def resolve(gdb, item):
"""
Given an item, recursively retrieve its base items, then merge according
to type. Returns the merged dict.
"""
is_edge = (item['type'] == 'edge')
spec = specs.toplevels[item['type']]
def go(i):
if i.get('base') is not None:
return go(gdb.get(i['base'])) + [i]
return [i]
items = map(flatten, go(item))
out = {}
for k in set(ik for i in items for ik in i.keys()):
sp = resolve_spec(spec, k.split('.'))
vs = [i.get(k) for i in items if k in i]
# TODO: dict and list negation; early-stage removal of negated knots?
if is_edge and isinstance(sp, (spectypes.Spline, spectypes.List)):
r = sum(vs, [])
else:
r = vs[-1]
out[k] = r
return unflatten(out)
def load_native(config: Mapping[str, Any]) -> None:
runtime_exe_path = build_runtime(config, "exe")
data_path = pathify(config["data"], root_dir, cache_path, True, True)
demo_data_path = pathify(config["demo_data"], root_dir, cache_path, True, True)
plugin_paths = threading_map(
lambda plugin_config: build_one_plugin(config, plugin_config),
[
plugin_config
for plugin_group in config["plugin_groups"]
for plugin_config in plugin_group["plugin_group"]
],
desc="Building plugins",
)
command_str = config["loader"].get("command", "%a")
main_cmd_lst = [str(runtime_exe_path), *map(str, plugin_paths)]
command_lst_sbst = list(
flatten1(
replace_all(
unflatten(shlex.split(command_str)),
{("%a",): main_cmd_lst, ("%b",): [shlex.quote(shlex.join(main_cmd_lst))]},
)
)
)
subprocess_run(
command_lst_sbst,
env_override=dict(ILLIXR_DATA=str(data_path), ILLIXR_DEMO_DATA=str(demo_data_path)),
)
def loss_and_grad(Wf):
"""Returns cost, gradient for current parameter vector."""
global fs, X, global_cov_A, global_whitened_A
W = u.unflatten(Wf, fs[1:]) # perftodo: this creates transposes
W.insert(0, X)
A = [None] * (n + 2)
A[1] = W[0]
for i in range(1, n + 1):
A[i + 1] = nonlin(W[i] @ A[i])
err = (A[n + 1] - A[1])
B = [None] * (n + 1)
B[n] = 2 * err * d_nonlin(A[n + 1])
for i in range(n - 1, -1, -1):
backprop = t(W[i + 1]) @ B[i + 1]
B[i] = backprop * d_nonlin(A[i + 1])
dW = [None] * (n + 1)
for i in range(1, n + 1):
dW[i] = (B[i] @ t(A[i]))
loss = u.L2(err)
grad = u.flatten(dW[1:])
return loss, grad
def loss_and_grad(Wf):
"""Returns cost, gradient for current parameter vector."""
global fs, X, global_cov_A, global_whitened_A
W = u.unflatten(Wf, fs[1:]) # perftodo: this creates transposes
W.insert(0, X)
A = [None] * (n + 2)
A[1] = W[0]
for i in range(1, n + 1):
A[i + 1] = tf.sigmoid(W[i] @ A[i])
err = (A[3] - A[1])
def d_sigmoid(y):
return y * (1 - y)
B = [None] * (n + 1)
B2 = [None] * (n + 1)
B[n] = err * d_sigmoid(A[n + 1])
sampled_labels = tf.random_normal((f(n), f(-1)), dtype=dtype, seed=0)
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]
B[i] = backprop * d_sigmoid(A[i + 1])
B2[i] = backprop2 * d_sigmoid(A[i + 1])
dW = [None] * (n + 1)
pre_dW = [None] * (n + 1) # preconditioned dW
cov_A = [None] * (n + 1) # covariance of activations[i]
whitened_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)
if global_cov_A is None:
global_cov_A = A[1] @ t(A[1]) / dsize
global_whitened_A = regularized_inverse(global_cov_A, lambda_) @ A[1]
cov_A[1] = global_cov_A
whitened_A[1] = global_whitened_A
for i in range(1, n + 1):
if i > 1:
cov_A[i] = A[i] @ t(A[i]) / dsize
whitened_A[i] = regularized_inverse(cov_A[i], lambda_) @ A[i]
cov_B2[i] = B2[i] @ t(B2[i]) / dsize
whitened_B = regularized_inverse(cov_B2[i], lambda_) @ B[i]
pre_dW[i] = (whitened_B @ t(whitened_A[i])) / dsize
dW[i] = (B[i] @ t(A[i])) / dsize
reconstruction = u.L2(err) / (2 * dsize)
loss = reconstruction
grad = u.flatten(dW[1:])
kfac_grad = u.flatten(pre_dW[1:])
return loss, grad, kfac_grad
def load_native(config: Mapping[str, Any]) -> None:
runtime_exe_path = build_runtime(config, "exe")
data_path = pathify(config["data"], root_dir, cache_path, True, True)
demo_data_path = pathify(config["demo_data"], root_dir, cache_path, True, True)
enable_offload_flag = config["enable_offload"]
enable_alignment_flag = config["enable_alignment"]
realsense_cam_string = config["realsense_cam"]
plugin_paths = threading_map(
lambda plugin_config: build_one_plugin(config, plugin_config),
[plugin_config for plugin_group in config["plugin_groups"] for plugin_config in plugin_group["plugin_group"]],
desc="Building plugins",
)
actual_cmd_str = config["action"].get("command", "$cmd")
illixr_cmd_list = [str(runtime_exe_path), *map(str, plugin_paths)]
env_override = dict(
ILLIXR_DATA=str(data_path),
ILLIXR_DEMO_DATA=str(demo_data_path),
ILLIXR_OFFLOAD_ENABLE=str(enable_offload_flag),
ILLIXR_ALIGNMENT_ENABLE=str(enable_alignment_flag),
ILLIXR_ENABLE_VERBOSE_ERRORS=str(config["enable_verbose_errors"]),
ILLIXR_RUN_DURATION=str(config["action"].get("ILLIXR_RUN_DURATION", 60)),
ILLIXR_ENABLE_PRE_SLEEP=str(config["enable_pre_sleep"]),
KIMERA_ROOT=config["action"]["kimera_path"],
AUDIO_ROOT=config["action"]["audio_path"],
REALSENSE_CAM=str(realsense_cam_string),
)
env_list = [f"{shlex.quote(var)}={shlex.quote(val)}" for var, val in env_override.items()]
actual_cmd_list = list(
flatten1(
replace_all(
unflatten(shlex.split(actual_cmd_str)),
{
("$env_cmd",): [
"env",
"-C",
Path(".").resolve(),
*env_list,
*illixr_cmd_list,
],
("$cmd",): illixr_cmd_list,
("$quoted_cmd",): [shlex.quote(shlex.join(illixr_cmd_list))],
("$env",): env_list,
},
)
)
)
log_stdout_str = config["action"].get("log_stdout", None)
log_stdout_ctx = cast(
ContextManager[Optional[BinaryIO]],
(open(log_stdout_str, "wb") if (log_stdout_str is not None) else noop_context(None)),
)
with log_stdout_ctx as log_stdout:
subprocess_run(
actual_cmd_list,
env_override=env_override,
stdout=log_stdout,
check=True,
)
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()
def transform(self, y):
check_is_fitted(self, 'classes_')
y = column_or_1d(y, warn=True)
y2, y2_cuts = flatten(y)
new_label = ~np.in1d(y2, self.classes_)
labels = np.searchsorted(self.classes_, y2)
labels[new_label] = len(self.classes_)
return unflatten(labels, y2_cuts)
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()
def resolve(gdb, item):
"""
Given an item, recursively retrieve its base items, then merge according
to type. Returns the merged dict.
