def correct(self, grad):
"""Accepts IndexedGrad object, produces corrected version."""
s = self
vars_ = []
grads_new = []
assert list(grad) == self.model.trainable_vars
dsize = get_batch_size(grad)
for var in grad:
vars_.append(var)
A = s.extract_A(grad, var) # extract activations
B = s.extract_B(grad, var)*dsize # extract backprops
if s.needs_correction(var):
# correct the gradient. Assume op is left matmul
A_svd = s[var].A.svd
B2_svd = s[var].B2.svd
if inverse_method == 'pseudo_inverse':
A_new = u.pseudo_inverse2(A_svd) @ A
B_new = u.pseudo_inverse2(B2_svd) @ B
elif inverse_method == 'inverse':
A_new = A_svd.inv @ A
B_new = B2_svd.inv @ B
else:
assert False
dW_new = (B_new @ t(A_new)) / dsize
grads_new.append(dW_new)
else:
dW = B@t(A)/dsize
grads_new.append(dW)
return IndexedGrad(grads=grads_new, vars_=vars_)
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()
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]))
# TODO: add tiling for natural sampling
cov_A = [None] * (n + 1)
cov_B2 = [None] * (n + 1)
vars_svd_A = [None] * (n + 1)
vars_svd_B2 = [None] * (n + 1)
# eps=1e-5 gives same behavior on mnist (converge in 17 steps)
eps_to_use = 1e-7
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] = SvdWrapper(cov_A[i], "svd_A_%d" % (i, ))
vars_svd_B2[i] = SvdWrapper(cov_B2[i], "svd_B2_%d" % (i, ))
whitened_A = u.regularized_inverse(cov_A[i]) @ A[i]
whitened_A = u.pseudo_inverse_sqrt2(vars_svd_A[i],
eps=eps_to_use) @ A[i]
whitened_A = u.pseudo_inverse2(vars_svd_A[i], eps=eps_to_use) @ A[i]
#whitened_A = u.pseudo_inverse_scipy(cov_A[i]) @ A[i]
# raise epsilon because b's get weird
# whitened_B2 = u.pseudo_inverse_scipy(cov_B2[i]) @ B[i]
whitened_B2 = u.pseudo_inverse_scipy(cov_B2[i]) @ B[i]
whitened_B2 = u.regularized_inverse(cov_B2[i]) @ B[i]
whitened_B2 = u.pseudo_inverse_sqrt2(vars_svd_B2[i],
eps=eps_to_use) @ B[i]
whitened_B2 = u.pseudo_inverse2(vars_svd_B2[i], eps=eps_to_use) @ B[i]
pre_dW[i] = (whitened_B2 @ t(whitened_A)) / 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]))
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 kfac_optimizer(model_creator):
stats_batch_size = 10000
main_batch_size = 10000
stats_model, loss, labels = model_creator(stats_batch_size)
# replace labels_node with synthetic labels
main_model, _, _ = model_creator(main_batch_size)
opt = tf.GradientDescentOptimizer(0.2)
grads_and_vars = opt.compute_gradients(loss)
trainable_vars = tf.trainable_variables()
# create SVD and preconditioning variables for matmul vars
for var in trainable_vars:
if var not in matmul_registry:
continue
dW = u.extract_grad(grads_and_vars, var)
A[var] = get_activations(var)
B[var] = get_backprops(var)
B2[var] = get_backprops2(var) # get backprops with synthetic labels
dW[var] = B[var] @ t(A[var]) # todo: sort out dsize division
cov_A[var] = init_var(A[var] @ t(A[var]) / dsize,
"cov_A_%s" % (var.name, ))
cov_B2[var] = init_var(B2[var] @ t(B2[var]) / dsize,
"cov_B2_%s" % (var.name, ))
vars_svd_A[var] = SvdWrapper(cov_A[var], "svd_A_%d" % (var.name, ))
vars_svd_B2[var] = SvdWrapper(cov_B2[var], "svd_B2_%d" % (var.name, ))
whitened_A = u.pseudo_inverse2(vars_svd_A[var]) @ A[var]
whitened_B2 = u.pseudo_inverse2(vars_svd_B2[var]) @ B[var]
whitened_A_stable = u.pseudo_inverse_sqrt2(vars_svd_A[var]) @ A[var]
whitened_B2_stable = u.pseudo_inverse_sqrt2(vars_svd_B2[var]) @ B[var]
pre_dW[var] = (whitened_B2 @ t(whitened_A)) / dsize
pre_dW_stable[var] = (
whitened_B2_stable @ t(whitened_A_stable)) / dsize
dW[var] = (B[var] @ t(A[var])) / dsize
