def test_kfac_jacobian_mnist():
u.seed_random(1)
data_width = 3
d = [data_width**2, 8, 10]
model: u.SimpleMLP = u.SimpleMLP(d, nonlin=False)
autograd_lib.register(model)
batch_size = 4
stats_steps = 2
n = batch_size * stats_steps
dataset = u.TinyMNIST(dataset_size=n,
data_width=data_width,
original_targets=True)
trainloader = torch.utils.data.DataLoader(dataset,
batch_size=batch_size,
shuffle=False)
train_iter = iter(trainloader)
loss_fn = torch.nn.CrossEntropyLoss()
activations = {}
jacobians = defaultdict(lambda: AttrDefault(float))
total_data = []
# sum up statistics over n examples
for train_step in range(stats_steps):
data, targets = next(train_iter)
total_data.append(data)
activations = {}
def save_activations(layer, A, _):
activations[layer] = A
jacobians[layer].AA += torch.einsum("ni,nj->ij", A, A)
with autograd_lib.module_hook(save_activations):
output = model(data)
loss = loss_fn(output, targets)
def compute_jacobian(layer, _, B):
A = activations[layer]
jacobians[layer].BB += torch.einsum("ni,nj->ij", B, B)
jacobians[layer].diag += torch.einsum("ni,nj->ij", B * B, A * A)
with autograd_lib.module_hook(compute_jacobian):
autograd_lib.backward_jacobian(output)
for layer in model.layers:
jacobian0 = jacobians[layer]
jacobian_full = torch.einsum('kl,ij->kilj', jacobian0.BB / n,
jacobian0.AA / n)
jacobian_diag = jacobian0.diag / n
J = u.jacobian(model(torch.cat(total_data)), layer.weight)
J_autograd = torch.einsum('noij,nokl->ijkl', J, J) / n
u.check_equal(jacobian_full, J_autograd)
u.check_equal(jacobian_diag, torch.einsum('ikik->ik', J_autograd))
def test_diagonal_hessian():
u.seed_random(1)
A, model = create_toy_model()
activations = {}
def save_activations(layer, a, _):
if layer != model.layers[0]:
return
activations[layer] = a
with autograd_lib.module_hook(save_activations):
Y = model(A.t())
loss = torch.sum(Y * Y) / 2
hess = [0]
def compute_hess(layer, _, B):
if layer != model.layers[0]:
return
A = activations[layer]
hess[0] += torch.einsum("ni,nj->ij", B * B, A * A).reshape(-1)
with autograd_lib.module_hook(compute_hess):
autograd_lib.backprop_identity(Y, retain_graph=True)
# check against autograd
hess0 = u.hessian(loss, model.layers[0].weight).reshape([4, 4])
u.check_equal(hess[0], torch.diag(hess0))
# check against manual solution
u.check_equal(hess[0], [425., 225., 680., 360.])
def test_gradient_norms():
"""Per-example gradient norms."""
u.seed_random(1)
A, model = create_toy_model()
activations = {}
def save_activations(layer, a, _):
if layer != model.layers[0]:
return
activations[layer] = a
with autograd_lib.module_hook(save_activations):
Y = model(A.t())
loss = torch.sum(Y * Y) / 2
norms = {}
def compute_norms(layer, _, b):
if layer != model.layers[0]:
return
a = activations[layer]
del activations[layer] # release memory kept by activations
norms[layer] = (a * a).sum(dim=1) * (b * b).sum(dim=1)
with autograd_lib.module_hook(compute_norms):
loss.backward()
u.check_equal(norms[model.layers[0]], [3493250, 9708800])
def test_full_hessian_xent_mnist_multilayer():
"""Test regular and diagonal hessian computation."""
u.seed_random(1)
data_width = 3
batch_size = 2
d = [data_width**2, 6, 10]
o = d[-1]
n = batch_size
train_steps = 1
model: u.SimpleModel = u.SimpleFullyConnected2(d, nonlin=False, bias=True)
autograd_lib.register(model)
dataset = u.TinyMNIST(dataset_size=batch_size,
data_width=data_width,
original_targets=True)
trainloader = torch.utils.data.DataLoader(dataset,
batch_size=batch_size,
shuffle=False)
train_iter = iter(trainloader)
loss_fn = torch.nn.CrossEntropyLoss()
hess = defaultdict(float)
hess_diag = defaultdict(float)
for train_step in range(train_steps):
data, targets = next(train_iter)
activations = {}
def save_activations(layer, a, _):
activations[layer] = a
with autograd_lib.module_hook(save_activations):
output = model(data)
loss = loss_fn(output, targets)
def compute_hess(layer, _, B):
A = activations[layer]
BA = torch.einsum("nl,ni->nli", B, A)
hess[layer] += torch.einsum('nli,nkj->likj', BA, BA)
hess_diag[layer] += torch.einsum("ni,nj->ij", B * B, A * A)
with autograd_lib.module_hook(compute_hess):
autograd_lib.backward_hessian(output,
loss='CrossEntropy',
retain_graph=True)
# compute Hessian through autograd
H_autograd = u.hessian(loss, model.layers[0].weight)
u.check_close(hess[model.layers[0]] / batch_size, H_autograd)
diag_autograd = torch.einsum('lili->li', H_autograd)
u.check_close(diag_autograd, hess_diag[model.layers[0]] / batch_size)
H_autograd = u.hessian(loss, model.layers[1].weight)
u.check_close(hess[model.layers[1]] / batch_size, H_autograd)
diag_autograd = torch.einsum('lili->li', H_autograd)
u.check_close(diag_autograd, hess_diag[model.layers[1]] / batch_size)
def test_kfac_fisher_mnist():
u.seed_random(1)
data_width = 3
d = [data_width**2, 8, 10]
model: u.SimpleMLP = u.SimpleMLP(d, nonlin=False)
autograd_lib.register(model)
batch_size = 4
stats_steps = 2
n = batch_size * stats_steps
dataset = u.TinyMNIST(dataset_size=n,
data_width=data_width,
original_targets=True)
trainloader = torch.utils.data.DataLoader(dataset,
batch_size=batch_size,
shuffle=False)
train_iter = iter(trainloader)
loss_fn = torch.nn.CrossEntropyLoss()
activations = {}
fishers = defaultdict(lambda: AttrDefault(float))
total_data = []
# sum up statistics over n examples
for train_step in range(stats_steps):
data, targets = next(train_iter)
total_data.append(data)
activations = {}
def save_activations(layer, A, _):
activations[layer] = A
fishers[layer].AA += torch.einsum("ni,nj->ij", A, A)
with autograd_lib.module_hook(save_activations):
output = model(data)
loss = loss_fn(output, targets) * len(
data) # remove data normalization
def compute_fisher(layer, _, B):
A = activations[layer]
fishers[layer].BB += torch.einsum("ni,nj->ij", B, B)
fishers[layer].diag += torch.einsum("ni,nj->ij", B * B, A * A)
with autograd_lib.module_hook(compute_fisher):
autograd_lib.backward_jacobian(output)
for layer in model.layers:
fisher0 = fishers[layer]
fisher_full = torch.einsum('kl,ij->kilj', fisher0.BB / n,
fisher0.AA / n)
fisher_diag = fisher0.diag / n
u.check_equal(torch.einsum('ikik->ik', fisher_full), fisher_diag)
def test_kron_mnist():
u.seed_random(1)
data_width = 3
batch_size = 3
d = [data_width**2, 10]
o = d[-1]
n = batch_size
train_steps = 1
# torch.set_default_dtype(torch.float64)
model: u.SimpleModel2 = u.SimpleFullyConnected2(d, nonlin=False, bias=True)
autograd_lib.add_hooks(model)
dataset = u.TinyMNIST(dataset_size=batch_size, data_width=data_width, original_targets=True)
trainloader = torch.utils.data.DataLoader(dataset, batch_size=batch_size, shuffle=False)
train_iter = iter(trainloader)
loss_fn = torch.nn.CrossEntropyLoss()
gl.token_count = 0
for train_step in range(train_steps):
data, targets = next(train_iter)
# get gradient values
u.clear_backprops(model)
autograd_lib.enable_hooks()
output = model(data)
autograd_lib.backprop_hess(output, hess_type='CrossEntropy')
i = 0
layer = model.layers[i]
autograd_lib.compute_hess(model, method='kron')
autograd_lib.compute_hess(model)
autograd_lib.disable_hooks()
# direct Hessian computation
H = layer.weight.hess
H_bias = layer.bias.hess
# factored Hessian computation
H2 = layer.weight.hess_factored
H2_bias = layer.bias.hess_factored
H2, H2_bias = u.expand_hess(H2, H2_bias)
# autograd Hessian computation
loss = loss_fn(output, targets) # TODO: change to d[i+1]*d[i]
H_autograd = u.hessian(loss, layer.weight).reshape(d[i] * d[i + 1], d[i] * d[i + 1])
H_bias_autograd = u.hessian(loss, layer.bias)
# compare direct against autograd
u.check_close(H, H_autograd)
u.check_close(H_bias, H_bias_autograd)
approx_error = u.symsqrt_dist(H, H2)
assert approx_error < 1e-2, approx_error
def _test_kfac_hessian_xent_mnist():
u.seed_random(1)
data_width = 3
batch_size = 2
d = [data_width**2, 10]
o = d[-1]
n = batch_size
train_steps = 1
model: u.SimpleModel = u.SimpleFullyConnected2(d, nonlin=False, bias=True)
autograd_lib.register(model)
dataset = u.TinyMNIST(dataset_size=batch_size,
data_width=data_width,
original_targets=True)
trainloader = torch.utils.data.DataLoader(dataset,
batch_size=batch_size,
shuffle=False)
train_iter = iter(trainloader)
loss_fn = torch.nn.CrossEntropyLoss()
activations = {}
hess = defaultdict(lambda: AttrDefault(float))
for train_step in range(train_steps):
data, targets = next(train_iter)
activations = {}
def save_activations(layer, a, _):
activations[layer] = a
with autograd_lib.module_hook(save_activations):
output = model(data)
loss = loss_fn(output, targets)
def compute_hess(layer, _, B):
A = activations[layer]
hess[layer].AA += torch.einsum("ni,nj->ij", A, A)
hess[layer].BB += torch.einsum("ni,nj->ij", B, B)
with autograd_lib.module_hook(compute_hess):
autograd_lib.backward_hessian(output,
loss='CrossEntropy',
retain_graph=True)
hess_factored = hess[model.layers[0]]
hess0 = torch.einsum('kl,ij->kilj', hess_factored.BB / n,
hess_factored.AA / o) # hess for sum loss
hess0 /= n # hess for mean loss
# compute Hessian through autograd
H_autograd = u.hessian(loss, model.layers[0].weight)
rel_error = torch.norm(
(hess0 - H_autograd).flatten()) / torch.norm(H_autograd.flatten())
assert rel_error < 0.01 # 0.0057
def test_full_hessian_xent_kfac2():
"""Test with uneven layers."""