"""
is_edge = (item['type'] == 'edge')
spec = specs.toplevels[item['type']]
def go(i):
if i.get('base') is not None:
return go(gdb.get(i['base'])) + [i]
return [i]
items = map(flatten, go(item))
out = {}
for k in set(ik for i in items for ik in i.keys()):
sp = resolve_spec(spec, k.split('.'))
vs = [i.get(k) for i in items if k in i]
# TODO: dict and list negation; early-stage removal of negated knots?
if is_edge and isinstance(sp, (spectypes.Spline, spectypes.List)):
r = sum(vs, [])
else:
r = vs[-1]
out[k] = r
return unflatten(out)
def rotations2_natural_sampled_kfac(num_samples=1):
tf.reset_default_graph()
np.random.seed(0)
tf.set_random_seed(0)
# override kr with no-shape-inferring version
def kr(A, B):
return u.kronecker(A, B, do_shape_inference=False)
X0 = np.genfromtxt('data/large_rotations2_X0.csv', delimiter=",")
Y0 = np.genfromtxt('data/large_rotations2_Y0.csv', delimiter=",")
W0f = v2c_np(np.genfromtxt('data/large_rotations2_W0f.csv', delimiter=","))
fs = np.genfromtxt('data/large_rotations2_fs.csv',
delimiter=",").astype(np.int32)
n = len(fs) - 2 # number of layers
def f(i):
return fs[i + 1] # W[i] has shape f[i] x f[i-1]
dsize = X0.shape[1]
assert f(-1) == dsize
# load W0f and do shape checks (can remove)
W0s = u.unflatten_np(W0f,
fs[1:]) # Wf doesn't have first layer (data matrix)
W0s.insert(0, X0)
Wf_holder = tf.placeholder(dtype, shape=W0f.shape)
Wf = tf.Variable(Wf_holder, name="Wf")
Wf_copy = tf.Variable(Wf_holder, name="Wf_copy")
init_dict = {Wf_holder: W0f}
# Create W's
# initialize data + layers
# W[0] is input matrix (X), W[n] is last matrix
# A[1] has activations for W[1], equal to W[0]=X
# A[n+1] has predictions
# Create W's
W = u.unflatten(Wf, fs[1:])
X = tf.constant(X0)
Y = tf.constant(Y0)
W.insert(0, X)
A = [0] * (n + 2)
A2 = [0] * (n + 2) # augmented forward props for natural gradient
A[0] = u.Identity(dsize)
A2[0] = u.Identity(dsize * num_samples)
for i in range(n + 1):
# fs is off by 2 from common notation, ie W[0] has shape f[0],f[-1]
A[i + 1] = tf.matmul(W[i], A[i], name="A" + str(i + 1))
if i == 0:
# replicate dataset multiple times corresponding to number of samples
A2[i + 1] = tf.concat([W[0]] * num_samples, axis=1)
else:
A2[i + 1] = tf.matmul(W[i], A2[i], name="A2" + str(i + 1))
# input dimensions match
assert W[0].get_shape() == X0.shape
# output dimensions match
assert W[-1].get_shape()[0], W[0].get_shape()[1] == Y0.shape
assert A[n + 1].get_shape() == Y0.shape
err = Y - A[n + 1]
loss = tf.reduce_sum(tf.square(err)) / (2 * dsize)
# lower learning rate by 10x
lr = tf.Variable(0.01, dtype=dtype)
# create backprop matrices
# B[i] has backprop for matrix i
B = [0] * (n + 1)
B2 = [0] * (n + 1)
B[n] = -err / dsize
B2[n] = tf.random_normal((f(n), dsize * num_samples),
0,
1,
seed=0,
dtype=dtype)
for i in range(n - 1, -1, -1):
B[i] = tf.matmul(tf.transpose(W[i + 1]), B[i + 1], name="B" + str(i))
B2[i] = tf.matmul(tf.transpose(W[i + 1]),
B2[i + 1],
name="B2" + str(i))
# Create gradient update. Make copy of variables and split update into
# two run calls. Using single set of variables will gives updates that
# occasionally produce wrong results/NaN's because of data race
dW = [0] * (n + 1)
dW2 = [0] * (n + 1)
updates1 = [0] * (n + 1) # compute updated value into Wcopy
updates2 = [0] * (n + 1) # copy value back into W
Wcopy = [0] * (n + 1)
for i in range(n + 1):
Wi_name = "Wcopy" + str(i)
Wi_shape = (fs[i + 1], fs[i])
Wi_init = tf.zeros(dtype=dtype, shape=Wi_shape, name=Wi_name + "_init")
Wcopy[i] = tf.Variable(Wi_init, name=Wi_name, trainable=False)
dW[i] = tf.matmul(B[i], tf.transpose(A[i]), name="dW" + str(i))
dW2[i] = tf.matmul(B2[i], tf.transpose(A2[i]), name="dW2" + str(i))
del dW[0] # get rid of W[0] update
del dW2[0] # get rid of W[0] update
# construct flattened gradient update vector
dWf = tf.concat([vec(grad) for grad in dW], axis=0)
# todo: divide both activations and backprops by size for cov calc
# Kronecker factored covariance blocks
iblocks = u.empty_grid(n + 1, n + 1)
for i in range(1, n + 1):
for j in range(1, n + 1):
if i == j:
acov = A2[i] @ t(A2[j]) / (dsize * num_samples)
bcov = B2[i] @ t(B2[j]) / (dsize * num_samples)
term = kr(u.pseudo_inverse(acov), u.pseudo_inverse(bcov))
else:
term = tf.zeros(shape=(f(i) * f(i - 1), f(j) * f(j - 1)),
dtype=dtype)
iblocks[i][j] = term
# remove leftmost blocks (those are with respect to W[0] which is input)
del iblocks[0]
for row in iblocks:
del row[0]
ifisher = u.concat_blocks(iblocks)
Wf_copy = tf.Variable(tf.zeros(dtype=dtype,
shape=Wf.shape,
name="Wf_copy_init"),
name="Wf_copy")
new_val_matrix = Wf - lr * (ifisher @ dWf)
train_op1 = Wf_copy.assign(new_val_matrix)
train_op2 = Wf.assign(Wf_copy)
sess = tf.Session()
sess.run(tf.global_variables_initializer(), feed_dict=init_dict)
observed_losses = []
u.reset_time()
for i in range(20):
loss0 = sess.run(loss)
print(loss0)
observed_losses.append(loss0)
sess.run(train_op1)
sess.run(train_op2)
u.record_time()
u.summarize_time()
u.summarize_graph()
def model_creator(batch_size, name='defaultmodel', dtype=np.float32):
"""Create MNIST autoencoder model. Dataset is part of model."""
global hack_global_init_dict
model = Model(name)
# TODO: actually use batch_size
init_dict = {} # todo: rename to feed_dict?
global_vars = []
local_vars = []
# TODO: rename to make_var
def init_var(val, name, is_global=False):
"""Helper to create variables with numpy or TF initial values."""
if isinstance(val, tf.Tensor):
var = u.get_variable(name=name, initializer=val, reuse=is_global)
else:
val = np.array(val)
assert u.is_numeric(val), "Non-numeric type."