# create update params ops
# new_grads_and_vars = []
# for grad, var in grads_and_vars:
# if var in kfac_registry:
# pre_A, pre_B = kfac_registry[var]
# new_grad_live = pre_B @ grad @ t(pre_A)
# new_grads_and_vars.append((new_grad, var))
# print("Preconditioning %s"%(var.name))
# else:
# new_grads_and_vars.append((grad, var))
# train_op = opt.apply_gradients(new_grads_and_vars)
# Each variable has an associated gradient, pre_gradient, variable save op
def update_grad():
ops = [grad_update_ops[var] for var in trainable_vars]
sess.run(ops)
def update_pre_grad():
ops = [pre_grad_update_ops[var] for var in trainable_vars]
sess.run(ops)
def update_pre_grad2():
ops = [pre_grad2_update_ops[var] for var in trainable_vars]
sess.run(ops)
def save_params():
ops = [var_save_ops[var] for var in trainable_vars]
sess.run(ops)
for step in range(num_steps):
update_covariances()
if step % whitened_every_n_steps == 0:
update_svds()
update_grad()
update_pre_grad() # perf todo: update one of these
update_pre_grad2() # stable alternative
lr0, loss0 = sess.run([lr, loss])
save_params()
# when grad norm<1, Fisher is unstable, switch to Sqrt(Fisher)
# TODO: switch to per-matrix normalization
stabilized_mode = grad_norm.eval() < 1
if stabilized_mode:
update_params2()
else:
update_params()
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
actual_delta = loss1 - loss0
actual_slope = actual_delta / lr0
slope_ratio = actual_slope / target_slope # between 0 and 1.01
losses.append(loss0)
step_lengths.append(lr0)
ratios.append(slope_ratio)
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()))
u.record_time()
def model_creator(batch_size, name='defaultmodel', dtype=np.float32):
"""Create MNIST autoencoder model. Dataset is part of model."""
model = Model(name)
init_dict = {}
global_vars = []
local_vars = []
# TODO: factor out to reuse between scripts
# TODO: change feed_dict logic to reuse value provided to VarStruct
# current situation makes reinitialization of global variable change
# it's value, counterinituitive
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]
test_patches = train_images[:, -batch_size:]
assert dsize < 25000
fs = [
batch_size, 28 * 28, 1024, 1024, 1024, 196, 1024, 1024, 1024, 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]
for i in range(1, n + 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]
# create test error eval
layer = init_var(test_patches, "X_test", is_global=False)
for i in range(1, n + 1):
layer = nonlin(W[i] @ layer)
verr = (layer - test_patches)
model.vloss = u.L2(verr) / (2 * batch_size)
# 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
# TODO: refactor this to take initial values out of Var struct
#global_init_op = tf.group(*[v.initializer for v in global_vars])
global_init_ops = [v.initializer for v in global_vars]
global_init_op = tf.group(*[v.initializer for v in global_vars])
global_init_query_op = [
tf.logical_not(tf.is_variable_initialized(v)) for v in global_vars
]
def initialize_global_vars(verbose=False, reinitialize=False):
"""If reinitialize is false, will not reinitialize variables already
initialized."""
sess = tf.get_default_session()
if not reinitialize:
uninited = sess.run(global_init_query_op)
# use numpy boolean indexing to select list of initializers to run
to_initialize = list(np.asarray(global_init_ops)[uninited])
else:
to_initialize = global_init_ops
if verbose:
print("Initializing following:")
for v in to_initialize:
print(" " + v.name)
sess.run(to_initialize, 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
return model
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")
def model_creator(batch_size, name="default", dtype=np.float32):
"""Create MNIST autoencoder model. Dataset is part of model."""