u.seed_random(1)
torch.set_default_dtype(torch.float64)
batch_size = 1
d = [3, 2]
o = d[-1]
n = batch_size
train_steps = 1
model: u.SimpleModel = u.SimpleFullyConnected2(d, nonlin=True, bias=False)
autograd_lib.register(model)
loss_fn = torch.nn.CrossEntropyLoss()
data = u.to_logits(torch.tensor([[0.7, 0.2, 0.1]]))
targets = torch.tensor([0])
data = data.repeat([3, 1])
targets = targets.repeat([3])
n = len(data)
activations = {}
hess = defaultdict(lambda: AttrDefault(float))
for i in range(n):
def save_activations(layer, A, _):
activations[layer] = A
hess[layer].AA += torch.einsum("ni,nj->ij", A, A)
with autograd_lib.module_hook(save_activations):
data_batch = data[i:i + 1]
targets_batch = targets[i:i + 1]
Y = model(data_batch)
o = Y.shape[1]
loss = loss_fn(Y, targets_batch)
def compute_hess(layer, _, B):
hess[layer].BB += torch.einsum("ni,nj->ij", B, B)
with autograd_lib.module_hook(compute_hess):
autograd_lib.backward_hessian(Y, loss='CrossEntropy')
# expand
hess_factored = hess[model.layers[0]]
hess0 = torch.einsum('kl,ij->kilj', hess_factored.BB / n,
hess_factored.AA / o) # hess for sum loss
hess0 /= n # hess for mean loss
# check against autograd
# 0.1459
Y = model(data)
loss = loss_fn(Y, targets)
hess_autograd = u.hessian(loss, model.layers[0].weight)
u.check_equal(hess_autograd, hess0)
def test_kron_1x2_conv():
"""Minimal example of a 1x2 convolution whose Hessian/grad covariance doesn't factor as Kronecker.
Two convolutional layers stacked on top of each other, followed by least squares loss.
Outputs:
0 tensor([[[[0., 1., 1., 1.]]]])
1 tensor([[[[2., 3.]]]])
2 tensor([[[[8.]]]])
Activations/backprops:
layerA 0 tensor([[[[0., 1.],
[1., 1.]]]])
layerB 0 tensor([[[[1., 2.]]]])
layerA 1 tensor([[[[2.],
[3.]]]])
layerB 1 tensor([[[[1.]]]])
layer 0 discrepancy: 0.6597963571548462
layer 1 discrepancy: 0.0
"""
u.seed_random(1)
n, Xh, Xw = 1, 1, 4
Kh, Kw = 1, 2
dd = [1, 1, 1]
o = dd[-1]
model: u.SimpleModel = u.StridedConvolutional2(dd, kernel_size=(Kh, Kw), nonlin=False, bias=True)
data = torch.tensor([0, 1., 1, 1]).reshape((n, dd[0], Xh, Xw))
model.layers[0].bias.data.zero_()
model.layers[0].weight.data.copy_(torch.tensor([1, 2]))
model.layers[1].bias.data.zero_()
model.layers[1].weight.data.copy_(torch.tensor([1, 2]))
sample_output = model(data)
autograd_lib.clear_backprops(model)
autograd_lib.add_hooks(model)
output = model(data)
autograd_lib.backprop_hess(output, hess_type='LeastSquares')
autograd_lib.compute_hess(model, method='kron', attr_name='hess_kron')
autograd_lib.compute_hess(model, method='exact')
autograd_lib.disable_hooks()
for i in range(len(model.layers)):
layer = model.layers[i]
H = layer.weight.hess
Hk = layer.weight.hess_kron
Hk = Hk.expand()
print(u.symsqrt_dist(H, Hk))
def test_kron_nano():
u.seed_random(1)
d = [1, 2]
n = 1
# torch.set_default_dtype(torch.float32)
loss_type = 'CrossEntropy'
model: u.SimpleModel = u.SimpleFullyConnected2(d, nonlin=False, bias=True)
if loss_type == 'LeastSquares':
loss_fn = u.least_squares
elif loss_type == 'DebugLeastSquares':
loss_fn = u.debug_least_squares
else:
loss_fn = nn.CrossEntropyLoss()
data = torch.randn(n, d[0])
data = torch.ones(n, d[0])
if loss_type.endswith('LeastSquares'):
target = torch.randn(n, d[-1])
elif loss_type == 'CrossEntropy':
target = torch.LongTensor(n).random_(0, d[-1])
target = torch.tensor([0])
# Hessian computation, saves regular and Kronecker factored versions into .hess and .hess_factored attributes
autograd_lib.add_hooks(model)
output = model(data)
autograd_lib.backprop_hess(output, hess_type=loss_type)
autograd_lib.compute_hess(model, method='kron')
autograd_lib.compute_hess(model)
autograd_lib.disable_hooks()
for layer in model.layers:
Hk: u.Kron = layer.weight.hess_factored
Hk_bias: u.Kron = layer.bias.hess_factored
Hk, Hk_bias = u.expand_hess(Hk, Hk_bias) # kronecker multiply the factors
# old approach, using direct computation
H2, H_bias2 = layer.weight.hess, layer.bias.hess
# compute Hessian through autograd
model.zero_grad()
output = model(data)
loss = loss_fn(output, target)
H_autograd = u.hessian(loss, layer.weight)
H_bias_autograd = u.hessian(loss, layer.bias)
# compare autograd with direct approach
u.check_close(H2, H_autograd.reshape(Hk.shape))
u.check_close(H_bias2, H_bias_autograd)
# compare factored with direct approach
assert(u.symsqrt_dist(Hk, H2) < 1e-6)
def test_full_hessian_xent_multibatch():
u.seed_random(1)
torch.set_default_dtype(torch.float64)
batch_size = 1
d = [2, 2]
o = d[-1]
n = batch_size
train_steps = 1
model: u.SimpleModel = u.SimpleFullyConnected2(d, nonlin=True, bias=True)
model.layers[0].weight.data.copy_(torch.eye(2))
autograd_lib.register(model)
loss_fn = torch.nn.CrossEntropyLoss()
data = u.to_logits(torch.tensor([[0.7, 0.3]]))
targets = torch.tensor([0])
data = data.repeat([3, 1])
targets = targets.repeat([3])
n = len(data)
activations = {}
hess = defaultdict(float)
def save_activations(layer, a, _):
activations[layer] = a
for i in range(n):
with autograd_lib.module_hook(save_activations):
data_batch = data[i:i + 1]
targets_batch = targets[i:i + 1]
Y = model(data_batch)
loss = loss_fn(Y, targets_batch)
def compute_hess(layer, _, B):
A = activations[layer]
BA = torch.einsum("nl,ni->nli", B, A)
hess[layer] += torch.einsum('nli,nkj->likj', BA, BA)
with autograd_lib.module_hook(compute_hess):
autograd_lib.backward_hessian(Y, loss='CrossEntropy')
# check against autograd
# 0.1459
Y = model(data)
loss = loss_fn(Y, targets)
hess_autograd = u.hessian(loss, model.layers[0].weight)
hess0 = hess[model.layers[0]] / n
u.check_equal(hess_autograd, hess0)
def test_symsqrt():
u.seed_random(1)
torch.set_default_dtype(torch.float32)
mat = torch.reshape(torch.arange(9) + 1, (3, 3)).float() + torch.eye(3) * 5
mat = mat + mat.t() # make symmetric
smat = u.symsqrt(mat)
u.check_close(mat, smat @ smat.t())
u.check_close(mat, smat @ smat)
def randomly_rotate(X):
"""Randomly rotate d,n data matrix X"""
d, n = X.shape
z = torch.randn((d, d), dtype=X.dtype)
q, r = torch.qr(z)
d = torch.diag(r)
ph = d / abs(d)
rot_mat = q * ph
return rot_mat @ X
n = 20
d = 10
X = torch.randn((d, n))
# embed in a larger space
X = torch.cat([X, torch.zeros_like(X)])
X = randomly_rotate(X)
cov = X @ X.t() / n
sqrt, rank = u.symsqrt(cov, return_rank=True)
assert rank == d
assert torch.allclose(sqrt @ sqrt, cov, atol=1e-5)
Y = torch.randn((d, n))
Y = torch.cat([Y, torch.zeros_like(X)])
Y = randomly_rotate(X)
cov = u.Kron(X @ X.t(), Y @ Y.t())
sqrt, rank = cov.symsqrt(return_rank=True)
assert rank == d * d
u.check_close(sqrt @ sqrt, cov, rtol=1e-4)
X = torch.tensor([[7., 0, 0, 0, 0]]).t()
X = randomly_rotate(X)
cov = X @ X.t()
u.check_close(u.sym_l2_norm(cov), 7 * 7)
Y = torch.tensor([[8., 0, 0, 0, 0]]).t()
Y = randomly_rotate(Y)
cov = u.Kron(X @ X.t(), Y @ Y.t())
u.check_close(cov.sym_l2_norm(), 7 * 7 * 8 * 8)
def test_factored_vs_regular():
"""Take simple network, compute values in two different ways, compare."""
