beta = 3
# debug
debug = False
##======================================================================
## STEP 1: Implement sampleIMAGES
#
# After implementing sampleIMAGES, the display_network command should
# display a random sample of 200 patches from the dataset
# Loading Sample Images
# patches = sample_images.sample_images()
# Loading 10K images from MNIST database
images = load_MNIST.load_MNIST_images('data/mnist/train-images-idx3-ubyte')
patches = images[:, 0:10000]
# Obtain random parameters theta
theta = sparse_autoencoder.initialize(hidden_size, visible_size)
##======================================================================
## STEP 2: Implement sparseAutoencoderCost
#
# You can implement all of the components (squared error cost, weight decay term,
# sparsity penalty) in the cost function at once, but it may be easier to do
# it step-by-step and run gradient checking (see STEP 3) after each step. We
# suggest implementing the sparseAutoencoderCost function using the following steps:
#
# (a) Implement forward propagation in your neural network, and implement the
# squared error term of the cost function. Implement backpropagation to
# STEP 0: Here we provide the relevant parameters values that will
# allow your sparse autoencoder to get good filters; you do not need to
# change the parameters below.
input_size = 28 * 28
num_classes = 10
hidden_size_L1 = 10 # Layer 1 Hidden Size
hidden_size_L2 = 10 # Layer 2 Hidden Size
lambda_ = 3e-3 # weight decay parameter
# ======================================================================
# STEP 1: Load data from the MNIST database
#
# This loads our training data from the MNIST database files.
train_images = load_MNIST.load_MNIST_images('train-images.idx3-ubyte')
train_labels = load_MNIST.load_MNIST_labels('train-labels.idx1-ubyte')
train_images = train_images[:, 0:10]
train_labels = train_labels[0:10]
# ======================================================================
# STEP 2: Train the first sparse autoencoder
# This trains the first sparse autoencoder on the unlabelled STL training
# images.
# If you've correctly implemented sparseAutoencoderCost.m, you don't need
# to change anything here.
# Randomly initialize the parameters
sae1_theta = utils_hw.initialize(hidden_size_L1, input_size)
J = lambda x: utils_hw.sparse_autoencoder_cost(x, input_size, hidden_size_L1,
# (This was denoted by the Greek alphabet rho, which looks like a lower-case "p",
# in the lecture notes).
lambda_ = 3e-3 # weight decay parameter
beta = 3 # weight of sparsity penalty term
maxiter = 400 # Maximum iterations for training
"""
STEP 1: Load data from the MNIST database
This loads our training data from the MNIST database files.
"""
# Load MNIST database files
# Load MNIST database files
train_data = load_MNIST_images('data/mnist/train-images-idx3-ubyte')
train_labels = load_MNIST_labels('data/mnist/train-labels-idx1-ubyte')
"""
STEP 2: Train the first sparse autoencoder
This trains the first sparse autoencoder on the unlabelled STL training images.
If you've correctly implemented sparse_autoencoder_cost, you don't need
to change anything here.
"""
# Randomly initialize the parameters
sae1_theta = initialize_parameters(hidden_size_L1, input_size)
# Instructions: Train the first layer sparse autoencoder, this layer has
# change the parameters below.
input_size = 28 * 28
num_classes = 10
hidden_size_L1 = 200 # Layer 1 Hidden Size
hidden_size_L2 = 200 # Layer 2 Hidden Size
sparsity_param = 0.1 # desired average activation of the hidden units.
lambda_ = 3e-3 # weight decay parameter
beta = 3 # weight of sparsity penalty term
##======================================================================
## STEP 1: Load data from the MNIST database
#
# This loads our training data from the MNIST database files.
train_images = load_MNIST.load_MNIST_images('data/mnist/train-images-idx3-ubyte')
train_labels = load_MNIST.load_MNIST_labels('data/mnist/train-labels-idx1-ubyte')