var_struct = u.get_var(name=name, initializer=val, reuse=is_global)
holder = var_struct.val_
init_dict[holder] = val
var = var_struct.var
if is_global:
global_vars.append(var)
else:
local_vars.append(var)
return var
# TODO: get rid of purely_relu
def nonlin(x):
if purely_relu:
return tf.nn.relu(x)
elif purely_linear:
return tf.identity(x)
else:
return tf.sigmoid(x)
# TODO: rename into "nonlin_d"
def d_nonlin(y):
if purely_relu:
return u.relu_mask(y)
elif purely_linear:
return 1
else:
return y * (1 - y)
train_images = load_MNIST.load_MNIST_images(
'data/train-images-idx3-ubyte').astype(dtype)
patches = train_images[:, :batch_size]
fs = [batch_size, 28 * 28, 196, 28 * 28]
def f(i):
return fs[i + 1] # W[i] has shape f[i] x f[i-1]
n = len(fs) - 2
X = init_var(patches, "X", is_global=False)
W = [None] * n
W.insert(0, X)
A = [None] * (n + 2)
A[1] = W[0]
W0f_old = W_uniform(fs[2],
fs[3]).astype(dtype) # to match previous generation
W0s_old = u.unflatten(W0f_old, fs[1:]) # perftodo: this creates transposes
for i in range(1, n + 1):
# temp = init_var(ng_init(f(i), f(i-1)), "W_%d"%(i,), is_global=True)
# init_val1 = W0s_old[i-1]
init_val = ng_init(f(i), f(i - 1)).astype(dtype)
W[i] = init_var(init_val, "W_%d" % (i, ), is_global=True)
A[i + 1] = nonlin(kfac_lib.matmul(W[i], A[i]))
err = A[n + 1] - A[1]
# manually compute backprop to use for sanity checking
B = [None] * (n + 1)
B2 = [None] * (n + 1)
B[n] = err * d_nonlin(A[n + 1])
_sampled_labels_live = tf.random_normal((f(n), f(-1)), dtype=dtype, seed=0)
if use_fixed_labels:
_sampled_labels_live = tf.ones(shape=(f(n), f(-1)), dtype=dtype)
_sampled_labels = init_var(_sampled_labels_live,
"to_be_deleted",
is_global=False)
B2[n] = _sampled_labels * d_nonlin(A[n + 1])
for i in range(n - 1, -1, -1):
backprop = t(W[i + 1]) @ B[i + 1]
B[i] = backprop * d_nonlin(A[i + 1])
backprop2 = t(W[i + 1]) @ B2[i + 1]
B2[i] = backprop2 * d_nonlin(A[i + 1])
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)
dW = [None] * (n + 1)
dW2 = [None] * (n + 1)
pre_dW = [None] * (n + 1) # preconditioned dW
for i in range(1, n + 1):
if regularized_svd:
cov_A[i] = init_var(
A[i] @ t(A[i]) / batch_size + LAMBDA * u.Identity(f(i - 1)),
"cov_A%d" % (i, ))
cov_B2[i] = init_var(
B2[i] @ t(B2[i]) / batch_size + LAMBDA * u.Identity(f(i)),
"cov_B2%d" % (i, ))
else:
cov_A[i] = init_var(A[i] @ t(A[i]) / batch_size, "cov_A%d" % (i, ))
cov_B2[i] = init_var(B2[i] @ t(B2[i]) / batch_size,
"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_inverse3(vars_svd_A[i], L=LAMBDA) @ A[i]
whitened_B2 = u.regularized_inverse3(vars_svd_B2[i],
L=LAMBDA) @ B[i]
else:
whitened_A = u.pseudo_inverse2(vars_svd_A[i]) @ A[i]
whitened_B2 = u.pseudo_inverse2(vars_svd_B2[i]) @ B[i]
dW[i] = (B[i] @ t(A[i])) / batch_size
dW2[i] = B[i] @ t(A[i])
pre_dW[i] = (whitened_B2 @ t(whitened_A)) / batch_size
# model.extra['A'] = A
# model.extra['B'] = B
# model.extra['B2'] = B2
# model.extra['cov_A'] = cov_A
# model.extra['cov_B2'] = cov_B2
# model.extra['vars_svd_A'] = vars_svd_A
# model.extra['vars_svd_B2'] = vars_svd_B2
# model.extra['W'] = W
# model.extra['dW'] = dW
# model.extra['dW2'] = dW2
# model.extra['pre_dW'] = pre_dW
model.loss = u.L2(err) / (2 * batch_size)
sampled_labels_live = A[n + 1] + tf.random_normal(
(f(n), f(-1)), dtype=dtype, seed=0)
if use_fixed_labels:
sampled_labels_live = A[n + 1] + tf.ones(shape=(f(n), f(-1)),
dtype=dtype)
sampled_labels = init_var(sampled_labels_live,
"sampled_labels",
is_global=False)
err2 = A[n + 1] - sampled_labels
model.loss2 = u.L2(err2) / (2 * batch_size)
model.global_vars = global_vars
model.local_vars = local_vars
model.trainable_vars = W[1:]
def advance_batch():
sess = tf.get_default_session()
# TODO: get rid of _sampled_labels
sess.run([sampled_labels.initializer, _sampled_labels.initializer])
model.advance_batch = advance_batch
global_init_op = tf.group(*[v.initializer for v in global_vars])
def initialize_global_vars():
sess = tf.get_default_session()
sess.run(global_init_op, feed_dict=init_dict)
model.initialize_global_vars = initialize_global_vars
local_init_op = tf.group(*[v.initializer for v in local_vars])
def initialize_local_vars():
sess = tf.get_default_session()
sess.run(X.initializer, feed_dict=init_dict) # A's depend on X
sess.run(_sampled_labels.initializer, feed_dict=init_dict)
sess.run(local_init_op, feed_dict=init_dict)
model.initialize_local_vars = initialize_local_vars
hack_global_init_dict = init_dict
return model
def simple_newton_kfac_test():
tf.reset_default_graph()
X0 = np.genfromtxt('data/rotations_simple_X0.csv',
delimiter= ",")
Y0 = np.genfromtxt('data/rotations_simple_Y0.csv',
delimiter= ",")
W0f = v2c_np(np.genfromtxt('data/rotations_simple_W0f.csv',
delimiter= ","))
assert W0f.shape == (8, 1)
fs = np.genfromtxt('data/rotations_simple_fs.csv',
delimiter= ",").astype(np.int32)
n = len(fs)-2 # number of layers
u.check_equal(fs, [10,2,2,2])
def f(i): return fs[i+1] # W[i] has shape f[i] x f[i-1]
dsize = X0.shape[1]
assert f(-1) == dsize
# load W0f and do shape checks (can remove)
W0s = u.unflatten_np(W0f, fs[1:]) # Wf doesn't have first layer (data matrix)
W0s.insert(0, X0)
Wf_holder = tf.placeholder(dtype, shape=W0f.shape)
Wf = tf.Variable(Wf_holder, name="Wf")
Wf_copy = tf.Variable(Wf_holder, name="Wf_copy")
init_dict = {Wf_holder: W0f}
# Create W's
W = u.unflatten(Wf, fs[1:])
X = tf.constant(X0)
Y = tf.constant(Y0)
W.insert(0, X)
for (numpy_W, tf_W) in zip(W0s, W):
u.check_equal(numpy_W.shape, u.fix_shape(tf_W.shape))
# Create A's
# A[1] == X
A = [0]*(n+2)
A[0] = u.Identity(dsize)
for i in range(n+1):
A[i+1] = tf.matmul(W[i], A[i], name="A"+str(i+1))
assert W[0].get_shape() == X0.shape
assert A[n+1].get_shape() == X0.shape
assert A[1].get_shape() == X0.shape
err = Y - A[n+1]
loss = tf.reduce_sum(tf.square(err))/(2*dsize)
lr = tf.Variable(0.5, dtype=dtype, name="learning_rate")
# Create B's
B = [0]*(n+1)
B[n] = -err/dsize
Bn = [0]*(n+1) # Newton-modified backprop
Bn[n] = u.Identity(f(n))
for i in range(n-1, -1, -1):
B[i] = t(W[i+1]) @ B[i+1]
Bn[i] = t(W[i+1]) @ Bn[i+1]
# inverse Hessian blocks
iblocks = u.empty_grid(n+1, n+1)
for i in range(1, n+1):
for j in range(1, n+1):
# reuse Hess tensor calculation in order to get off-diag block sizes
dummy_term = kr(A[i] @ t(A[j]), Bn[i] @ t(Bn[j])) / dsize;
if i == j:
acov = A[i] @ t(A[j])
bcov = Bn[i] @ t(Bn[j]) / dsize;
term = kr(u.pseudo_inverse(acov), u.pseudo_inverse(bcov))
else:
term = tf.zeros(shape=dummy_term.get_shape(), dtype=dtype)
iblocks[i][j]=term
# remove leftmost blocks (those are with respect to W[0] which is input)
del iblocks[0]
for row in iblocks:
del row[0]
ihess = u.concat_blocks(iblocks)
sess = tf.Session()
sess.run(tf.global_variables_initializer(), feed_dict=init_dict)
# create dW's
dW = [0]*(n+1)
for i in range(n+1):
dW[i] = tf.matmul(B[i], tf.transpose(A[i]), name="dW"+str(i))
del dW[0] # get rid of W[0] update
dWf = tf.concat([u.vec(dWi) for dWi in dW], axis=0)
Wf_new = Wf - lr * ihess @ dWf
train_op1 = Wf_copy.assign(Wf_new)
train_op2 = Wf.assign(Wf_copy)
expected_losses = np.loadtxt("data/rotations_simple_newtonkfac_losses.csv",
delimiter= ",")
observed_losses = []
# from accompanying notebook
# {0.0111498, 0.0000171591, 4.11445*10^-11, 2.33653*10^-22,
# 6.88354*10^-33,
for i in range(10):
observed_losses.append(sess.run([loss])[0])
sess.run(train_op1)
sess.run(train_op2)
u.check_equal(observed_losses, expected_losses)
def relu_gradient_test():
tf.reset_default_graph()
X0 = np.genfromtxt('data/rotations_X0.csv',
delimiter= ",")
Y0 = np.genfromtxt('data/rotations_Y0.csv',
delimiter= ",")
W0f = v2c_np(np.genfromtxt('data/rotations_W0f.csv',
delimiter= ","))
assert W0f.shape == (8, 1)
fs = np.genfromtxt('data/rotations_relu_fs.csv',
delimiter= ",").astype(np.int32)
n = len(fs)-2 # number of layers
u.check_equal(fs, [4,2,2,2])
def f(i): return fs[i+1] # W[i] has shape f[i] x f[i-1]
dsize = X0.shape[1]
assert f(-1) == dsize
# load W0f and do shape checks (can remove)
W0s = u.unflatten_np(W0f, fs[1:]) # Wf doesn't have first layer (data matrix)
W0s.insert(0, X0)
Wf_holder = tf.placeholder(dtype, shape=W0f.shape)
Wf = tf.Variable(Wf_holder, name="Wf")
Wf_copy = tf.Variable(Wf_holder, name="Wf_copy")
init_dict = {Wf_holder: W0f}
# Create W's
W = u.unflatten(Wf, fs[1:])
X = tf.constant(X0, name="X0")
Y = tf.constant(Y0, name="Y0")
W.insert(0, X)
for (numpy_W, tf_W) in zip(W0s, W):
u.check_equal(numpy_W.shape, u.fix_shape(tf_W.shape))
# Create A's
# A[1] == X
A = [0]*(n+2)
A[0] = u.Identity(dsize)
for i in range(n+1):
if i == 0:
A[i+1] = X
else:
A[i+1] = tf.nn.relu(tf.matmul(W[i], A[i], name="A"+str(i+1)))
assert W[0].get_shape() == X0.shape
assert A[n+1].get_shape() == X0.shape
assert A[1].get_shape() == X0.shape
err = Y - A[n+1]
loss = tf.reduce_sum(tf.square(err))/(2*dsize)
lr = tf.Variable(0.1, dtype=dtype)
# Create B's
B = [0]*(n+1)
B[n] = (-err/dsize)*u.relu_mask(A[n+1])
for i in range(n-1, -1, -1):
B[i] = t(W[i+1]) @ B[i+1]
if i > 0: # there's no relu on first matrix
B[i] = B[i]*u.relu_mask(A[i+1])
# create dW's
dW = [0]*(n+1)
for i in range(n+1):
dW[i] = tf.matmul(B[i], tf.transpose(A[i]), name="dW"+str(i))
del dW[0] # get rid of W[0] update
dWf = tf.concat([u.vec(dWi) for dWi in dW], axis=0)
Wf_new = Wf - lr * dWf
train_op1 = Wf_copy.assign(Wf_new)
train_op2 = Wf.assign(Wf_copy)
sess = tf.Session()
sess.run(tf.global_variables_initializer(), feed_dict=init_dict)
expected_losses = np.loadtxt("data/rotations_relu_gradient_losses.csv",
delimiter= ",")
observed_losses = []
# From accompanying notebook
# {0.407751, 0.0683822, 0.0138657, 0.0039221, 0.00203637, 0.00164892,
# 0.00156137, 0.00153857, 0.00153051, 0.00152593}
for i in range(10):
observed_losses.append(sess.run([loss])[0])
sess.run(train_op1)
sess.run(train_op2)
u.check_equal(observed_losses, expected_losses)
def simple_newton_bd_test():
tf.reset_default_graph()
X0 = np.genfromtxt('data/rotations_simple_X0.csv',
delimiter= ",")
Y0 = np.genfromtxt('data/rotations_simple_Y0.csv',
delimiter= ",")
W0f = v2c_np(np.genfromtxt('data/rotations_simple_W0f.csv',
delimiter= ","))
assert W0f.shape == (8, 1)
fs = np.genfromtxt('data/rotations_simple_fs.csv',
delimiter= ",").astype(np.int32)
n = len(fs)-2 # number of layers
u.check_equal(fs, [10,2,2,2])
def f(i): return fs[i+1] # W[i] has shape f[i] x f[i-1]
dsize = X0.shape[1]
assert f(-1) == dsize
# load W0f and do shape checks (can remove)
W0s = u.unflatten_np(W0f, fs[1:]) # Wf doesn't have first layer (data matrix)
W0s.insert(0, X0)
Wf_holder = tf.placeholder(dtype, shape=W0f.shape)
Wf = tf.Variable(Wf_holder, name="Wf")
Wf_copy = tf.Variable(Wf_holder, name="Wf_copy")
init_dict = {Wf_holder: W0f}
# Create W's
W = u.unflatten(Wf, fs[1:])
X = tf.constant(X0)
Y = tf.constant(Y0)
W.insert(0, X)
for (numpy_W, tf_W) in zip(W0s, W):
u.check_equal(numpy_W.shape, u.fix_shape(tf_W.shape))
# Create A's
# A[1] == X
A = [0]*(n+2)
A[0] = u.Identity(dsize)
for i in range(n+1):
A[i+1] = tf.matmul(W[i], A[i], name="A"+str(i+1))
assert W[0].get_shape() == X0.shape
assert A[n+1].get_shape() == X0.shape
assert A[1].get_shape() == X0.shape
err = Y - A[n+1]
loss = tf.reduce_sum(tf.square(err))/(2*dsize)
lr = tf.Variable(0.5, dtype=dtype, name="learning_rate")
# Create B's
B = [0]*(n+1)
B[n] = -err/dsize
Bn = [0]*(n+1) # Newton-modified backprop
Bn[n] = u.Identity(f(n))
for i in range(n-1, -1, -1):
B[i] = t(W[i+1]) @ B[i+1]
Bn[i] = t(W[i+1]) @ Bn[i+1]
# Create U's
U = [list(range(n+1)) for _ in range(n+1)]
for bottom in range(n+1):
for top in range(n+1):
if bottom > top:
prod = u.Identity(f(top))
else:
prod = u.Identity(f(bottom-1))
for i in range(bottom, top+1):
prod = prod@t(W[i])
U[bottom][top] = prod
# Block i, j gives hessian block between layer i and layer j
blocks = [list(range(n+1)) for _ in range(n+1)]
for i in range(1, n+1):
for j in range(1, n+1):
term1 = kr(A[i] @ t(A[j]), Bn[i] @ t(Bn[j])) / dsize;
if i == j:
term2 = tf.zeros((f(i)*f(i-1), f(i)*f(i-1)), dtype=dtype)
elif i < j:
term2 = kr(A[i] @ t(B[j]), U[i+1][j-1])
else:
term2 = kr(t(U[j+1][i-1]), B[i] @ t(A[j]))
blocks[i][j]=term1 + term2 @ Kmat(f(j), f(j-1))
# remove leftmost blocks (those are with respect to W[0] which is input)
del blocks[0]
for row in blocks:
del row[0]
#hess = u.concat_blocks(blocks)
ihess = u.concat_blocks(u.block_diagonal_inverse(blocks))
# ihess = u.pseudo_inverse(hess)
sess = tf.Session()
sess.run(tf.global_variables_initializer(), feed_dict=init_dict)
# create dW's
dW = [0]*(n+1)
for i in range(n+1):
dW[i] = tf.matmul(B[i], tf.transpose(A[i]), name="dW"+str(i))
del dW[0] # get rid of W[0] update
dWf = tf.concat([u.vec(dWi) for dWi in dW], axis=0)
Wf_new = Wf - lr * ihess @ dWf
train_op1 = Wf_copy.assign(Wf_new)
train_op2 = Wf.assign(Wf_copy)
expected_losses = np.loadtxt("data/rotations_simple_newtonbd_losses.csv",
delimiter= ",")
observed_losses = []