u.seed_random(1)
gl.project_name = 'test'
gl.logdir_base = '/tmp/runs'
u.setup_logdir_and_event_writer(run_name=sys._getframe().f_code.co_name)
d = 3
n = 3
model: u.SimpleFullyConnected2 = u.SimpleFullyConnected2([d, d],
bias=False,
nonlin=False)
param = model.layers[0].weight
# param.data.copy_(torch.eye(d))
#param.data.copy_(torch.arange(9).reshape(3, 3))
# param.data.copy_(torch.zeros(d, d))
# create simple matrix which is not quite symmetric
source = 2 * torch.eye(d)
source[0, 0] = 3
source[0, 1] = 4
source[1, 0] = -2
data = source.repeat([n, 1])
noise = source.repeat_interleave(n, dim=0)
autograd_lib.add_hooks(model)
output = model(data)
output.backward(retain_graph=True, gradient=noise)
loss = u.least_squares(output)
autograd_lib.backprop_hess(output, hess_type='LeastSquares', model=model)
autograd_lib.compute_grad1(model)
autograd_lib.compute_hess(model)
autograd_lib.compute_hess(model, method='kron', attr_name='hess2')
autograd_lib.compute_stats(model,
attr_name='stats_regular',
sigma_centering=True)
autograd_lib.compute_stats_factored(model,
attr_name='stats_factored',
sigma_centering=False)
stats = param.stats_regular
stats_factored = param.stats_factored
for name in stats:
print(name, stats[name], stats_factored[name])
def test_cross_entropy_hessian_mnist():
u.seed_random(1)
data_width = 3
batch_size = 2
d = [data_width**2, 10]
o = d[-1]
n = batch_size
train_steps = 1
model: u.SimpleModel = u.SimpleFullyConnected(d, nonlin=False, bias=True)
dataset = u.TinyMNIST(dataset_size=batch_size, data_width=data_width, original_targets=True)
trainloader = torch.utils.data.DataLoader(dataset, batch_size=batch_size, shuffle=False)
train_iter = iter(trainloader)
loss_fn = torch.nn.CrossEntropyLoss()
loss_hessian = u.HessianExactCrossEntropyLoss()
gl.token_count = 0
for train_step in range(train_steps):
data, targets = next(train_iter)
# get gradient values
u.clear_backprops(model)
model.skip_forward_hooks = False
model.skip_backward_hooks = False
output = model(data)
for bval in loss_hessian(output):
output.backward(bval, retain_graph=True)
i = 0
layer = model.layers[i]
H, Hbias = u.hessian_from_backprops(layer.activations,
layer.backprops_list,
bias=True)
model.skip_forward_hooks = True
model.skip_backward_hooks = True
# compute Hessian through autograd
model.zero_grad()
output = model(data)
loss = loss_fn(output, targets)
H_autograd = u.hessian(loss, layer.weight).reshape(d[i] * d[i + 1], d[i] * d[i + 1])
u.check_close(H, H_autograd)
Hbias_autograd = u.hessian(loss, layer.bias)
u.check_close(Hbias, Hbias_autograd)
def test_cross_entropy_hessian_tiny():
u.seed_random(1)
batch_size = 1
d = [2, 2]
o = d[-1]
n = batch_size
train_steps = 1
model: u.SimpleModel = u.SimpleFullyConnected(d, nonlin=True, bias=True)
model.layers[0].weight.data.copy_(torch.eye(2))
loss_fn = torch.nn.CrossEntropyLoss()
loss_hessian = u.HessianExactCrossEntropyLoss()
data = u.to_logits(torch.tensor([[0.7, 0.3]]))
targets = torch.tensor([0])
# get gradient values
u.clear_backprops(model)
model.skip_forward_hooks = False
model.skip_backward_hooks = False
output = model(data)
for bval in loss_hessian(output):
output.backward(bval, retain_graph=True)
i = 0
layer = model.layers[i]
H, Hbias = u.hessian_from_backprops(layer.activations,
layer.backprops_list,
bias=True)
model.skip_forward_hooks = True
model.skip_backward_hooks = True
# compute Hessian through autograd
model.zero_grad()
output = model(data)
loss = loss_fn(output, targets)
H_autograd = u.hessian(loss, layer.weight)
u.check_close(H, H_autograd.reshape(d[i] * d[i + 1], d[i] * d[i + 1]))
Hbias_autograd = u.hessian(loss, layer.bias)
u.check_close(Hbias, Hbias_autograd)
def test_autoencoder_newton():
"""Use Newton's method to train autoencoder."""
image_size = 3
batch_size = 64
dataset = u.TinyMNIST(data_width=image_size, targets_width=image_size,
dataset_size=batch_size)
trainloader = torch.utils.data.DataLoader(dataset, batch_size=batch_size, shuffle=False)
d = image_size ** 2 # hidden layer size
u.seed_random(1)
model: u.SimpleModel = u.SimpleFullyConnected([d, d])
model.disable_hooks()
optimizer = optim.SGD(model.parameters(), lr=0.1, momentum=0.9)
def loss_fn(data, targets):
err = data - targets.view(-1, data.shape[1])
assert len(data) == batch_size
return torch.sum(err * err) / 2 / len(data)
for i in range(10):
data, targets = next(iter(trainloader))
optimizer.zero_grad()
loss = loss_fn(model(data), targets)
if i > 0:
assert loss < 1e-9
loss.backward()
W = model.layers[0].weight
grad = u.tvec(W.grad)
loss = loss_fn(model(data), targets)
H = u.hessian(loss, W)
# for col-major: H = H.transpose(0, 1).transpose(2, 3).reshape(d**2, d**2)
H = H.reshape(d ** 2, d ** 2)
# For col-major: W1 = u.unvec(u.vec(W) - u.pinv(H) @ grad, d)
# W1 = u.untvec(u.tvec(W) - grad @ u.pinv(H), d)
W1 = u.untvec(u.tvec(W) - grad @ H.pinverse(), d)
W.data.copy_(W1)
def test_full_fisher_multibatch():
torch.set_default_dtype(torch.float64)
u.seed_random(1)
A, model = create_toy_model()
activations = {}
def save_activations(layer, a, _):
if layer != model.layers[0]:
return
activations[layer] = a
fisher = [0]
def compute_fisher(layer, _, B):
if layer != model.layers[0]:
return
A = activations[layer]
n = A.shape[0]
di = A.shape[1]
do = B.shape[1]
Jo = torch.einsum("ni,nj->nij", B, A).reshape(n, -1)
fisher[0] += torch.einsum('ni,nj->ij', Jo, Jo)
for x in A.t():
with autograd_lib.module_hook(save_activations):
y = model(x)
loss = torch.sum(y * y) / 2
with autograd_lib.module_hook(compute_fisher):
loss.backward()
# result computed using single step forward prop
result0 = torch.tensor(
[[5.383625e+06, -3.675000e+03, 4.846250e+06, -6.195000e+04],
[-3.675000e+03, 1.102500e+04, -6.195000e+04, 1.858500e+05],
[4.846250e+06, -6.195000e+04, 4.674500e+06, -1.044300e+06],
[-6.195000e+04, 1.858500e+05, -1.044300e+06, 3.132900e+06]])
u.check_close(fisher[0], result0)
def test_full_fisher():
u.seed_random(1)
A, model = create_toy_model()
activations = {}
def save_activations(layer, a, _):
if layer != model.layers[0]:
return
activations[layer] = a
with autograd_lib.module_hook(save_activations):
Y = model(A.t())
loss = torch.sum(Y * Y) / 2
fisher = [0]
def compute_fisher(layer, _, B):
if layer != model.layers[0]:
return
A = activations[layer]
n = A.shape[0]
di = A.shape[1]
do = B.shape[1]
Jo = torch.einsum("ni,nj->nij", B, A).reshape(n, -1)
fisher[0] += torch.einsum('ni,nj->ij', Jo, Jo)
with autograd_lib.module_hook(compute_fisher):
loss.backward()
result0 = torch.tensor(
[[5.383625e+06, -3.675000e+03, 4.846250e+06, -6.195000e+04],
[-3.675000e+03, 1.102500e+04, -6.195000e+04, 1.858500e+05],
[4.846250e+06, -6.195000e+04, 4.674500e+06, -1.044300e+06],
[-6.195000e+04, 1.858500e+05, -1.044300e+06, 3.132900e+06]])
u.check_close(fisher[0], result0)
def test_full_hessian():
u.seed_random(1)
A, model = create_toy_model()
data = A.t()
# data = data.repeat(3, 1)
activations = {}
hess = defaultdict(float)
def save_activations(layer, a, _):
activations[layer] = a
with autograd_lib.module_hook(save_activations):
Y = model(A.t())
loss = torch.sum(Y * Y) / 2
def compute_hess(layer, _, B):
A = activations[layer]
n = A.shape[0]
di = A.shape[1]
do = B.shape[1]
BA = torch.einsum("nl,ni->nli", B, A)
hess[layer] += torch.einsum('nli,nkj->likj', BA, BA)
with autograd_lib.module_hook(compute_hess):
autograd_lib.backprop_identity(Y, retain_graph=True)
# check against autograd
hess_autograd = u.hessian(loss, model.layers[0].weight)
hess0 = hess[model.layers[0]]
u.check_equal(hess_autograd, hess0)
# check against manual solution
u.check_equal(hess0.reshape(4, 4),
[[425, -75, 170, -30], [-75, 225, -30, 90],
[170, -30, 680, -120], [-30, 90, -120, 360]])
def test_autoencoder_minimize():
"""Minimize autoencoder for a few steps."""