##======================================================================
## STEP 2: Train the first sparse autoencoder
# This trains the first sparse autoencoder on the unlabelled STL training
# images.
# If you've correctly implemented sparseAutoencoderCost.m, you don't need
# to change anything here.
# Randomly initialize the parameters
sae1_theta = sparse_autoencoder.initialize(hidden_size_L1, input_size)
J = lambda x: sparse_autoencoder.sparse_autoencoder_cost(x, input_size, hidden_size_L1,
lambda_, sparsity_param,
# weight decay parameter
lambda_ = 0.0001
# debug (set to True in Ex 3)
debug = False
# ======================================================================
# Exercise 1: Load MNIST
# In this exercise, you will load the mnist dataset
# First download the dataset from the following website:
# Training Images: http://yann.lecun.com/exdb/mnist/train-images-idx3-ubyte.gz
# Training Labels: http://yann.lecun.com/exdb/mnist/train-labels-idx1-ubyte.gz
# Loading Sample Images
# Loading 10K images from MNIST database
images = load_MNIST.load_MNIST_images('train-images.idx3-ubyte')
patches = images[:, 0:10000]
patches = patches[:, 1:200]
display_network.display_network(patches[:, 0:100])
# Now you will use the display network function to display different sets if the MNIST dataset
# The display is saved in the directory under the name weigths.
# Display 10, 50 and 100 datasets
### YOUR CODE HERE ###
# display 10
display_network.display_network(patches[:, 0:10], 'weights10.png')
# display 50
display_network.display_network(patches[:, 0:50], 'weights50.png')
# display 100
display_network.display_network(patches[:, 0:100], 'weights100.png')
r = np.sqrt(6) / np.sqrt(s1 + s2 + 1)
result = np.random.random(2*s2*s1)*2*r-r
return result
if __name__=='__main__':
np.random.seed(0)
tf.set_random_seed(0)
dtype = np.float32
# 64-bit doesn't help much, search for 64-bit in
# https://www.wolframcloud.com/objects/5f297f41-30f7-4b1b-972c-cac8d1f8d8e4
u.default_dtype = dtype
machine_epsilon = np.finfo(dtype).eps # 1e-7 or 1e-16
train_images = load_MNIST.load_MNIST_images('data/train-images-idx3-ubyte')
dsize = 1000
patches = train_images[:,:dsize];
fs = [dsize, 28*28, 196, 28*28]
# values from deeplearning.stanford.edu/wiki/index.php/UFLDL_Tutorial
X0=patches
lambda_=3e-3
rho=tf.constant(0.1, dtype=dtype)
beta=3
W0f = W_uniform(fs[2],fs[3])
def f(i): return fs[i+1] # W[i] has shape f[i] x f[i-1]
dsize = f(-1)
n = len(fs) - 2
def main():
np.random.seed(0)
tf.set_random_seed(0)
dtype = np.float32
# 64-bit doesn't help much, search for 64-bit in
# https://www.wolframcloud.com/objects/5f297f41-30f7-4b1b-972c-cac8d1f8d8e4
u.default_dtype = dtype
machine_epsilon = np.finfo(dtype).eps # 1e-7 or 1e-16
train_images = load_MNIST.load_MNIST_images('data/train-images-idx3-ubyte')
dsize = 10000
patches = train_images[:, :dsize]
fs = [dsize, 28 * 28, 196, 28 * 28]
# values from deeplearning.stanford.edu/wiki/index.php/UFLDL_Tutorial
X0 = patches
lambda_ = 3e-3
rho = tf.constant(0.1, dtype=dtype)
beta = 3
W0f = W_uniform(fs[2], fs[3])
def f(i):
return fs[i + 1] # W[i] has shape f[i] x f[i-1]
dsize = f(-1)
n = len(fs) - 2
# helper to create variables with numpy or TF initial value
init_dict = {} # {var_placeholder: init_value}
vard = {} # {var: util.VarInfo}
def init_var(val, name, trainable=False, noinit=False):