# from accompanying notebook
# 0.0111498, 0.0000171591, 4.11445*10^-11, 2.33652*10^-22,
# 1.21455*10^-32,
for i in range(10):
observed_losses.append(sess.run([loss])[0])
sess.run(train_op1)
sess.run(train_op2)
u.check_equal(observed_losses, expected_losses)
def rotations1_gradient_test():
# https://www.wolframcloud.com/objects/ff6ecaf0-fccd-44e3-b26f-970d8fc2a57c
tf.reset_default_graph()
X0 = np.genfromtxt('data/large_rotations1_X0.csv', delimiter=",")
Y0 = np.genfromtxt('data/large_rotations1_Y0.csv', delimiter=",")
W0f = v2c_np(np.genfromtxt('data/large_rotations1_W0f.csv', delimiter=","))
fs = np.genfromtxt('data/large_rotations1_fs.csv',
delimiter=",").astype(np.int32)
n = len(fs) - 2 # number of layers
def f(i):
return fs[i + 1] # W[i] has shape f[i] x f[i-1]
dsize = X0.shape[1]
assert f(-1) == dsize
# load W0f and do shape checks (can remove)
W0s = u.unflatten_np(W0f,
fs[1:]) # Wf doesn't have first layer (data matrix)
W0s.insert(0, X0)
Wf_holder = tf.placeholder(dtype, shape=W0f.shape)
Wf = tf.Variable(Wf_holder, name="Wf")
Wf_copy = tf.Variable(Wf_holder, name="Wf_copy")
init_dict = {Wf_holder: W0f}
# Create W's
W = u.unflatten(Wf, fs[1:])
X = tf.constant(X0)
Y = tf.constant(Y0)
W.insert(0, X)
for (numpy_W, tf_W) in zip(W0s, W):
u.check_equal(numpy_W.shape, u.fix_shape(tf_W.shape))
# Create A's
# A[1] == X
A = [0] * (n + 2)
A[0] = u.Identity(dsize)
for i in range(n + 1):
A[i + 1] = tf.matmul(W[i], A[i], name="A" + str(i + 1))
assert W[0].get_shape() == X0.shape
assert A[n + 1].get_shape() == X0.shape
assert A[1].get_shape() == X0.shape
err = Y - A[n + 1]
loss = tf.reduce_sum(tf.square(err)) / (2 * dsize)
lr0 = np.genfromtxt('data/large_rotations1_gradient_lr.csv')
lr = tf.Variable(lr0, dtype=dtype)
# Create B's
B = [0] * (n + 1)
B[n] = -err / dsize
for i in range(n - 1, -1, -1):
B[i] = t(W[i + 1]) @ B[i + 1]
# create dW's
dW = [0] * (n + 1)
for i in range(n + 1):
dW[i] = tf.matmul(B[i], tf.transpose(A[i]), name="dW" + str(i))
del dW[0] # get rid of W[0] update
dWf = tf.concat([u.vec(dWi) for dWi in dW], axis=0)
Wf_new = Wf - lr * dWf
train_op1 = Wf_copy.assign(Wf_new)
train_op2 = Wf.assign(Wf_copy)
sess = tf.Session()
sess.run(tf.global_variables_initializer(), feed_dict=init_dict)
expected_losses = np.loadtxt("data/large_rotations1_gradient_losses.csv",
delimiter=",")
observed_losses = []
# from accompanying notebook
# {0.102522, 0.028124, 0.00907214, 0.00418929, 0.00293379,
for i in range(10):
observed_losses.append(sess.run([loss])[0])
sess.run(train_op1)
sess.run(train_op2)
u.check_equal(observed_losses, expected_losses)
def main():
np.random.seed(0)
tf.set_random_seed(0)
dtype = np.float32
train_images = u.get_mnist_images()
dsize = 10000
patches = train_images[:, :dsize].astype(dtype)
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
W0_0 = u.ng_init(fs[2], fs[3])
W1_0 = u.ng_init(fs[3], fs[2])
W0f = u.flatten([W0_0.flatten(), W1_0.flatten()])
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: u.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")
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):
return tf.sigmoid(x)
def d_sigmoid(y):
return y * (1 - y)
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)
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]
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_op = A[i] @ t(A[i]) / dsize + lambda_ * u.Identity(A[i].shape[0])
cov_A[i] = init_var(cov_op, "cov_A%d" % (i, ))
cov_op = B2[i] @ t(B2[i]) / dsize + lambda_ * u.Identity(
B2[i].shape[0])
cov_B2[i] = init_var(cov_op, "cov_B2%d" % (i, ))
vars_svd_A[i] = u.SvdWrapper(cov_A[i],
"svd_A_%d" % (i, ),
do_inverses=True)
vars_svd_B2[i] = u.SvdWrapper(cov_B2[i],
"svd_B2_%d" % (i, ),
do_inverses=True)
whitened_A = vars_svd_A[i].inv @ A[i]
whitened_B = vars_svd_B2[i].inv @ B[i]
pre_dW[i] = (whitened_B @ t(whitened_A)) / dsize
dW[i] = (B[i] @ t(A[i])) / dsize
# Loss function
reconstruction = u.L2(err) / (2 * dsize)
loss = reconstruction
grad_live = u.flatten(dW[1:])
pre_grad_live = u.flatten(pre_dW[1:]) # fisher preconditioned gradient
grad = init_var(grad_live, "grad")
pre_grad = init_var(pre_grad_live, "pre_grad")
update_params_op = Wf.assign(Wf - lr * pre_grad).op
save_params_op = Wf_copy.assign(Wf).op
pre_grad_dot_grad = tf.reduce_sum(pre_grad * grad)
grad_norm = tf.reduce_sum(grad * grad)
pre_grad_norm = u.L2(pre_grad)
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])
u.dump(s0, "A_%d_%d" % (i, step))
A0 = A[i].eval()
At0 = v0.T @ A0
u.dump(A0 @ A0.T, "Acov_%d_%d" % (i, step))
u.dump(At0 @ At0.T, "Atcov_%d_%d" % (i, step))
u.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])
u.dump(s0, "B2_%d_%d" % (i, step))
B0 = B[i].eval()
Bt0 = v0.T @ B0
u.dump(B0 @ B0.T, "Bcov_%d_%d" % (i, step))
u.dump(Bt0 @ Bt0.T, "Btcov_%d_%d" % (i, step))
u.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():
vars_svd_A[2].update()
vars_svd_B2[2].update()
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()
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.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 = []
# 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
vars_svd_A[1].update()
for step in range(40):
update_covariances()
update_svds()
sess.run(grad.initializer)
sess.run(pre_grad.initializer)
lr0, loss0 = sess.run([lr, loss])
update_params_op.run()
advance_batch()
losses.append(loss0)
step_lengths.append(lr0)
print("Step %d loss %.2f" % (step, loss0))
u.record_time()
assert losses[-1] < 0.59
assert losses[-1] > 0.57
assert 20e-3 < min(
u.global_time_list) < 50e-3, "Time should be 40ms on 1080"
u.summarize_time()
print("Test passed")
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] = VarInfo(var_setter, var_p)
return var
lr = init_var(0.2, "lr")
Wf = init_var(W0f, "Wf", True)
Wf_copy = init_var(W0f, "Wf_copy", True)
W = u.unflatten(Wf, fs[1:]) # todo: get rid of this because transposes
X = init_var(X0, "X")
W.insert(0, X)
def sigmoid(x):
return tf.sigmoid(x)
def d_sigmoid(y):
return y * (1 - y)
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
def rotations2_newton_bd():
# override kr with no-shape-inferring version
def kr(A, B):
return u.kronecker(A, B, do_shape_inference=False)
tf.reset_default_graph()
X0 = np.genfromtxt('data/large_rotations2_X0.csv', delimiter=",")
Y0 = np.genfromtxt('data/large_rotations2_Y0.csv', delimiter=",")
W0f = v2c_np(np.genfromtxt('data/large_rotations2_W0f.csv', delimiter=","))
fs = np.genfromtxt('data/large_rotations2_fs.csv',
delimiter=",").astype(np.int32)
n = len(fs) - 2 # number of layers