u.seed_random(1)
torch.set_default_dtype(torch.float32)
data_width = 4
targets_width = 2
batch_size = 64
dataset = u.TinyMNIST(data_width=data_width, targets_width=targets_width,
dataset_size=batch_size)
trainloader = torch.utils.data.DataLoader(dataset, batch_size=batch_size, shuffle=False)
d1 = data_width ** 2
d2 = 10
d3 = targets_width ** 2
model: u.SimpleModel = u.SimpleFullyConnected([d1, d2, d3], nonlin=True)
model.disable_hooks()
optimizer = optim.SGD(model.parameters(), lr=0.1, momentum=0.9)
def loss_fn(data, targets):
err = data - targets.view(-1, data.shape[1])
assert len(data) == batch_size
return torch.sum(err * err) / 2 / len(data)
loss = 0
for i in range(10):
data, targets = next(iter(trainloader))
optimizer.zero_grad()
loss = loss_fn(model(data), targets)
if i == 0:
assert loss > 0.054
pass
loss.backward()
optimizer.step()
assert loss < 0.0398
def test_main():
parser = argparse.ArgumentParser(description='PyTorch MNIST Example')
parser.add_argument('--test-batch-size',
type=int,
default=1000,
metavar='N',
help='input batch size for testing (default: 1000)')
parser.add_argument('--epochs',
type=int,
default=10,
metavar='N',
help='number of epochs to train (default: 10)')
parser.add_argument('--lr',
type=float,
default=0.01,
metavar='LR',
help='learning rate (default: 0.01)')
parser.add_argument('--momentum',
type=float,
default=0.5,
metavar='M',
help='SGD momentum (default: 0.5)')
parser.add_argument('--no-cuda',
action='store_true',
default=False,
help='disables CUDA training')
parser.add_argument('--seed',
type=int,
default=1,
metavar='S',
help='random seed (default: 1)')
parser.add_argument(
'--log-interval',
type=int,
default=10,
metavar='N',
help='how many batches to wait before logging training status')
parser.add_argument('--save-model',
action='store_true',
default=False,
help='For Saving the current Model')
parser.add_argument('--wandb',
type=int,
default=1,
help='log to weights and biases')
parser.add_argument('--autograd_check',
type=int,
default=0,
help='autograd correctness checks')
parser.add_argument('--logdir',
type=str,
default='/temp/runs/curv_train_tiny/run')
parser.add_argument('--train_batch_size', type=int, default=100)
parser.add_argument('--stats_batch_size', type=int, default=60000)
parser.add_argument('--dataset_size', type=int, default=60000)
parser.add_argument('--train_steps',
type=int,
default=100,
help="this many train steps between stat collection")
parser.add_argument('--stats_steps',
type=int,
default=1000000,
help="total number of curvature stats collections")
parser.add_argument('--nonlin',
type=int,
default=1,
help="whether to add ReLU nonlinearity between layers")
parser.add_argument('--method',
type=str,
choices=['gradient', 'newton'],
default='gradient',
help="descent method, newton or gradient")
parser.add_argument('--layer',
type=int,
default=-1,
help="restrict updates to this layer")
parser.add_argument('--data_width', type=int, default=28)
parser.add_argument('--targets_width', type=int, default=28)
parser.add_argument('--lmb', type=float, default=1e-3)
parser.add_argument(
'--hess_samples',
type=int,
default=1,
help='number of samples when sub-sampling outputs, 0 for exact hessian'
)
parser.add_argument('--hess_kfac',
type=int,
default=0,
help='whether to use KFAC approximation for hessian')
parser.add_argument('--compute_rho',
type=int,
default=1,
help='use expensive method to compute rho')
parser.add_argument('--skip_stats',
type=int,
default=0,
help='skip all stats collection')
parser.add_argument('--full_batch',
type=int,
default=0,
help='do stats on the whole dataset')
parser.add_argument('--weight_decay', type=float, default=1e-4)
#args = parser.parse_args()
args = AttrDict()
args.lmb = 1e-3
args.compute_rho = 1
args.weight_decay = 1e-4
args.method = 'gradient'
args.logdir = '/tmp'
args.data_width = 2
args.targets_width = 2
args.train_batch_size = 10
args.full_batch = False
args.skip_stats = False
args.autograd_check = False
u.seed_random(1)
logdir = u.create_local_logdir(args.logdir)
run_name = os.path.basename(logdir)
#gl.event_writer = SummaryWriter(logdir)
gl.event_writer = u.NoOp()
# print(f"Logging to {run_name}")
# small values for debugging
# loss_type = 'LeastSquares'
loss_type = 'CrossEntropy'
args.wandb = 0
args.stats_steps = 10
args.train_steps = 10
args.stats_batch_size = 10
args.data_width = 2
args.targets_width = 2
args.nonlin = False
d1 = args.data_width**2
d2 = 2
d3 = args.targets_width**2
d1 = args.data_width**2
assert args.data_width == args.targets_width
o = d1
n = args.stats_batch_size
d = [d1, 30, 30, 30, 20, 30, 30, 30, d1]
if loss_type == 'CrossEntropy':
d3 = 10
o = d3
n = args.stats_batch_size
d = [d1, d2, d3]
dsize = max(args.train_batch_size, args.stats_batch_size) + 1
model = u.SimpleFullyConnected2(d, bias=True, nonlin=args.nonlin)
model = model.to(gl.device)
try:
# os.environ['WANDB_SILENT'] = 'true'
if args.wandb:
wandb.init(project='curv_train_tiny', name=run_name)
wandb.tensorboard.patch(tensorboardX=False)
wandb.config['train_batch'] = args.train_batch_size
wandb.config['stats_batch'] = args.stats_batch_size
wandb.config['method'] = args.method
wandb.config['n'] = n
except Exception as e:
print(f"wandb crash with {e}")
# optimizer = torch.optim.SGD(model.parameters(), lr=0.03, momentum=0.9)
optimizer = torch.optim.Adam(
model.parameters(), lr=0.03) # make 10x smaller for least-squares loss
dataset = u.TinyMNIST(data_width=args.data_width,
targets_width=args.targets_width,
dataset_size=dsize,
original_targets=True)
train_loader = torch.utils.data.DataLoader(
dataset,
batch_size=args.train_batch_size,
shuffle=False,
drop_last=True)
train_iter = u.infinite_iter(train_loader)
stats_iter = None
if not args.full_batch:
stats_loader = torch.utils.data.DataLoader(
dataset,
batch_size=args.stats_batch_size,
shuffle=False,
drop_last=True)
stats_iter = u.infinite_iter(stats_loader)
test_dataset = u.TinyMNIST(data_width=args.data_width,
targets_width=args.targets_width,
train=False,
dataset_size=dsize,
original_targets=True)
test_loader = torch.utils.data.DataLoader(test_dataset,
batch_size=args.train_batch_size,
shuffle=False,
drop_last=True)
test_iter = u.infinite_iter(test_loader)
if loss_type == 'LeastSquares':
loss_fn = u.least_squares
elif loss_type == 'CrossEntropy':
loss_fn = nn.CrossEntropyLoss()
autograd_lib.add_hooks(model)
gl.token_count = 0
last_outer = 0
val_losses = []
for step in range(args.stats_steps):
if last_outer:
u.log_scalars(
{"time/outer": 1000 * (time.perf_counter() - last_outer)})
last_outer = time.perf_counter()
with u.timeit("val_loss"):
test_data, test_targets = next(test_iter)
test_output = model(test_data)
val_loss = loss_fn(test_output, test_targets)
# print("val_loss", val_loss.item())
val_losses.append(val_loss.item())
u.log_scalar(val_loss=val_loss.item())
# compute stats
if args.full_batch:
data, targets = dataset.data, dataset.targets
else:
data, targets = next(stats_iter)
# Capture Hessian and gradient stats
autograd_lib.enable_hooks()
autograd_lib.clear_backprops(model)
autograd_lib.clear_hess_backprops(model)
with u.timeit("backprop_g"):
output = model(data)
loss = loss_fn(output, targets)
loss.backward(retain_graph=True)
with u.timeit("backprop_H"):
autograd_lib.backprop_hess(output, hess_type=loss_type)
autograd_lib.disable_hooks() # TODO(y): use remove_hooks
with u.timeit("compute_grad1"):
autograd_lib.compute_grad1(model)
with u.timeit("compute_hess"):
autograd_lib.compute_hess(model)
for (i, layer) in enumerate(model.layers):
# input/output layers are unreasonably expensive if not using Kronecker factoring
if d[i] > 50 or d[i + 1] > 50:
print(
f'layer {i} is too big ({d[i], d[i + 1]}), skipping stats')
continue
if args.skip_stats:
continue
s = AttrDefault(str, {}) # dictionary-like object for layer stats
#############################
# Gradient stats
#############################
A_t = layer.activations