if isinstance(val, tf.Tensor):
collections = [] if noinit else None
var = tf.Variable(val, name=name, collections=collections)
else:
val = np.array(val)
assert u.is_numeric, "Unknown type"
holder = tf.placeholder(dtype,
shape=val.shape,
name=name + "_holder")
var = tf.Variable(holder, name=name, trainable=trainable)
init_dict[holder] = val
var_p = tf.placeholder(var.dtype, var.shape)
var_setter = var.assign(var_p)
vard[var] = u.VarInfo(var_setter, var_p)
return var
lr = init_var(0.2, "lr")
if purely_linear: # need lower LR without sigmoids
lr = init_var(.02, "lr")
Wf = init_var(W0f, "Wf", True)
Wf_copy = init_var(W0f, "Wf_copy", True)
W = u.unflatten(Wf, fs[1:]) # perftodo: this creates transposes
X = init_var(X0, "X")
W.insert(0, X)
def sigmoid(x):
if not purely_linear:
return tf.sigmoid(x)
else:
return tf.identity(x)
def d_sigmoid(y):
if not purely_linear:
return y * (1 - y)
else:
return 1
def kl(x, y):
return x * tf.log(x / y) + (1 - x) * tf.log((1 - x) / (1 - y))
def d_kl(x, y):
return (1 - x) / (1 - y) - x / y
# A[i] = activations needed to compute gradient of W[i]
# A[n+1] = network output
A = [None] * (n + 2)
# A[0] is just for shape checks, assert fail on run
# tf.assert always fails because of static assert
# fail_node = tf.assert_equal(1, 0, message="too huge")
fail_node = tf.Print(0, [0], "fail, this must never run")
with tf.control_dependencies([fail_node]):
A[0] = u.Identity(dsize, dtype=dtype)
A[1] = W[0]
for i in range(1, n + 1):
A[i + 1] = sigmoid(W[i] @ A[i])
# reconstruction error and sparsity error
err = (A[3] - A[1])
rho_hat = tf.reduce_sum(A[2], axis=1, keep_dims=True) / dsize
# B[i] = backprops needed to compute gradient of W[i]
# B2[i] = backprops from sampled labels needed for natural gradient
B = [None] * (n + 1)
B2 = [None] * (n + 1)
B[n] = err * d_sigmoid(A[n + 1])
sampled_labels_live = tf.random_normal((f(n), f(-1)), dtype=dtype, seed=0)
sampled_labels = init_var(sampled_labels_live,
"sampled_labels",
noinit=True)
B2[n] = sampled_labels * d_sigmoid(A[n + 1])
for i in range(n - 1, -1, -1):
backprop = t(W[i + 1]) @ B[i + 1]
backprop2 = t(W[i + 1]) @ B2[i + 1]
if i == 1 and not drop_sparsity:
backprop += beta * d_kl(rho, rho_hat)
backprop2 += beta * d_kl(rho, rho_hat)
B[i] = backprop * d_sigmoid(A[i + 1])
B2[i] = backprop2 * d_sigmoid(A[i + 1])
# dW[i] = gradient of W[i]
dW = [None] * (n + 1)
pre_dW = [None] * (n + 1) # preconditioned dW
pre_dW_stable = [None] * (n + 1) # preconditioned stable dW
cov_A = [None] * (n + 1) # covariance of activations[i]
cov_B2 = [None] * (n + 1) # covariance of synthetic backprops[i]
vars_svd_A = [None] * (n + 1)
vars_svd_B2 = [None] * (n + 1)
for i in range(1, n + 1):
cov_A[i] = init_var(A[i] @ t(A[i]) / dsize, "cov_A%d" % (i, ))
cov_B2[i] = init_var(B2[i] @ t(B2[i]) / dsize, "cov_B2%d" % (i, ))
vars_svd_A[i] = u.SvdWrapper(cov_A[i], "svd_A_%d" % (i, ))
vars_svd_B2[i] = u.SvdWrapper(cov_B2[i], "svd_B2_%d" % (i, ))
if use_tikhonov:
whitened_A = u.regularized_inverse2(vars_svd_A[i], L=Lambda) @ A[i]
else:
whitened_A = u.pseudo_inverse2(vars_svd_A[i]) @ A[i]
if use_tikhonov:
whitened_B2 = u.regularized_inverse2(vars_svd_B2[i],
L=Lambda) @ B[i]
else:
whitened_B2 = u.pseudo_inverse2(vars_svd_B2[i]) @ B[i]
whitened_A_stable = u.pseudo_inverse_sqrt2(vars_svd_A[i]) @ A[i]
whitened_B2_stable = u.pseudo_inverse_sqrt2(vars_svd_B2[i]) @ B[i]