def f(i):
return fs[i + 1] # W[i] has shape f[i] x f[i-1]
dsize = X0.shape[1]
assert f(-1) == dsize
# load W0f and do shape checks (can remove)
W0s = u.unflatten_np(W0f,
fs[1:]) # Wf doesn't have first layer (data matrix)
W0s.insert(0, X0)
Wf_holder = tf.placeholder(dtype, shape=W0f.shape)
Wf = tf.Variable(Wf_holder, name="Wf")
Wf_copy = tf.Variable(Wf_holder, name="Wf_copy")
init_dict = {Wf_holder: W0f}
# Create W's
W = u.unflatten(Wf, fs[1:])
X = tf.constant(X0)
Y = tf.constant(Y0)
W.insert(0, X)
for (numpy_W, tf_W) in zip(W0s, W):
u.check_equal(numpy_W.shape, u.fix_shape(tf_W.shape))
# Create A's
# A[1] == X
A = [0] * (n + 2)
A[0] = u.Identity(dsize)
for i in range(n + 1):
A[i + 1] = tf.matmul(W[i], A[i], name="A" + str(i + 1))
assert W[0].get_shape() == X0.shape
assert A[n + 1].get_shape() == X0.shape
assert A[1].get_shape() == X0.shape
err = Y - A[n + 1]
loss = tf.reduce_sum(tf.square(err)) / (2 * dsize)
lr = tf.Variable(0.1, dtype=dtype, name="learning_rate")
# Create B's
B = [0] * (n + 1)
B[n] = -err / dsize
Bn = [0] * (n + 1) # Newton-modified backprop
Bn[n] = u.Identity(f(n))
for i in range(n - 1, -1, -1):
B[i] = t(W[i + 1]) @ B[i + 1]
Bn[i] = t(W[i + 1]) @ Bn[i + 1]
# Create U's
U = [list(range(n + 1)) for _ in range(n + 1)]
for bottom in range(n + 1):
for top in range(n + 1):
if bottom > top:
prod = u.Identity(f(top))
else:
prod = u.Identity(f(bottom - 1))
for i in range(bottom, top + 1):
prod = prod @ t(W[i])
U[bottom][top] = prod
# Block i, j gives hessian block between layer i and layer j
blocks = [list(range(n + 1)) for _ in range(n + 1)]
for i in range(1, n + 1):
for j in range(1, n + 1):
term1 = kr(A[i] @ t(A[j]), Bn[i] @ t(Bn[j])) / dsize
if i == j:
term2 = tf.zeros((f(i) * f(i - 1), f(i) * f(i - 1)),
dtype=dtype)
elif i < j:
term2 = kr(A[i] @ t(B[j]), U[i + 1][j - 1])
else:
term2 = kr(t(U[j + 1][i - 1]), B[i] @ t(A[j]))
blocks[i][j] = term1 + term2 @ Kmat(f(j), f(j - 1))
# remove leftmost blocks (those are with respect to W[0] which is input)
del blocks[0]
for row in blocks:
del row[0]
ihess = u.concat_blocks(u.block_diagonal_inverse(blocks))
sess = tf.Session()
sess.run(tf.global_variables_initializer(), feed_dict=init_dict)
# create dW's
dW = [0] * (n + 1)
for i in range(n + 1):
dW[i] = tf.matmul(B[i], tf.transpose(A[i]), name="dW" + str(i))
del dW[0] # get rid of W[0] update
dWf = tf.concat([u.vec(dWi) for dWi in dW], axis=0)
Wf_new = Wf - lr * ihess @ dWf
train_op1 = Wf_copy.assign(Wf_new)
train_op2 = Wf.assign(Wf_copy)
observed_losses = []
u.reset_time()
for i in range(20):
loss0 = sess.run([loss])[0]
print(loss0)
observed_losses.append(loss0)
sess.run(train_op1)
sess.run(train_op2)
u.record_time()
u.summarize_time()
u.summarize_graph()
def loss_and_output_and_grad(Wf):
"""Returns cost, gradient for current parameter vector."""
global fs, X, global_cov_A, global_whitened_A
W = u.unflatten(Wf, fs[1:]) # perftodo: this creates transposes
W.insert(0, X)
A = [None] * (n + 2)
A[1] = W[0]
for i in range(1, n + 1):
A[i + 1] = nonlin(W[i] @ A[i])
# print(A[i+1])
# # print(A[i+1])
err = (A[n + 1] - A[1])
B = [None] * (n + 1)
B2 = [None] * (n + 1)
B[n] = err * d_nonlin(A[n + 1])
# sampled_labels = tf.random_normal((f(n), f(-1)), dtype=dtype, seed=0)
# print('random')
# print(np.random.randn(*X.shape).astype(dtype))
noise = tf.constant(np.random.randn(*err.shape).astype(dtype))
# print(noise)
B2[n] = noise * d_nonlin(A[n + 1])
# print("B2[n]", B2[n])
# print(B[n])
for i in range(n - 1, -1, -1):
backprop = t(W[i + 1]) @ B[i + 1]
backprop2 = t(W[i + 1]) @ B2[i + 1]
B[i] = backprop * d_nonlin(A[i + 1])
B2[i] = backprop2 * d_nonlin(A[i + 1])
dW = [None] * (n + 1)
pre_dW = [None] * (n + 1) # preconditioned dW
cov_A = [None] * (n + 1) # covariance of activations[i]
whitened_A = [None] * (n + 1) # covariance of activations[i]
cov_B2 = [None] * (n + 1) # covariance of synthetic backprops[i]
cov_B = [None] * (n + 1) # covariance of synthetic backprops[i]
vars_svd_A = [None] * (n + 1)
vars_svd_B2 = [None] * (n + 1)
if global_cov_A is None:
global_cov_A = A[1] @ t(A[1]) / dsize
global_whitened_A = regularized_inverse(global_cov_A) @ A[1]
cov_A[1] = global_cov_A
whitened_A[1] = global_whitened_A
for i in range(1, n + 1):
if i > 1:
cov_A[i] = A[i] @ t(A[i]) / dsize
whitened_A[i] = regularized_inverse(cov_A[i]) @ A[i]
cov_B2[i] = B2[i] @ t(B2[i]) / dsize
cov_B[i] = B[i] @ t(B[i]) / dsize
if SYNTHETIC_LABELS:
whitened_B = regularized_inverse(cov_B2[i]) @ B[i]
else:
whitened_B = regularized_inverse(cov_B[i]) @ B[i]
#regularized_inverse(cov_B[i])
# print("A", i, cov_A[i], regularized_inverse(cov_A[i]))
# print("B", i, cov_B[i], regularized_inverse(cov_B[i]))
# pre_dW[i] = (whitened_B @ t(whitened_A[i]))/dsize
# print(i, 'A', A[i].numpy())
# print(regularized_inverse(cov_A[i]).numpy())
pre_dW[i] = (whitened_B @ t(whitened_A[i])) / dsize
dW[i] = (B[i] @ t(A[i])) / dsize
loss = u.L2(err) / 2 / dsize
grad = u.flatten(dW[1:])
kfac_grad = u.flatten(pre_dW[1:])
return loss, A[n + 1], grad, kfac_grad
def rotations2_natural_empirical():
tf.reset_default_graph()
# override kr with no-shape-inferring version
def kr(A, B):
return u.kronecker(A, B, do_shape_inference=False)
X0 = np.genfromtxt('data/large_rotations2_X0.csv', delimiter=",")
Y0 = np.genfromtxt('data/large_rotations2_Y0.csv', delimiter=",")
W0f = v2c_np(np.genfromtxt('data/large_rotations2_W0f.csv', delimiter=","))
fs = np.genfromtxt('data/large_rotations2_fs.csv',
delimiter=",").astype(np.int32)
n = len(fs) - 2 # number of layers
def f(i):
return fs[i + 1] # W[i] has shape f[i] x f[i-1]
dsize = X0.shape[1]
assert f(-1) == dsize
# load W0f and do shape checks (can remove)
W0s = u.unflatten_np(W0f,
fs[1:]) # Wf doesn't have first layer (data matrix)
W0s.insert(0, X0)
Wf_holder = tf.placeholder(dtype, shape=W0f.shape)
Wf = tf.Variable(Wf_holder, name="Wf")
Wf_copy = tf.Variable(Wf_holder, name="Wf_copy")
init_dict = {Wf_holder: W0f}
# Create W's
# initialize data + layers
# W[0] is input matrix (X), W[n] is last matrix
# A[1] has activations for W[1], equal to W[0]=X
# A[n+1] has predictions
# Create W's
W = u.unflatten(Wf, fs[1:])
X = tf.constant(X0)
Y = tf.constant(Y0)
W.insert(0, X)
A = [0] * (n + 2)
A[0] = u.Identity(dsize)
for i in range(n + 1):
# fs is off by 2 from common notation, ie W[0] has shape f[0],f[-1]
A[i + 1] = tf.matmul(W[i], A[i], name="A" + str(i + 1))
# input dimensions match
assert W[0].get_shape() == X0.shape