assert A_t.shape == (n, d[i])
# add factor of n because backprop takes loss averaged over batch, while we need per-example loss
B_t = layer.backprops_list[0] * n
assert B_t.shape == (n, d[i + 1])
with u.timeit(f"khatri_g-{i}"):
G = u.khatri_rao_t(B_t, A_t) # batch loss Jacobian
assert G.shape == (n, d[i] * d[i + 1])
g = G.sum(dim=0, keepdim=True) / n # average gradient
assert g.shape == (1, d[i] * d[i + 1])
u.check_equal(G.reshape(layer.weight.grad1.shape),
layer.weight.grad1)
if args.autograd_check:
u.check_close(B_t.t() @ A_t / n, layer.weight.saved_grad)
u.check_close(g.reshape(d[i + 1], d[i]),
layer.weight.saved_grad)
s.sparsity = torch.sum(layer.output <= 0) / layer.output.numel(
) # proportion of activations that are zero
s.mean_activation = torch.mean(A_t)
s.mean_backprop = torch.mean(B_t)
# empirical Fisher
with u.timeit(f'sigma-{i}'):
efisher = G.t() @ G / n
sigma = efisher - g.t() @ g
s.sigma_l2 = u.sym_l2_norm(sigma)
s.sigma_erank = torch.trace(sigma) / s.sigma_l2
lambda_regularizer = args.lmb * torch.eye(d[i + 1] * d[i]).to(
gl.device)
H = layer.weight.hess
with u.timeit(f"invH-{i}"):
invH = torch.cholesky_inverse(H + lambda_regularizer)
with u.timeit(f"H_l2-{i}"):
s.H_l2 = u.sym_l2_norm(H)
s.iH_l2 = u.sym_l2_norm(invH)
with u.timeit(f"norms-{i}"):
s.H_fro = H.flatten().norm()
s.iH_fro = invH.flatten().norm()
s.grad_fro = g.flatten().norm()
s.param_fro = layer.weight.data.flatten().norm()
u.nan_check(H)
if args.autograd_check:
model.zero_grad()
output = model(data)
loss = loss_fn(output, targets)
H_autograd = u.hessian(loss, layer.weight)
H_autograd = H_autograd.reshape(d[i] * d[i + 1],
d[i] * d[i + 1])
u.check_close(H, H_autograd)
# u.dump(sigma, f'/tmp/sigmas/H-{step}-{i}')
def loss_direction(dd: torch.Tensor, eps):
"""loss improvement if we take step eps in direction dd"""
return u.to_python_scalar(eps * (dd @ g.t()) -
0.5 * eps**2 * dd @ H @ dd.t())
def curv_direction(dd: torch.Tensor):
"""Curvature in direction dd"""
return u.to_python_scalar(dd @ H @ dd.t() /
(dd.flatten().norm()**2))
with u.timeit(f"pinvH-{i}"):
pinvH = H.pinverse()
with u.timeit(f'curv-{i}'):
s.grad_curv = curv_direction(g)
ndir = g @ pinvH # newton direction
s.newton_curv = curv_direction(ndir)
setattr(layer.weight, 'pre',
pinvH) # save Newton preconditioner
s.step_openai = s.grad_fro**2 / s.grad_curv if s.grad_curv else 999
s.step_max = 2 / s.H_l2
s.step_min = torch.tensor(2) / torch.trace(H)
s.newton_fro = ndir.flatten().norm(
) # frobenius norm of Newton update
s.regret_newton = u.to_python_scalar(
g @ pinvH @ g.t() / 2) # replace with "quadratic_form"
s.regret_gradient = loss_direction(g, s.step_openai)
with u.timeit(f'rho-{i}'):
p_sigma = u.lyapunov_spectral(H, sigma)
discrepancy = torch.max(abs(p_sigma - p_sigma.t()) / p_sigma)
s.psigma_erank = u.sym_erank(p_sigma)
s.rho = H.shape[0] / s.psigma_erank
with u.timeit(f"batch-{i}"):
s.batch_openai = torch.trace(H @ sigma) / (g @ H @ g.t())
s.diversity = torch.norm(G, "fro")**2 / torch.norm(g)**2 / n
# Faster approaches for noise variance computation
# s.noise_variance = torch.trace(H.inverse() @ sigma)
# try:
# # this fails with singular sigma
# s.noise_variance = torch.trace(torch.solve(sigma, H)[0])
# # s.noise_variance = torch.trace(torch.lstsq(sigma, H)[0])
# pass
# except RuntimeError as _:
s.noise_variance_pinv = torch.trace(pinvH @ sigma)
s.H_erank = torch.trace(H) / s.H_l2
s.batch_jain_simple = 1 + s.H_erank
s.batch_jain_full = 1 + s.rho * s.H_erank
u.log_scalars(u.nest_stats(layer.name, s))
# gradient steps
with u.timeit('inner'):
for i in range(args.train_steps):
optimizer.zero_grad()
data, targets = next(train_iter)
model.zero_grad()
output = model(data)
loss = loss_fn(output, targets)
loss.backward()
# u.log_scalar(train_loss=loss.item())
if args.method != 'newton':
optimizer.step()
if args.weight_decay:
for group in optimizer.param_groups:
for param in group['params']:
param.data.mul_(1 - args.weight_decay)
else:
for (layer_idx, layer) in enumerate(model.layers):
param: torch.nn.Parameter = layer.weight
param_data: torch.Tensor = param.data
param_data.copy_(param_data - 0.1 * param.grad)
if layer_idx != 1: # only update 1 layer with Newton, unstable otherwise
continue
u.nan_check(layer.weight.pre)
u.nan_check(param.grad.flatten())
u.nan_check(
u.v2r(param.grad.flatten()) @ layer.weight.pre)
param_new_flat = u.v2r(param_data.flatten()) - u.v2r(
param.grad.flatten()) @ layer.weight.pre
u.nan_check(param_new_flat)
param_data.copy_(
param_new_flat.reshape(param_data.shape))
gl.token_count += data.shape[0]
gl.event_writer.close()
assert val_losses[0] > 2.4 # 2.4828238487243652
assert val_losses[-1] < 2.25 # 2.20609712600708
def main():
u.seed_random(1)
logdir = u.create_local_logdir(args.logdir)
run_name = os.path.basename(logdir)
gl.event_writer = SummaryWriter(logdir)
print(f"Logging to {run_name}")
d1 = args.data_width ** 2
assert args.data_width == args.targets_width
o = d1
n = args.stats_batch_size
d = [d1, 30, 30, 30, 20, 30, 30, 30, d1]
# small values for debugging
# loss_type = 'LeastSquares'
loss_type = 'CrossEntropy'
args.wandb = 0
args.stats_steps = 10
args.train_steps = 10
args.stats_batch_size = 10
args.data_width = 2
args.targets_width = 2
args.nonlin = False
d1 = args.data_width ** 2
d2 = 2
d3 = args.targets_width ** 2
if loss_type == 'CrossEntropy':
d3 = 10
o = d3
n = args.stats_batch_size
d = [d1, d2, d3]
dsize = max(args.train_batch_size, args.stats_batch_size)+1
model = u.SimpleFullyConnected2(d, bias=True, nonlin=args.nonlin)
model = model.to(gl.device)
try:
# os.environ['WANDB_SILENT'] = 'true'
if args.wandb:
wandb.init(project='curv_train_tiny', name=run_name)
wandb.tensorboard.patch(tensorboardX=False)
wandb.config['train_batch'] = args.train_batch_size
wandb.config['stats_batch'] = args.stats_batch_size
wandb.config['method'] = args.method
wandb.config['n'] = n
except Exception as e:
print(f"wandb crash with {e}")
#optimizer = torch.optim.SGD(model.parameters(), lr=0.03, momentum=0.9)
optimizer = torch.optim.Adam(model.parameters(), lr=0.03) # make 10x smaller for least-squares loss
dataset = u.TinyMNIST(data_width=args.data_width, targets_width=args.targets_width, dataset_size=dsize, original_targets=True)
train_loader = torch.utils.data.DataLoader(dataset, batch_size=args.train_batch_size, shuffle=False, drop_last=True)
train_iter = u.infinite_iter(train_loader)
stats_iter = None
if not args.full_batch:
stats_loader = torch.utils.data.DataLoader(dataset, batch_size=args.stats_batch_size, shuffle=False, drop_last=True)
stats_iter = u.infinite_iter(stats_loader)
test_dataset = u.TinyMNIST(data_width=args.data_width, targets_width=args.targets_width, train=False, dataset_size=dsize, original_targets=True)
test_loader = torch.utils.data.DataLoader(test_dataset, batch_size=args.train_batch_size, shuffle=False, drop_last=True)
test_iter = u.infinite_iter(test_loader)
if loss_type == 'LeastSquares':
loss_fn = u.least_squares
elif loss_type == 'CrossEntropy':
loss_fn = nn.CrossEntropyLoss()
autograd_lib.add_hooks(model)
gl.token_count = 0
last_outer = 0
val_losses = []
for step in range(args.stats_steps):
if last_outer:
u.log_scalars({"time/outer": 1000*(time.perf_counter() - last_outer)})
last_outer = time.perf_counter()
with u.timeit("val_loss"):
test_data, test_targets = next(test_iter)
test_output = model(test_data)
val_loss = loss_fn(test_output, test_targets)
print("val_loss", val_loss.item())
val_losses.append(val_loss.item())
u.log_scalar(val_loss=val_loss.item())
# compute stats
if args.full_batch:
data, targets = dataset.data, dataset.targets
else:
data, targets = next(stats_iter)
# Capture Hessian and gradient stats
autograd_lib.enable_hooks()
autograd_lib.clear_backprops(model)
autograd_lib.clear_hess_backprops(model)
with u.timeit("backprop_g"):
output = model(data)
loss = loss_fn(output, targets)
loss.backward(retain_graph=True)
with u.timeit("backprop_H"):