model = Model(name)
def get_batch_size(data):
if isinstance(data, IndexedGrad):
return int(data.live[0].shape[1])
else:
return int(data.shape[1])
init_dict = {}
global_vars = []
local_vars = []
# TODO: factor out to reuse between scripts
# TODO: change feed_dict logic to reuse value provided to VarStruct
# current situation makes reinitialization of global variable change
# it's value, counterinituitive
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)
patches = train_images[:,:args.batch_size];
test_patches = test_images[:,:args.batch_size];
if args.dataset == 'cifar':
input_dim = 3*32*32
elif args.dataset == 'mnist':
input_dim = 28*28
else:
assert False
fs = [args.batch_size, input_dim, 1024, 1024, 1024, 196, 1024, 1024, 1024,
input_dim]
def f(i): return fs[i+1] # W[i] has shape f[i] x f[i-1]
n = len(fs) - 2
# Full dataset from which new batches are sampled
X_full = init_var(train_images, "X_full", is_global=True)
X = init_var(patches, "X", is_global=False) # stores local batch per model
W = [None]*n
W.insert(0, X)
A = [None]*(n+2)
A[1] = W[0]
for i in range(1, n+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]
model.loss = u.L2(err) / (2 * get_batch_size(err))
# create test error eval
layer0 = init_var(test_patches, "X_test", is_global=True)
layer = layer0
for i in range(1, n+1):
layer = nonlin(W[i] @ layer)
verr = (layer - layer0)
model.vloss = u.L2(verr) / (2 * get_batch_size(verr))
# 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 args.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
# todo: decouple initial value from covariance update
# maybe need start with identity and do running average
for i in range(1,n+1):
if regularized_svd:
cov_A[i] = init_var(A[i]@t(A[i])/args.batch_size+args.Lambda*u.Identity(f(i-1)), "cov_A%d"%(i,))
cov_B2[i] = init_var(B2[i]@t(B2[i])/args.batch_size+args.Lambda*u.Identity(f(i)), "cov_B2%d"%(i,))
else:
cov_A[i] = init_var(A[i]@t(A[i])/args.batch_size, "cov_A%d"%(i,))
cov_B2[i] = init_var(B2[i]@t(B2[i])/args.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=args.Lambda) @ A[i]
whitened_B2 = u.regularized_inverse3(vars_svd_B2[i],L=args.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]))/args.batch_size
dW2[i] = B[i] @ t(A[i])
pre_dW[i] = (whitened_B2 @ t(whitened_A))/args.batch_size
sampled_labels_live = A[n+1] + tf.random_normal((f(n), f(-1)),
dtype=dtype, seed=0)
if args.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 * args.batch_size)
model.global_vars = global_vars
model.local_vars = local_vars
model.trainable_vars = W[1:]
# todo, we have 3 places where model step is tracked, reduce
model.step = init_var(u.as_int32(0), "step", is_global=False)
advance_step_op = model.step.assign_add(1)
assert get_batch_size(X_full) % args.batch_size == 0
batches_per_dataset = (get_batch_size(X_full) // args.batch_size)
batch_idx = tf.mod(model.step, batches_per_dataset)
start_idx = batch_idx * args.batch_size
advance_batch_op = X.assign(X_full[:,start_idx:start_idx + args.batch_size])
def advance_batch():
print("Step for model(%s) is %s"%(model.name, u.eval(model.step)))
sess = u.get_default_session()
# TODO: get rid of _sampled_labels
sessrun([sampled_labels.initializer, _sampled_labels.initializer])
if args.advance_batch:
with u.timeit("advance_batch"):
sessrun(advance_batch_op)
sessrun(advance_step_op)
model.advance_batch = advance_batch
# TODO: refactor this to take initial values out of Var struct
#global_init_op = tf.group(*[v.initializer for v in global_vars])
global_init_ops = [v.initializer for v in global_vars]
global_init_op = tf.group(*[v.initializer for v in global_vars])
global_init_query_ops = [tf.logical_not(tf.is_variable_initialized(v))
for v in global_vars]
def initialize_global_vars(verbose=False, reinitialize=False):
"""If reinitialize is false, will not reinitialize variables already
initialized."""
sess = u.get_default_session()
if not reinitialize:
uninited = sessrun(global_init_query_ops)
# use numpy boolean indexing to select list of initializers to run
to_initialize = list(np.asarray(global_init_ops)[uninited])
else:
to_initialize = global_init_ops
if verbose:
print("Initializing following:")
for v in to_initialize:
print(" " + v.name)
sessrun(to_initialize, feed_dict=init_dict)
model.initialize_global_vars = initialize_global_vars
# didn't quite work (can't initialize var in same run call as deps likely)
# enforce that batch is initialized before everything
# except fake labels opa
# for v in local_vars:
# if v != X and v != sampled_labels and v != _sampled_labels:
# print("Adding dep %s on %s"%(v.initializer.name, X.initializer.name))
# u.add_dep(v.initializer, on_op=X.initializer)
local_init_op = tf.group(*[v.initializer for v in local_vars],
name="%s_localinit"%(model.name))
print("Local vars:")
for v in local_vars:
print(v.name)
def initialize_local_vars():
sess = u.get_default_session()
sessrun(_sampled_labels.initializer, feed_dict=init_dict)
sessrun(X.initializer, feed_dict=init_dict)
sessrun(local_init_op, feed_dict=init_dict)
model.initialize_local_vars = initialize_local_vars
return model