pre_dW[i] = (whitened_B2 @ t(whitened_A)) / dsize
pre_dW_stable[i] = (whitened_B2_stable @ t(whitened_A_stable)) / dsize
dW[i] = (B[i] @ t(A[i])) / dsize
# Loss function
reconstruction = u.L2(err) / (2 * dsize)
sparsity = beta * tf.reduce_sum(kl(rho, rho_hat))
L2 = (lambda_ / 2) * (u.L2(W[1]) + u.L2(W[1]))
loss = reconstruction
if not drop_l2:
loss = loss + L2
if not drop_sparsity:
loss = loss + sparsity
grad_live = u.flatten(dW[1:])
pre_grad_live = u.flatten(pre_dW[1:]) # fisher preconditioned gradient
pre_grad_stable_live = u.flatten(
pre_dW_stable[1:]) # sqrt fisher preconditioned grad
grad = init_var(grad_live, "grad")
pre_grad = init_var(pre_grad_live, "pre_grad")
pre_grad_stable = init_var(pre_grad_stable_live, "pre_grad_stable")
update_params_op = Wf.assign(Wf - lr * pre_grad).op
update_params_stable_op = Wf.assign(Wf - lr * pre_grad_stable).op
save_params_op = Wf_copy.assign(Wf).op
pre_grad_dot_grad = tf.reduce_sum(pre_grad * grad)
pre_grad_stable_dot_grad = tf.reduce_sum(pre_grad * grad)
grad_norm = tf.reduce_sum(grad * grad)
pre_grad_norm = u.L2(pre_grad)
pre_grad_stable_norm = u.L2(pre_grad_stable)
def dump_svd_info(step):
"""Dump singular values and gradient values in those coordinates."""
for i in range(1, n + 1):
svd = vars_svd_A[i]
s0, u0, v0 = sess.run([svd.s, svd.u, svd.v])
util.dump(s0, "A_%d_%d" % (i, step))
A0 = A[i].eval()
At0 = v0.T @ A0
util.dump(A0 @ A0.T, "Acov_%d_%d" % (i, step))
util.dump(At0 @ At0.T, "Atcov_%d_%d" % (i, step))
util.dump(s0, "As_%d_%d" % (i, step))
for i in range(1, n + 1):
svd = vars_svd_B2[i]
s0, u0, v0 = sess.run([svd.s, svd.u, svd.v])
util.dump(s0, "B2_%d_%d" % (i, step))
B0 = B[i].eval()
Bt0 = v0.T @ B0
util.dump(B0 @ B0.T, "Bcov_%d_%d" % (i, step))
util.dump(Bt0 @ Bt0.T, "Btcov_%d_%d" % (i, step))
util.dump(s0, "Bs_%d_%d" % (i, step))
def advance_batch():
sess.run(sampled_labels.initializer) # new labels for next call
def update_covariances():
ops_A = [cov_A[i].initializer for i in range(1, n + 1)]
ops_B2 = [cov_B2[i].initializer for i in range(1, n + 1)]
sess.run(ops_A + ops_B2)
def update_svds():
if whitening_mode > 1:
vars_svd_A[2].update()
if whitening_mode > 2:
vars_svd_B2[2].update()
if whitening_mode > 3:
vars_svd_B2[1].update()
def init_svds():
"""Initialize our SVD to identity matrices."""
ops = []
for i in range(1, n + 1):
ops.extend(vars_svd_A[i].init_ops)
ops.extend(vars_svd_B2[i].init_ops)
sess = tf.get_default_session()
sess.run(ops)
init_op = tf.global_variables_initializer()
# tf.get_default_graph().finalize()
from tensorflow.core.protobuf import rewriter_config_pb2
rewrite_options = rewriter_config_pb2.RewriterConfig(
disable_model_pruning=True,
constant_folding=rewriter_config_pb2.RewriterConfig.OFF,
memory_optimization=rewriter_config_pb2.RewriterConfig.MANUAL)
optimizer_options = tf.OptimizerOptions(opt_level=tf.OptimizerOptions.L0)
graph_options = tf.GraphOptions(optimizer_options=optimizer_options,
rewrite_options=rewrite_options)
config = tf.ConfigProto(graph_options=graph_options)
#sess = tf.Session(config=config)
sess = tf.InteractiveSession(config=config)
sess.run(Wf.initializer, feed_dict=init_dict)
sess.run(X.initializer, feed_dict=init_dict)
advance_batch()
update_covariances()
init_svds()
sess.run(init_op, feed_dict=init_dict) # initialize everything else
print("Running training.")