autograd_lib.backprop_hess(output, hess_type=loss_type)
autograd_lib.disable_hooks() # TODO(y): use remove_hooks
with u.timeit("compute_grad1"):
autograd_lib.compute_grad1(model)
with u.timeit("compute_hess"):
autograd_lib.compute_hess(model)
for (i, layer) in enumerate(model.layers):
# input/output layers are unreasonably expensive if not using Kronecker factoring
if d[i]>50 or d[i+1]>50:
print(f'layer {i} is too big ({d[i],d[i+1]}), skipping stats')
continue
if args.skip_stats:
continue
s = AttrDefault(str, {}) # dictionary-like object for layer stats
#############################
# Gradient stats
#############################
A_t = layer.activations
assert A_t.shape == (n, d[i])
# add factor of n because backprop takes loss averaged over batch, while we need per-example loss
B_t = layer.backprops_list[0] * n
assert B_t.shape == (n, d[i + 1])
with u.timeit(f"khatri_g-{i}"):
G = u.khatri_rao_t(B_t, A_t) # batch loss Jacobian
assert G.shape == (n, d[i] * d[i + 1])
g = G.sum(dim=0, keepdim=True) / n # average gradient
assert g.shape == (1, d[i] * d[i + 1])
u.check_equal(G.reshape(layer.weight.grad1.shape), layer.weight.grad1)
if args.autograd_check:
u.check_close(B_t.t() @ A_t / n, layer.weight.saved_grad)
u.check_close(g.reshape(d[i + 1], d[i]), layer.weight.saved_grad)
s.sparsity = torch.sum(layer.output <= 0) / layer.output.numel() # proportion of activations that are zero
s.mean_activation = torch.mean(A_t)
s.mean_backprop = torch.mean(B_t)
# empirical Fisher
with u.timeit(f'sigma-{i}'):
efisher = G.t() @ G / n
sigma = efisher - g.t() @ g
s.sigma_l2 = u.sym_l2_norm(sigma)
s.sigma_erank = torch.trace(sigma)/s.sigma_l2
lambda_regularizer = args.lmb * torch.eye(d[i + 1]*d[i]).to(gl.device)
H = layer.weight.hess
with u.timeit(f"invH-{i}"):
invH = torch.cholesky_inverse(H+lambda_regularizer)
with u.timeit(f"H_l2-{i}"):
s.H_l2 = u.sym_l2_norm(H)
s.iH_l2 = u.sym_l2_norm(invH)
with u.timeit(f"norms-{i}"):
s.H_fro = H.flatten().norm()
s.iH_fro = invH.flatten().norm()
s.grad_fro = g.flatten().norm()
s.param_fro = layer.weight.data.flatten().norm()
u.nan_check(H)
if args.autograd_check:
model.zero_grad()
output = model(data)
loss = loss_fn(output, targets)
H_autograd = u.hessian(loss, layer.weight)
H_autograd = H_autograd.reshape(d[i] * d[i + 1], d[i] * d[i + 1])
u.check_close(H, H_autograd)
# u.dump(sigma, f'/tmp/sigmas/H-{step}-{i}')
def loss_direction(dd: torch.Tensor, eps):
"""loss improvement if we take step eps in direction dd"""
return u.to_python_scalar(eps * (dd @ g.t()) - 0.5 * eps ** 2 * dd @ H @ dd.t())
def curv_direction(dd: torch.Tensor):
"""Curvature in direction dd"""
return u.to_python_scalar(dd @ H @ dd.t() / (dd.flatten().norm() ** 2))
with u.timeit(f"pinvH-{i}"):
pinvH = u.pinv(H)
with u.timeit(f'curv-{i}'):
s.grad_curv = curv_direction(g)
ndir = g @ pinvH # newton direction
s.newton_curv = curv_direction(ndir)
setattr(layer.weight, 'pre', pinvH) # save Newton preconditioner
s.step_openai = s.grad_fro**2 / s.grad_curv if s.grad_curv else 999
s.step_max = 2 / s.H_l2
s.step_min = torch.tensor(2) / torch.trace(H)
s.newton_fro = ndir.flatten().norm() # frobenius norm of Newton update
s.regret_newton = u.to_python_scalar(g @ pinvH @ g.t() / 2) # replace with "quadratic_form"
s.regret_gradient = loss_direction(g, s.step_openai)
with u.timeit(f'rho-{i}'):
p_sigma = u.lyapunov_svd(H, sigma)
if u.has_nan(p_sigma) and args.compute_rho: # use expensive method
print('using expensive method')
import pdb; pdb.set_trace()
H0, sigma0 = u.to_numpys(H, sigma)
p_sigma = scipy.linalg.solve_lyapunov(H0, sigma0)
p_sigma = torch.tensor(p_sigma).to(gl.device)
if u.has_nan(p_sigma):
# import pdb; pdb.set_trace()
s.psigma_erank = H.shape[0]
s.rho = 1
else:
s.psigma_erank = u.sym_erank(p_sigma)
s.rho = H.shape[0] / s.psigma_erank
with u.timeit(f"batch-{i}"):
s.batch_openai = torch.trace(H @ sigma) / (g @ H @ g.t())
s.diversity = torch.norm(G, "fro") ** 2 / torch.norm(g) ** 2 / n
# Faster approaches for noise variance computation
# s.noise_variance = torch.trace(H.inverse() @ sigma)
# try:
# # this fails with singular sigma
# s.noise_variance = torch.trace(torch.solve(sigma, H)[0])
# # s.noise_variance = torch.trace(torch.lstsq(sigma, H)[0])
# pass
# except RuntimeError as _:
s.noise_variance_pinv = torch.trace(pinvH @ sigma)
s.H_erank = torch.trace(H) / s.H_l2
s.batch_jain_simple = 1 + s.H_erank
s.batch_jain_full = 1 + s.rho * s.H_erank
u.log_scalars(u.nest_stats(layer.name, s))
# gradient steps
with u.timeit('inner'):
for i in range(args.train_steps):
optimizer.zero_grad()
data, targets = next(train_iter)
model.zero_grad()
output = model(data)
loss = loss_fn(output, targets)
loss.backward()
# u.log_scalar(train_loss=loss.item())
if args.method != 'newton':
optimizer.step()
if args.weight_decay:
for group in optimizer.param_groups:
for param in group['params']:
param.data.mul_(1-args.weight_decay)
else:
for (layer_idx, layer) in enumerate(model.layers):
param: torch.nn.Parameter = layer.weight
param_data: torch.Tensor = param.data
param_data.copy_(param_data - 0.1 * param.grad)
if layer_idx != 1: # only update 1 layer with Newton, unstable otherwise
continue
u.nan_check(layer.weight.pre)
u.nan_check(param.grad.flatten())
u.nan_check(u.v2r(param.grad.flatten()) @ layer.weight.pre)
param_new_flat = u.v2r(param_data.flatten()) - u.v2r(param.grad.flatten()) @ layer.weight.pre
u.nan_check(param_new_flat)
param_data.copy_(param_new_flat.reshape(param_data.shape))
gl.token_count += data.shape[0]
gl.event_writer.close()
def main():
attemp_count = 0
while os.path.exists(f"{args.logdir}{attemp_count:02d}"):
attemp_count += 1
logdir = f"{args.logdir}{attemp_count:02d}"
run_name = os.path.basename(logdir)
gl.event_writer = SummaryWriter(logdir)
print(f"Logging to {run_name}")
u.seed_random(1)
try:
# os.environ['WANDB_SILENT'] = 'true'
if args.wandb:
wandb.init(project='curv_train_tiny', name=run_name)
wandb.tensorboard.patch(tensorboardX=False)
wandb.config['train_batch'] = args.train_batch_size
wandb.config['stats_batch'] = args.stats_batch_size
wandb.config['method'] = args.method
except Exception as e:
print(f"wandb crash with {e}")
# data_width = 4
# targets_width = 2
d1 = args.data_width**2
d2 = 10
d3 = args.targets_width**2
o = d3
n = args.stats_batch_size
d = [d1, d2, d3]
model = u.SimpleFullyConnected(d, nonlin=args.nonlin)
optimizer = torch.optim.SGD(model.parameters(), lr=0.1, momentum=0.9)
dataset = u.TinyMNIST(data_width=args.data_width,
targets_width=args.targets_width,
dataset_size=args.dataset_size)
train_loader = torch.utils.data.DataLoader(
dataset,
batch_size=args.train_batch_size,
shuffle=False,
drop_last=True)
train_iter = u.infinite_iter(train_loader)
stats_loader = torch.utils.data.DataLoader(
dataset,
batch_size=args.stats_batch_size,
shuffle=False,
drop_last=True)
stats_iter = u.infinite_iter(stats_loader)
def capture_activations(module, input, _output):
if skip_forward_hooks:
return
assert gl.backward_idx == 0 # no need to forward-prop on Hessian computation
assert not hasattr(
module, 'activations'
), "Seeing activations from previous forward, call util.zero_grad to clear"
assert len(input) == 1, "this works for single input layers only"
setattr(module, "activations", input[0].detach())
def capture_backprops(module: nn.Module, _input, output):
if skip_backward_hooks:
return
assert len(output) == 1, "this works for single variable layers only"
if gl.backward_idx == 0:
assert not hasattr(
module, 'backprops'
), "Seeing results of previous autograd, call util.zero_grad to clear"
setattr(module, 'backprops', [])
assert gl.backward_idx == len(module.backprops)
module.backprops.append(output[0])
def save_grad(param: nn.Parameter) -> Callable[[torch.Tensor], None]:
"""Hook to save gradient into 'param.saved_grad', so it can be accessed after model.zero_grad(). Only stores gradient
if the value has not been set, call util.zero_grad to clear it."""
