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 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()
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_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()