u.reset_time()
step_lengths = [] # keep track of learning rates
losses = []
ratios = [] # actual loss decrease / expected decrease
grad_norms = []
pre_grad_norms = [] # preconditioned grad norm squared
pre_grad_stable_norms = [] # sqrt preconditioned grad norms squared
target_delta_list = [] # predicted decrease linear approximation
target_delta2_list = [] # predicted decrease quadratic appromation
actual_delta_list = [] # actual decrease
# adaptive line search parameters
alpha = 0.3 # acceptable fraction of predicted decrease
beta = 0.8 # how much to shrink when violation
growth_rate = 1.05 # how much to grow when too conservative
def update_cov_A(i):
sess.run(cov_A[i].initializer)
def update_cov_B2(i):
sess.run(cov_B2[i].initializer)
# only update whitening matrix of input activations in the beginning
if whitening_mode > 0:
vars_svd_A[1].update()
# compute t(delta).H.delta/2
def hessian_quadratic(delta):
# update_covariances()
W = u.unflatten(delta, fs[1:])
W.insert(0, None)
total = 0
for l in range(1, n + 1):
decrement = tf.trace(t(W[l]) @ cov_B2[l] @ W[l] @ cov_A[l])
total += decrement
return (total / 2).eval()
# compute t(delta).H^-1.delta/2
def hessian_quadratic_inv(delta):
# update_covariances()
W = u.unflatten(delta, fs[1:])
W.insert(0, None)
total = 0
for l in range(1, n + 1):
invB2 = u.pseudo_inverse2(vars_svd_B2[l])
invA = u.pseudo_inverse2(vars_svd_A[l])
decrement = tf.trace(t(W[l]) @ invB2 @ W[l] @ invA)
total += decrement
return (total / 2).eval()
# do line search, dump values as csv
def line_search(initial_value, direction, step, num_steps):
saved_val = tf.Variable(Wf)
sess.run(saved_val.initializer)
pl = tf.placeholder(dtype, shape=(), name="linesearch_p")
assign_op = Wf.assign(initial_value - direction * step * pl)
vals = []
for i in range(num_steps):
sess.run(assign_op, feed_dict={pl: i})
vals.append(loss.eval())
sess.run(Wf.assign(saved_val)) # restore original value
return vals
for step in range(num_steps):
update_covariances()
if step % whiten_every_n_steps == 0:
update_svds()
sess.run(grad.initializer)
sess.run(pre_grad.initializer)
lr0, loss0 = sess.run([lr, loss])
save_params_op.run()
# regular inverse becomes unstable when grad norm exceeds 1
stabilized_mode = grad_norm.eval() < 1
if stabilized_mode and not use_tikhonov:
update_params_stable_op.run()
else:
update_params_op.run()
loss1 = loss.eval()
advance_batch()
# line search stuff
target_slope = (-pre_grad_dot_grad.eval() if stabilized_mode else
-pre_grad_stable_dot_grad.eval())
target_delta = lr0 * target_slope
target_delta_list.append(target_delta)
# second order prediction of target delta
# TODO: the sign is wrong, debug this
# https://www.wolframcloud.com/objects/8f287f2f-ceb7-42f7-a599-1c03fda18f28
if local_quadratics:
x0 = Wf_copy.eval()
x_opt = x0 - pre_grad.eval()
# computes t(x)@H^-1 @(x)/2
y_opt = loss0 - hessian_quadratic_inv(grad)
# computes t(x)@H @(x)/2
y_expected = hessian_quadratic(Wf - x_opt) + y_opt
target_delta2 = y_expected - loss0
target_delta2_list.append(target_delta2)
actual_delta = loss1 - loss0
actual_slope = actual_delta / lr0
slope_ratio = actual_slope / target_slope # between 0 and 1.01
actual_delta_list.append(actual_delta)
if do_line_search:
vals1 = line_search(Wf_copy, pre_grad, lr / 100, 40)
vals2 = line_search(Wf_copy, grad, lr / 100, 40)
u.dump(vals1, "line1-%d" % (i, ))
u.dump(vals2, "line2-%d" % (i, ))
losses.append(loss0)
step_lengths.append(lr0)
ratios.append(slope_ratio)
grad_norms.append(grad_norm.eval())
pre_grad_norms.append(pre_grad_norm.eval())