def save_grad_fn(grad):
if not hasattr(param, 'saved_grad'):
setattr(param, 'saved_grad', grad)
return save_grad_fn
for layer in model.layers:
layer.register_forward_hook(capture_activations)
layer.register_backward_hook(capture_backprops)
layer.weight.register_hook(save_grad(layer.weight))
def loss_fn(data, targets):
err = data - targets.view(-1, data.shape[1])
assert len(data) == len(targets)
return torch.sum(err * err) / 2 / len(data)
gl.token_count = 0
for step in range(args.stats_steps):
data, targets = next(stats_iter)
skip_forward_hooks = False
skip_backward_hooks = False
# get gradient values
gl.backward_idx = 0
u.zero_grad(model)
output = model(data)
loss = loss_fn(output, targets)
loss.backward(retain_graph=True)
print("loss", loss.item())
# get Hessian values
skip_forward_hooks = True
id_mat = torch.eye(o)
u.log_scalars({'loss': loss.item()})
# o = 0
for out_idx in range(o):
model.zero_grad()
# backprop to get section of batch output jacobian for output at position out_idx
output = model(
data
) # opt: using autograd.grad means I don't have to zero_grad
ei = id_mat[out_idx]
bval = torch.stack([ei] * n)
gl.backward_idx = out_idx + 1
output.backward(bval)
skip_backward_hooks = True #
for (i, layer) in enumerate(model.layers):
s = AttrDefault(str, {}) # dictionary-like object for layer stats
#############################
# Gradient stats
#############################
A_t = layer.activations
assert A_t.shape == (n, d[i])
# add factor of n because backprop takes loss averaged over batch, while we need per-example loss
B_t = layer.backprops[0] * n
assert B_t.shape == (n, d[i + 1])
G = u.khatri_rao_t(B_t, A_t) # batch loss Jacobian
assert G.shape == (n, d[i] * d[i + 1])
g = G.sum(dim=0, keepdim=True) / n # average gradient
assert g.shape == (1, d[i] * d[i + 1])
if args.autograd_check:
u.check_close(B_t.t() @ A_t / n, layer.weight.saved_grad)
u.check_close(g.reshape(d[i + 1], d[i]),
layer.weight.saved_grad)
# empirical Fisher
efisher = G.t() @ G / n
sigma = efisher - g.t() @ g
# u.dump(sigma, f'/tmp/sigmas/{step}-{i}')
s.sigma_l2 = u.l2_norm(sigma)
#############################
# Hessian stats
#############################
A_t = layer.activations
Bh_t = [layer.backprops[out_idx + 1] for out_idx in range(o)]
Amat_t = torch.cat([A_t] * o, dim=0)
Bmat_t = torch.cat(Bh_t, dim=0)
assert Amat_t.shape == (n * o, d[i])
assert Bmat_t.shape == (n * o, d[i + 1])
Jb = u.khatri_rao_t(Bmat_t,
Amat_t) # batch Jacobian, in row-vec format
H = Jb.t() @ Jb / n
pinvH = u.pinv(H)
s.hess_l2 = u.l2_norm(H)
s.invhess_l2 = u.l2_norm(pinvH)
s.hess_fro = H.flatten().norm()
s.invhess_fro = pinvH.flatten().norm()
s.jacobian_l2 = u.l2_norm(Jb)
s.grad_fro = g.flatten().norm()
s.param_fro = layer.weight.data.flatten().norm()
u.nan_check(H)
if args.autograd_check:
model.zero_grad()
output = model(data)
loss = loss_fn(output, targets)
H_autograd = u.hessian(loss, layer.weight)
H_autograd = H_autograd.reshape(d[i] * d[i + 1],
d[i] * d[i + 1])
u.check_close(H, H_autograd)
# u.dump(sigma, f'/tmp/sigmas/H-{step}-{i}')
def loss_direction(dd: torch.Tensor, eps):
"""loss improvement if we take step eps in direction dd"""
return u.to_python_scalar(eps * (dd @ g.t()) -
0.5 * eps**2 * dd @ H @ dd.t())
def curv_direction(dd: torch.Tensor):
"""Curvature in direction dd"""
return u.to_python_scalar(dd @ H @ dd.t() /
dd.flatten().norm()**2)
s.regret_newton = u.to_python_scalar(g @ u.pinv(H) @ g.t() / 2)
s.grad_curv = curv_direction(g)
ndir = g @ u.pinv(H) # newton direction
s.newton_curv = curv_direction(ndir)
setattr(layer.weight, 'pre',
u.pinv(H)) # save Newton preconditioner
s.step_openai = 1 / s.grad_curv if s.grad_curv else 999
s.newton_fro = ndir.flatten().norm(
) # frobenius norm of Newton update
s.regret_gradient = loss_direction(g, s.step_openai)
u.log_scalars(u.nest_stats(layer.name, s))
# gradient steps
for i in range(args.train_steps):
optimizer.zero_grad()
data, targets = next(train_iter)
model.zero_grad()
output = model(data)
loss = loss_fn(output, targets)
loss.backward()
u.log_scalar(train_loss=loss.item())
if args.method != 'newton':
optimizer.step()
else:
for (layer_idx, layer) in enumerate(model.layers):
param: torch.nn.Parameter = layer.weight
param_data: torch.Tensor = param.data
param_data.copy_(param_data - 0.1 * param.grad)
if layer_idx != 1: # only update 1 layer with Newton, unstable otherwise
continue
u.nan_check(layer.weight.pre)
u.nan_check(param.grad.flatten())
u.nan_check(u.v2r(param.grad.flatten()) @ layer.weight.pre)
param_new_flat = u.v2r(param_data.flatten()) - u.v2r(
param.grad.flatten()) @ layer.weight.pre
u.nan_check(param_new_flat)
param_data.copy_(param_new_flat.reshape(param_data.shape))
gl.token_count += data.shape[0]
gl.event_writer.close()
def main():
parser = argparse.ArgumentParser(description='PyTorch MNIST Example')
parser.add_argument('--batch-size',
type=int,
default=64,
metavar='N',
help='input batch size for training (default: 64)')
parser.add_argument('--test-batch-size',
type=int,
default=1000,
metavar='N',
help='input batch size for testing (default: 1000)')
parser.add_argument('--epochs',
type=int,
default=10,
metavar='N',
help='number of epochs to train (default: 10)')
parser.add_argument('--no-cuda',
action='store_true',
default=False,
help='disables CUDA training')
parser.add_argument('--seed',
type=int,
default=1,
metavar='S',
help='random seed (default: 1)')
parser.add_argument(
'--log-interval',
type=int,
default=10,
metavar='N',
help='how many batches to wait before logging training status')
parser.add_argument('--save-model',
action='store_true',
default=False,
help='For Saving the current Model')
parser.add_argument('--wandb',
type=int,
default=0,
help='log to weights and biases')
parser.add_argument('--autograd_check',
type=int,
default=0,
help='autograd correctness checks')
parser.add_argument('--logdir',
type=str,
default='/tmp/runs/curv_train_tiny/run')
parser.add_argument('--nonlin',
type=int,
default=1,
help="whether to add ReLU nonlinearity between layers")
parser.add_argument('--bias',
type=int,
default=1,
help="whether to add bias between layers")
parser.add_argument('--layer',
type=int,
default=-1,
help="restrict updates to this layer")
parser.add_argument('--data_width', type=int, default=28)
parser.add_argument('--targets_width', type=int, default=28)
parser.add_argument(
'--hess_samples',
type=int,
default=1,
help='number of samples when sub-sampling outputs, 0 for exact hessian'
)
parser.add_argument('--hess_kfac',
type=int,
default=0,
help='whether to use KFAC approximation for hessian')
parser.add_argument('--compute_rho',
type=int,
default=0,
help='use expensive method to compute rho')
parser.add_argument('--skip_stats',
type=int,
default=1,
help='skip all stats collection')
parser.add_argument('--dataset_size', type=int, default=60000)
parser.add_argument('--train_steps',
type=int,
default=1000,
help="this many train steps between stat collection")
parser.add_argument('--stats_steps',
type=int,
default=1000000,
help="total number of curvature stats collections")
parser.add_argument('--full_batch',
type=int,
default=0,
help='do stats on the whole dataset')
parser.add_argument('--lr', type=float, default=1e-3)
parser.add_argument('--weight_decay', type=float, default=2e-5)
parser.add_argument('--momentum', type=float, default=0.9)
parser.add_argument('--dropout', type=int, default=0)
parser.add_argument('--swa', type=int, default=0)
parser.add_argument('--lmb', type=float, default=1e-3)
parser.add_argument('--train_batch_size', type=int, default=64)
parser.add_argument('--stats_batch_size', type=int, default=10000)
parser.add_argument('--uniform',
type=int,
default=0,
help='use uniform architecture (all layers same size)')
parser.add_argument('--run_name', type=str, default='noname')
gl.args = parser.parse_args()
args = gl.args
u.seed_random(1)
gl.project_name = 'train_ciresan'
u.setup_logdir_and_event_writer(args.run_name)
print(f"Logging to {gl.logdir}")
d1 = 28 * 28
if args.uniform:
d = [784, 784, 784, 784, 784, 784, 10]
else:
d = [784, 2500, 2000, 1500, 1000, 500, 10]
o = 10
n = args.stats_batch_size
model = u.SimpleFullyConnected2(d,
nonlin=args.nonlin,
bias=args.bias,
dropout=args.dropout)
model = model.to(gl.device)
optimizer = torch.optim.SGD(model.parameters(),
lr=args.lr,
momentum=args.momentum)
dataset = u.TinyMNIST(data_width=args.data_width,
targets_width=args.targets_width,
original_targets=True,
dataset_size=args.dataset_size)
train_loader = torch.utils.data.DataLoader(
dataset,
batch_size=args.train_batch_size,
shuffle=True,
drop_last=True)
train_iter = u.infinite_iter(train_loader)
assert not args.full_batch, "fixme: validation still uses stats_iter"
if not args.full_batch:
stats_loader = torch.utils.data.DataLoader(
dataset,
batch_size=args.stats_batch_size,
shuffle=False,
drop_last=True)
stats_iter = u.infinite_iter(stats_loader)
else:
stats_iter = None
test_dataset = u.TinyMNIST(data_width=args.data_width,
targets_width=args.targets_width,
train=False,
original_targets=True,
dataset_size=args.dataset_size)
test_loader = torch.utils.data.DataLoader(test_dataset,
batch_size=args.stats_batch_size,
shuffle=False,
drop_last=False)
loss_fn = torch.nn.CrossEntropyLoss()
autograd_lib.add_hooks(model)
autograd_lib.disable_hooks()
gl.token_count = 0
last_outer = 0
