x - y)**2
predict_fn_mse = predict.gradient_descent_mse(
ntk_train_train, y_train, trace_axes=trace_axes)
predict_fn_mse_ensemble = predict.gradient_descent_mse_ensemble(
kernel_fn,
x_train,
y_train,
trace_axes=trace_axes,
params=params)
if x is None:
p_train_mse = predict_fn_mse(ts, fx_train_0)
else:
p_train_mse, p_test_mse = predict_fn_mse(
ts, fx_train_0, fx_test_0, ntk_test_train)
self.assertAllClose(y_test_shape, p_test_mse.shape)
self.assertAllClose(y_train_shape, p_train_mse.shape)
p_nngp_mse_ens, p_ntk_mse_ens = predict_fn_mse_ensemble(
ts, x, ('nngp', 'ntk'), compute_cov=True)
ref_shape = y_train_shape if x is None else y_test_shape
self.assertAllClose(ref_shape,
p_ntk_mse_ens.mean.shape)
self.assertAllClose(ref_shape,
p_nngp_mse_ens.mean.shape)
if ts is not None:
predict_fn = predict.gradient_descent(
loss,
ntk_train_train,
y_train,
trace_axes=trace_axes)
if x is None:
p_train = predict_fn(ts, fx_train_0)
else:
p_train, p_test = predict_fn(
ts, fx_train_0, fx_test_0, ntk_test_train)
self.assertAllClose(y_test_shape, p_test.shape)
self.assertAllClose(y_train_shape, p_train.shape)
def testTrainedEnsemblePredCov(self, train_shape, test_shape, network,
out_logits):
training_steps = 1000
learning_rate = 0.1
ensemble_size = 1024
init_fn, apply_fn, kernel_fn = stax.serial(
stax.Dense(128, W_std=1.2, b_std=0.05), stax.Erf(),
stax.Dense(out_logits, W_std=1.2, b_std=0.05))
opt_init, opt_update, get_params = optimizers.sgd(learning_rate)
opt_update = jit(opt_update)
key, x_test, x_train, y_train = self._get_inputs(
out_logits, test_shape, train_shape)
predict_fn_mse_ens = predict.gradient_descent_mse_ensemble(
kernel_fn,
x_train,
y_train,
learning_rate=learning_rate,
diag_reg=0.)
train = (x_train, y_train)
ensemble_key = tf_random_split(key, ensemble_size)
loss = jit(lambda params, x, y: 0.5 * np.mean(
(apply_fn(params, x) - y)**2))
grad_loss = jit(lambda state, x, y: grad(loss)
(get_params(state), x, y))
def train_network(key):
_, params = init_fn(key, (-1, ) + train_shape[1:])
opt_state = opt_init(params)
for i in range(training_steps):
opt_state = opt_update(i, grad_loss(opt_state, *train),
opt_state)
return get_params(opt_state)
params = vmap(train_network)(ensemble_key)
rtol = 0.08
for x in [None, 'x_test']:
with self.subTest(x=x):
x = x if x is None else x_test
x_fin = x_train if x is None else x_test
ensemble_fx = vmap(apply_fn, (0, None))(params, x_fin)
mean_emp = np.mean(ensemble_fx, axis=0)
mean_subtracted = ensemble_fx - mean_emp
cov_emp = np.einsum(
'ijk,ilk->jl',
mean_subtracted,
mean_subtracted,
optimize=True) / (mean_subtracted.shape[0] *
mean_subtracted.shape[-1])
ntk = predict_fn_mse_ens(training_steps,
x,
'ntk',
compute_cov=True)
self._assertAllClose(mean_emp, ntk.mean, rtol)
self._assertAllClose(cov_emp, ntk.covariance, rtol)
def testNTKGDPrediction(self, train_shape, test_shape, network, out_logits,
fn_and_kernel, momentum, learning_rate, t, loss):
key, x_test, x_train, y_train = self._get_inputs(
out_logits, test_shape, train_shape)
params, f, ntk = fn_and_kernel(key, train_shape[1:], network,
out_logits)
g_dd = ntk(x_train, None, 'ntk')
g_td = ntk(x_test, x_train, 'ntk')
# Regress to an MSE loss.
loss_fn = lambda y, y_hat: 0.5 * np.mean((y - y_hat)**2)
grad_loss = jit(grad(lambda params, x: loss_fn(f(params, x), y_train)))
trace_axes = () if g_dd.ndim == 4 else (-1, )
if loss == 'mse_analytic':
if momentum is not None:
raise absltest.SkipTest(momentum)
predictor = predict.gradient_descent_mse(
g_dd,
y_train,
learning_rate=learning_rate,
trace_axes=trace_axes)
elif loss == 'mse':
predictor = predict.gradient_descent(loss_fn,
g_dd,
y_train,
learning_rate=learning_rate,
momentum=momentum,
trace_axes=trace_axes)
else:
raise NotImplementedError(loss)
predictor = jit(predictor)
fx_train_0 = f(params, x_train)
fx_test_0 = f(params, x_test)
self._test_zero_time(predictor, fx_train_0, fx_test_0, g_td, momentum)
self._test_multi_step(predictor, fx_train_0, fx_test_0, g_td, momentum)
if loss == 'mse_analytic':
self._test_inf_time(predictor, fx_train_0, fx_test_0, g_td,
y_train)
if momentum is None:
opt_init, opt_update, get_params = optimizers.sgd(learning_rate)
else:
opt_init, opt_update, get_params = optimizers.momentum(
learning_rate, momentum)
opt_state = opt_init(params)
for i in range(t):
params = get_params(opt_state)
opt_state = opt_update(i, grad_loss(params, x_train), opt_state)
params = get_params(opt_state)
fx_train_nn, fx_test_nn = f(params, x_train), f(params, x_test)
fx_train_t, fx_test_t = predictor(t, fx_train_0, fx_test_0, g_td)
self.assertAllClose(fx_train_nn, fx_train_t, rtol=RTOL, atol=ATOL)
self.assertAllClose(fx_test_nn, fx_test_t, rtol=RTOL, atol=ATOL)
def _accuracy(y, y_hat):
"""Compute the accuracy of the predictions with respect to one-hot labels."""
return np.mean(np.argmax(y, axis=1) == np.argmax(y_hat, axis=1))