pre_grad_stable_norms.append(pre_grad_stable_norm.eval())
if step % report_frequency == 0:
print(
"Step %d loss %.2f, target decrease %.3f, actual decrease, %.3f ratio %.2f grad norm: %.2f pregrad norm: %.2f"
% (step, loss0, target_delta, actual_delta, slope_ratio,
grad_norm.eval(), pre_grad_norm.eval()))
if adaptive_step_frequency and adaptive_step and step > adaptive_step_burn_in:
# shrink if wrong prediction, don't shrink if prediction is tiny
if slope_ratio < alpha and abs(
target_delta) > 1e-6 and adaptive_step:
print("%.2f %.2f %.2f" % (loss0, loss1, slope_ratio))
print(
"Slope optimality %.2f, shrinking learning rate to %.2f" %
(
slope_ratio,
lr0 * beta,
))
sess.run(vard[lr].setter, feed_dict={vard[lr].p: lr0 * beta})
# grow learning rate, slope_ratio .99 worked best for gradient
elif step > 0 and i % 50 == 0 and slope_ratio > 0.90 and adaptive_step:
print("%.2f %.2f %.2f" % (loss0, loss1, slope_ratio))
print("Growing learning rate to %.2f" % (lr0 * growth_rate))
sess.run(vard[lr].setter,
feed_dict={vard[lr].p: lr0 * growth_rate})
u.record_time()
# check against expected loss
if 'Apple' in sys.version:
pass
# u.dump(losses, "kfac_small_final_mac.csv")
targets = np.loadtxt("data/kfac_small_final_mac.csv", delimiter=",")
else:
pass
# u.dump(losses, "kfac_small_final_linux.csv")
targets = np.loadtxt("data/kfac_small_final_linux.csv", delimiter=",")
u.check_equal(targets, losses[:len(targets)], rtol=1e-1)
u.summarize_time()
print("Test passed")
lambda_ = 1e-4 # Weight decay parameter
"""
STEP 1: Load data
In this section, we load the input and output data.
For softmax regression on MNIST pixels,
the input data is the images, and
the output data is the labels.
Change the filenames if you've saved the files under different names
On some platforms, the files might be saved as
train-images.idx3-ubyte / train-labels.idx1-ubyte
"""
images = load_MNIST_images('data/mnist/train-images-idx3-ubyte')
labels = load_MNIST_labels('data/mnist/train-labels-idx1-ubyte')
input_data = images
# For debugging purposes, you may wish to reduce the size of the input data
# in order to speed up gradient checking.
# Here, we create synthetic dataset using random data for testing
debug = False
if debug:
input_size = 8 * 8
input_data = np.random.randn(input_size, 100)
labels = np.random.randint(n_classes, size=100)
# Randomly initialise theta
theta = 0.005 * np.random.randn(n_classes * input_size)
result = np.random.random(rows*cols)*2*r-r
return result.reshape((rows, cols))
if args.dataset == 'cifar':
# load data globally once
from keras.datasets import cifar10
(X_train, y_train), (X_test, y_test) = cifar10.load_data()
X_train = X_train.astype(np.float32)
X_train = X_train.reshape((X_train.shape[0], -1))
X_test = X_test.astype(np.float32)
X_test = X_test.reshape((X_test.shape[0], -1))
X_train /= 255
X_test /= 255
elif args.dataset == 'mnist':
train_images = load_MNIST.load_MNIST_images('data/train-images-idx3-ubyte').astype(np.float32)
# todo: load test images from separate file like with cifar
# todo: remove this extra truncation since it happens later
# test_patches = train_images[:,-args.dataset_size:]
test_images = load_MNIST.load_MNIST_images('data/t10k-images-idx3-ubyte').astype(np.float32)
X_train = train_images[:,:args.dataset_size].T # batch last
X_test = test_images.T # test_patches.T
# todo: rename to better names
train_images = X_train.T # batch first
test_images = X_test.T
full_trace_options = tf.RunOptions(trace_level=tf.RunOptions.FULL_TRACE,
output_partition_graphs=True)