# output dimensions match
assert W[-1].get_shape()[0], W[0].get_shape()[1] == Y0.shape
assert A[n + 1].get_shape() == Y0.shape
err = Y - A[n + 1]
loss = tf.reduce_sum(tf.square(err)) / (2 * dsize)
lr = tf.Variable(0.000001, dtype=dtype)
# create backprop matrices
# B[i] has backprop for matrix i
B = [0] * (n + 1)
B[n] = -err / dsize
for i in range(n - 1, -1, -1):
B[i] = tf.matmul(tf.transpose(W[i + 1]), B[i + 1], name="B" + str(i))
# Create gradient update. Make copy of variables and split update into
# two run calls. Using single set of variables will gives updates that
# occasionally produce wrong results/NaN's because of data race
dW = [0] * (n + 1)
updates1 = [0] * (n + 1) # compute updated value into Wcopy
updates2 = [0] * (n + 1) # copy value back into W
Wcopy = [0] * (n + 1)
for i in range(n + 1):
Wi_name = "Wcopy" + str(i)
Wi_shape = (fs[i + 1], fs[i])
Wi_init = tf.zeros(dtype=dtype, shape=Wi_shape, name=Wi_name + "_init")
Wcopy[i] = tf.Variable(Wi_init, name=Wi_name, trainable=False)
dW[i] = tf.matmul(B[i], tf.transpose(A[i]), name="dW" + str(i))
del dW[0] # get rid of W[0] update
# construct flattened gradient update vector
dWf = tf.concat([vec(grad) for grad in dW], axis=0)
# inverse fisher preconditioner
grads = tf.concat([u.khatri_rao(A[i], B[i]) for i in range(1, n + 1)],
axis=0)
fisher = grads @ tf.transpose(grads) / dsize
ifisher = u.pseudo_inverse(fisher)
Wf_copy = tf.Variable(tf.zeros(dtype=dtype,
shape=Wf.shape,
name="Wf_copy_init"),
name="Wf_copy")
new_val_matrix = Wf - lr * (ifisher @ dWf)
train_op1 = Wf_copy.assign(new_val_matrix)
train_op2 = Wf.assign(Wf_copy)
sess = tf.Session()
sess.run(tf.global_variables_initializer(), feed_dict=init_dict)
observed_losses = []
u.reset_time()
for i in range(10):
loss0 = sess.run(loss)
print(loss0)
observed_losses.append(loss0)
sess.run(train_op1)
sess.run(train_op2)
u.record_time()
u.summarize_time()
u.summarize_graph()
def rotations2_newton_kfac():
tf.reset_default_graph()
# override kr with no-shape-inferring version
def kr(A, B):
return u.kronecker(A, B, do_shape_inference=False)
X0 = np.genfromtxt('data/large_rotations2_X0.csv', delimiter=",")
Y0 = np.genfromtxt('data/large_rotations2_Y0.csv', delimiter=",")
W0f = v2c_np(np.genfromtxt('data/large_rotations2_W0f.csv', delimiter=","))
fs = np.genfromtxt('data/large_rotations2_fs.csv',
delimiter=",").astype(np.int32)
n = len(fs) - 2 # number of layers
def f(i):
return fs[i + 1] # W[i] has shape f[i] x f[i-1]
dsize = X0.shape[1]
assert f(-1) == dsize
def f(i):
return fs[i + 1] # W[i] has shape f[i] x f[i-1]
dsize = X0.shape[1]
assert f(-1) == dsize
# load W0f and do shape checks (can remove)
W0s = u.unflatten_np(W0f,
fs[1:]) # Wf doesn't have first layer (data matrix)
W0s.insert(0, X0)
Wf_holder = tf.placeholder(dtype, shape=W0f.shape)
Wf = tf.Variable(Wf_holder, name="Wf")
Wf_copy = tf.Variable(Wf_holder, name="Wf_copy")
init_dict = {Wf_holder: W0f}
# Create W's
W = u.unflatten(Wf, fs[1:])
X = tf.constant(X0)
Y = tf.constant(Y0)
W.insert(0, X)
for (numpy_W, tf_W) in zip(W0s, W):
u.check_equal(numpy_W.shape, u.fix_shape(tf_W.shape))
# Create A's
# A[1] == X
A = [0] * (n + 2)
A[0] = u.Identity(dsize)
for i in range(n + 1):
A[i + 1] = tf.matmul(W[i], A[i], name="A" + str(i + 1))
assert W[0].get_shape() == X0.shape
assert A[n + 1].get_shape() == X0.shape
assert A[1].get_shape() == X0.shape
err = Y - A[n + 1]
loss = tf.reduce_sum(tf.square(err)) / (2 * dsize)
lr = tf.Variable(0.1, dtype=dtype, name="learning_rate")
# Create B's
B = [0] * (n + 1)
B[n] = -err / dsize
Bn = [0] * (n + 1) # Newton-modified backprop
Bn[n] = u.Identity(f(n))
for i in range(n - 1, -1, -1):
B[i] = t(W[i + 1]) @ B[i + 1]
Bn[i] = t(W[i + 1]) @ Bn[i + 1]
# inverse Hessian blocks
iblocks = u.empty_grid(n + 1, n + 1)
for i in range(1, n + 1):
for j in range(1, n + 1):
# reuse Hess tensor calculation in order to get off-diag block sizes
dummy_term = kr(A[i] @ t(A[j]), Bn[i] @ t(Bn[j])) / dsize
if i == j:
acov = A[i] @ t(A[j])
bcov = (Bn[i] @ t(Bn[j])) / dsize
term = kr(u.pseudo_inverse(acov), u.pseudo_inverse(bcov))
else:
term = tf.zeros(shape=dummy_term.get_shape(), dtype=dtype)
iblocks[i][j] = term
# remove leftmost blocks (those are with respect to W[0] which is input)
del iblocks[0]
for row in iblocks:
del row[0]
ihess = u.concat_blocks(iblocks)
sess = tf.Session()
sess.run(tf.global_variables_initializer(), feed_dict=init_dict)
# create dW's
dW = [0] * (n + 1)
for i in range(n + 1):
dW[i] = tf.matmul(B[i], tf.transpose(A[i]), name="dW" + str(i))
del dW[0] # get rid of W[0] update
dWf = tf.concat([u.vec(dWi) for dWi in dW], axis=0)
Wf_new = Wf - lr * ihess @ dWf
train_op1 = Wf_copy.assign(Wf_new)
train_op2 = Wf.assign(Wf_copy)
observed_losses = []
elapsed_times = []
u.reset_time()
for i in range(10):
loss0 = sess.run([loss])[0]
print(loss0)
observed_losses.append(loss0)
sess.run(train_op1)
sess.run(train_op2)
u.record_time()
u.summarize_time()
u.summarize_graph()
dsize = f(-1)
n = len(fs) - 2
init_dict = {}
def init_var(val, name, trainable=False):
val = np.array(val)
holder = tf.placeholder(dtype, shape=val.shape, name=name + "_holder")
var = tf.Variable(holder, name=name + "_var", trainable=trainable)
init_dict[holder] = val
return var
lr = init_var(0.1, "lr")
Wf = init_var(W0f, "Wf", True)
Wf_copy = init_var(W0f, "Wf_copy")
W = u.unflatten(Wf, fs[1:])
X = init_var(X0, "X")
W.insert(0, X)
def sigmoid(x):
return tf.sigmoid(x)
def d_sigmoid(y):
return y * (1 - y)
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
def f(i): return fs[i+1] # W[i] has shape f[i] x f[i-1]
dsize = X0.shape[1]
assert f(-1) == dsize
# load W0f and do shape checks (can remove)
W0s = u.unflatten_np(W0f, fs[1:]) # Wf doesn't have first layer (data matrix)
W0s.insert(0, X0)
Wf_holder = tf.placeholder(dtype, shape=W0f.shape)
Wf = tf.Variable(Wf_holder, name="Wf")
Wf_copy = tf.Variable(Wf_holder, name="Wf_copy")
init_dict = {Wf_holder: W0f}
# Create W's
W = u.unflatten(Wf, fs[1:])
X = tf.constant(X0)
Y = tf.constant(Y0)
W.insert(0, X)
for (numpy_W, tf_W) in zip(W0s, W):
u.check_equal(numpy_W.shape, u.fix_shape(tf_W.shape))
# Create A's
# A[1] == X
A = [0]*(n+2)
A[0] = u.Identity(dsize)
for i in range(n+1):
A[i+1] = tf.matmul(W[i], A[i], name="A"+str(i+1))
assert W[0].get_shape() == X0.shape
assert A[n+1].get_shape() == X0.shape
def cost_and_grad(W0f=None,
fs=None,
lambda_=3e-3,
rho=0.1,
beta=3,
X0=None,
lr=0.1):
"""Construct sparse autoencoder loss and gradient.
Args:
W0f: initial value of weights (flattened representation)
fs: list of sizes [dsize, visible, hidden, visible]
sparsity_param: global feature sparsity target
beta: weight on sparsity penalty
X0: value of X (aka W[0])
Returns:
cost, train_step
"""
np.random.seed(0)
tf.set_random_seed(0)
dtype = np.float32
if not fs:
fs = [dsize, 28 * 28, 196, 28 * 28]
if not W0f:
W0f = W_uniform(fs[2], fs[3])
rho = tf.constant(rho, dtype=dtype)
def f(i):
return fs[i + 1] # W[i] has shape f[i] x f[i-1]
dsize = f(-1)
n = len(fs) - 2
init_dict = {}
def init_var(val, name, trainable=True):
holder = tf.placeholder(dtype, shape=val.shape, name=name + "_holder")
var = tf.Variable(holder, name=name + "_var", trainable=trainable)
init_dict[holder] = val
return var
Wf = init_var(W0f, "Wf")
Wf_copy = init_var(W0f, "Wf_copy")
W = u.unflatten(Wf, fs[1:])
X = init_var(X0, "X", False)
W.insert(0, X)
def sigmoid(x):
return tf.sigmoid(x)
def d_sigmoid(y):
return y * (1 - y)
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] = 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]
B = [None] * (n + 1)
B[n] = err * d_sigmoid(A[n + 1])
for i in range(n - 1, -1, -1):
backprop = t(W[i + 1]) @ B[i + 1]
if i == 1:
backprop += beta * d_kl(rho, rho_hat)
B[i] = backprop * d_sigmoid(A[i + 1])
# dW[i] = gradient of W[i]
dW = [None] * (n + 1)
for i in range(n + 1):
dW[i] = (B[i] @ t(A[i])) / dsize
# Cost 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]))
cost = reconstruction + sparsity + L2
grad = u.flatten(dW[1:])
copy_op = Wf_copy.assign(Wf - lr * grad)
with tf.control_dependencies([copy_op]):
train_op = Wf.assign(Wf_copy)
sess = tf.InteractiveSession()
sess.run(tf.global_variables_initializer(), feed_dict=init_dict)
return cost, train_op
def flam3_to_node(flame):
n = util.unflatten(util.flatten(apply_structure(flame_structure, flame)))
n['type'] = 'node'
return n
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 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
# TODO: rename into "nonlin"
def sigmoid(x):
if purely_relu:
return tf.nn.relu(x)
elif purely_linear:
return tf.identity(x)
else:
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
train_data_node = tf.placeholder(dtype, shape=(dsize, 28, 28, 1))
eval_data = tf.placeholder(dtype, shape=(eval_batch_size, 28, 28, 1))
W0f = W_uniform(fs[2], fs[3]).astype(dtype)
W0 = u.unflatten(W0f, fs[1:])
X = init_var(X0, "X")
W = [X]
for layer in range(1, n + 1):
W.append(init_var(W0[layer - 1], "W" + str(layer)))
def nonlin(x):
return tf.nn.relu(x)
# return tf.sigmoid(x)
A = [None] * (n + 2)
with tf.control_dependencies([tf.assert_equal(1, 0, message="too huge")]):
A[0] = u.Identity(dsize, dtype=dtype)
A[1] = W[0]
def simple_gradient_test():
tf.reset_default_graph()
X0 = np.genfromtxt('data/rotations_simple_X0.csv',
delimiter= ",")
Y0 = np.genfromtxt('data/rotations_simple_Y0.csv',
delimiter= ",")
W0f = v2c_np(np.genfromtxt('data/rotations_simple_W0f.csv',
delimiter= ","))
assert W0f.shape == (8, 1)
fs = np.genfromtxt('data/rotations_simple_fs.csv',
delimiter= ",").astype(np.int32)
n = len(fs)-2 # number of layers
u.check_equal(fs, [10,2,2,2])
def f(i): return fs[i+1] # W[i] has shape f[i] x f[i-1]
dsize = X0.shape[1]
assert f(-1) == dsize
# load W0f and do shape checks (can remove)
W0s = u.unflatten_np(W0f, fs[1:]) # Wf doesn't have first layer (data matrix)
W0s.insert(0, X0)
Wf_holder = tf.placeholder(dtype, shape=W0f.shape)
Wf = tf.Variable(Wf_holder, name="Wf")
Wf_copy = tf.Variable(Wf_holder, name="Wf_copy")
init_dict = {Wf_holder: W0f}
# Create W's
W = u.unflatten(Wf, fs[1:])
X = tf.constant(X0)
Y = tf.constant(Y0)
W.insert(0, X)
for (numpy_W, tf_W) in zip(W0s, W):
u.check_equal(numpy_W.shape, u.fix_shape(tf_W.shape))
# Create A's
# A[1] == X
A = [0]*(n+2)
A[0] = u.Identity(dsize)
for i in range(n+1):
A[i+1] = tf.matmul(W[i], A[i], name="A"+str(i+1))
assert W[0].get_shape() == X0.shape
assert A[n+1].get_shape() == X0.shape
assert A[1].get_shape() == X0.shape
err = Y - A[n+1]
loss = tf.reduce_sum(tf.square(err))/(2*dsize)
lr = tf.Variable(1.0, dtype=dtype)
# Create B's
B = [0]*(n+1)
B[n] = -err/dsize
for i in range(n-1, -1, -1):
B[i] = t(W[i+1]) @ B[i+1]
# create dW's
dW = [0]*(n+1)
for i in range(n+1):
dW[i] = tf.matmul(B[i], tf.transpose(A[i]), name="dW"+str(i))
del dW[0] # get rid of W[0] update
dWf = tf.concat([u.vec(dWi) for dWi in dW], axis=0)
Wf_new = Wf - lr * dWf
train_op1 = Wf_copy.assign(Wf_new)
train_op2 = Wf.assign(Wf_copy)
sess = tf.Session()
sess.run(tf.global_variables_initializer(), feed_dict=init_dict)
expected_losses = np.loadtxt("data/rotations_simple_gradient_losses.csv",
delimiter= ",")
observed_losses = []
# from accompanying notebook
# {0.0111498, 0.00694816, 0.00429464, 0.00248228, 0.00159361,
# 0.000957424, 0.000651653, 0.000423802, 0.000306749, 0.00021772,
for i in range(20):
observed_losses.append(sess.run([loss])[0])
sess.run(train_op1)
sess.run(train_op2)
u.check_equal(observed_losses, expected_losses)
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")