for step in range(args.stats_steps):
epoch = gl.token_count // 60000
print(gl.token_count)
if last_outer:
u.log_scalars(
{"time/outer": 1000 * (time.perf_counter() - last_outer)})
last_outer = time.perf_counter()
# compute validation loss
if args.swa:
model.eval()
with u.timeit('swa'):
base_opt = torch.optim.SGD(model.parameters(),
lr=args.lr,
momentum=args.momentum)
opt = torchcontrib.optim.SWA(base_opt,
swa_start=0,
swa_freq=1,
swa_lr=args.lr)
for _ in range(100):
optimizer.zero_grad()
data, targets = next(train_iter)
model.zero_grad()
output = model(data)
loss = loss_fn(output, targets)
loss.backward()
opt.step()
opt.swap_swa_sgd()
with u.timeit("validate"):
val_accuracy, val_loss = validate(model, test_loader,
f'test (epoch {epoch})')
train_accuracy, train_loss = validate(model, stats_loader,
f'train (epoch {epoch})')
# save log
metrics = {
'epoch': epoch,
'val_accuracy': val_accuracy,
'val_loss': val_loss,
'train_loss': train_loss,
'train_accuracy': train_accuracy,
'lr': optimizer.param_groups[0]['lr'],
'momentum': optimizer.param_groups[0].get('momentum', 0)
}
u.log_scalars(metrics)
# compute stats
if args.full_batch:
data, targets = dataset.data, dataset.targets
else:
data, targets = next(stats_iter)
if not args.skip_stats:
autograd_lib.enable_hooks()
autograd_lib.clear_backprops(model)
autograd_lib.clear_hess_backprops(model)
with u.timeit("backprop_g"):
output = model(data)
loss = loss_fn(output, targets)
loss.backward(retain_graph=True)
with u.timeit("backprop_H"):
autograd_lib.backprop_hess(output, hess_type='CrossEntropy')
autograd_lib.disable_hooks() # TODO(y): use remove_hooks
with u.timeit("compute_grad1"):
autograd_lib.compute_grad1(model)
with u.timeit("compute_hess"):
autograd_lib.compute_hess(model,
method='kron',
attr_name='hess2')
autograd_lib.compute_stats_factored(model)
for (i, layer) in enumerate(model.layers):
param_names = {layer.weight: "weight", layer.bias: "bias"}
for param in [layer.weight, layer.bias]:
if param is None:
continue
if not hasattr(param, 'stats'):
continue
s = param.stats
param_name = param_names[param]
u.log_scalars(u.nest_stats(f"{param_name}", s))
# gradient steps
model.train()
last_inner = 0
for i in range(args.train_steps):
if last_inner:
u.log_scalars(
{"time/inner": 1000 * (time.perf_counter() - last_inner)})
last_inner = time.perf_counter()
optimizer.zero_grad()
data, targets = next(train_iter)
model.zero_grad()
output = model(data)
loss = loss_fn(output, targets)
loss.backward()
optimizer.step()
if args.weight_decay:
for group in optimizer.param_groups:
for param in group['params']:
param.data.mul_(1 - args.weight_decay)
gl.token_count += data.shape[0]
gl.event_writer.close()
def main():
u.install_pdb_handler()
u.seed_random(1)
logdir = u.create_local_logdir(args.logdir)
run_name = os.path.basename(logdir)
gl.event_writer = SummaryWriter(logdir)
print(f"Logging to {logdir}")
loss_type = 'CrossEntropy'
d1 = args.data_width ** 2
args.stats_batch_size = min(args.stats_batch_size, args.dataset_size)
args.train_batch_size = min(args.train_batch_size, args.dataset_size)
n = args.stats_batch_size
o = 10
d = [d1, 60, 60, 60, o]
# dataset_size = args.dataset_size
model = u.SimpleFullyConnected2(d, bias=True, nonlin=args.nonlin, last_layer_linear=True)
model = model.to(gl.device)
u.mark_expensive(model.layers[0]) # to stop grad1/hess calculations on this layer
print(model)
try:
if args.wandb:
wandb.init(project='curv_train_tiny', name=run_name, dir='/tmp/wandb.runs')
wandb.tensorboard.patch(tensorboardX=False)
wandb.config['train_batch'] = args.train_batch_size
wandb.config['stats_batch'] = args.stats_batch_size
wandb.config['n'] = n
except Exception as e:
print(f"wandb crash with {e}")
optimizer = torch.optim.SGD(model.parameters(), lr=args.lr, momentum=0.9)
# optimizer = torch.optim.Adam(model.parameters(), lr=0.03) # make 10x smaller for least-squares loss
dataset = u.TinyMNIST(data_width=args.data_width, dataset_size=args.dataset_size, loss_type=loss_type)
train_loader = torch.utils.data.DataLoader(dataset, batch_size=args.train_batch_size, shuffle=False, drop_last=True)
train_iter = u.infinite_iter(train_loader)
stats_loader = torch.utils.data.DataLoader(dataset, batch_size=args.stats_batch_size, shuffle=False, drop_last=True)
stats_iter = u.infinite_iter(stats_loader)
stats_data, stats_targets = next(stats_iter)
test_dataset = u.TinyMNIST(data_width=args.data_width, train=False, dataset_size=args.dataset_size, loss_type=loss_type)
test_batch_size = min(args.dataset_size, 1000)
test_loader = torch.utils.data.DataLoader(test_dataset, batch_size=test_batch_size, shuffle=False, drop_last=True)
test_iter = u.infinite_iter(test_loader)
if loss_type == 'LeastSquares':
loss_fn = u.least_squares
else: # loss_type == 'CrossEntropy':
loss_fn = nn.CrossEntropyLoss()
autograd_lib.add_hooks(model)
gl.reset_global_step()
last_outer = 0
val_losses = []
for step in range(args.stats_steps):
if last_outer:
u.log_scalars({"time/outer": 1000*(time.perf_counter() - last_outer)})
last_outer = time.perf_counter()
with u.timeit("val_loss"):
test_data, test_targets = next(test_iter)
test_output = model(test_data)
val_loss = loss_fn(test_output, test_targets)
print("val_loss", val_loss.item())
val_losses.append(val_loss.item())
u.log_scalar(val_loss=val_loss.item())
with u.timeit("validate"):
if loss_type == 'CrossEntropy':
val_accuracy, val_loss = validate(model, test_loader, f'test (stats_step {step})')
# train_accuracy, train_loss = validate(model, train_loader, f'train (stats_step {step})')
metrics = {'stats_step': step, 'val_accuracy': val_accuracy, 'val_loss': val_loss}
u.log_scalars(metrics)
data, targets = stats_data, stats_targets
if not args.skip_stats:
# Capture Hessian and gradient stats
autograd_lib.enable_hooks()
autograd_lib.clear_backprops(model)
autograd_lib.clear_hess_backprops(model)
with u.timeit("backprop_g"):
output = model(data)
loss = loss_fn(output, targets)
loss.backward(retain_graph=True)
with u.timeit("backprop_H"):
autograd_lib.backprop_hess(output, hess_type=loss_type)
autograd_lib.disable_hooks() # TODO(y): use remove_hooks
with u.timeit("compute_grad1"):
autograd_lib.compute_grad1(model)
with u.timeit("compute_hess"):
autograd_lib.compute_hess(model)
for (i, layer) in enumerate(model.layers):
if hasattr(layer, 'expensive'):
continue
param_names = {layer.weight: "weight", layer.bias: "bias"}
for param in [layer.weight, layer.bias]:
# input/output layers are unreasonably expensive if not using Kronecker factoring
if d[i]*d[i+1] > 8000:
print(f'layer {i} is too big ({d[i],d[i+1]}), skipping stats')
continue
s = AttrDefault(str, {}) # dictionary-like object for layer stats
#############################
# Gradient stats
#############################
A_t = layer.activations
B_t = layer.backprops_list[0] * n
s.sparsity = torch.sum(layer.output <= 0) / layer.output.numel() # proportion of activations that are zero
s.mean_activation = torch.mean(A_t)
s.mean_backprop = torch.mean(B_t)
# empirical Fisher
G = param.grad1.reshape((n, -1))
g = G.mean(dim=0, keepdim=True)
u.nan_check(G)
with u.timeit(f'sigma-{i}'):
efisher = G.t() @ G / n
sigma = efisher - g.t() @ g
# sigma_spectrum =
s.sigma_l2 = u.sym_l2_norm(sigma)
s.sigma_erank = torch.trace(sigma)/s.sigma_l2
H = param.hess
lambda_regularizer = args.lmb * torch.eye(H.shape[0]).to(gl.device)
u.nan_check(H)
with u.timeit(f"invH-{i}"):
invH = torch.cholesky_inverse(H+lambda_regularizer)
with u.timeit(f"H_l2-{i}"):
s.H_l2 = u.sym_l2_norm(H)
s.iH_l2 = u.sym_l2_norm(invH)
with u.timeit(f"norms-{i}"):
s.H_fro = H.flatten().norm()
s.iH_fro = invH.flatten().norm()
s.grad_fro = g.flatten().norm()
s.param_fro = param.data.flatten().norm()
def loss_direction(dd: torch.Tensor, eps):
"""loss improvement if we take step eps in direction dd"""
return u.to_python_scalar(eps * (dd @ g.t()) - 0.5 * eps ** 2 * dd @ H @ dd.t())
def curv_direction(dd: torch.Tensor):
"""Curvature in direction dd"""
return u.to_python_scalar(dd @ H @ dd.t() / (dd.flatten().norm() ** 2))
with u.timeit(f"pinvH-{i}"):
pinvH = u.pinv(H)
with u.timeit(f'curv-{i}'):
s.grad_curv = curv_direction(g) # curvature (eigenvalue) in direction g
ndir = g @ pinvH # newton direction
s.newton_curv = curv_direction(ndir)
setattr(layer.weight, 'pre', pinvH) # save Newton preconditioner
s.step_openai = 1 / s.grad_curv if s.grad_curv else 1234567
s.step_div_inf = 2 / s.H_l2 # divegent step size for batch_size=infinity
s.step_div_1 = torch.tensor(2) / torch.trace(H) # divergent step for batch_size=1
s.newton_fro = ndir.flatten().norm() # frobenius norm of Newton update
s.regret_newton = u.to_python_scalar(g @ pinvH @ g.t() / 2) # replace with "quadratic_form"
s.regret_gradient = loss_direction(g, s.step_openai)
with u.timeit(f'rho-{i}'):
s.rho, s.lyap_erank, lyap_evals = u.truncated_lyapunov_rho(H, sigma)
s.step_div_1_adjusted = s.step_div_1/s.rho
with u.timeit(f"batch-{i}"):
s.batch_openai = torch.trace(H @ sigma) / (g @ H @ g.t())
s.diversity = torch.norm(G, "fro") ** 2 / torch.norm(g) ** 2 / n # Gradient diversity / n
s.noise_variance_pinv = torch.trace(pinvH @ sigma)
s.H_erank = torch.trace(H) / s.H_l2
s.batch_jain_simple = 1 + s.H_erank
s.batch_jain_full = 1 + s.rho * s.H_erank
param_name = f"{layer.name}={param_names[param]}"
u.log_scalars(u.nest_stats(f"{param_name}", s))
H_evals = u.symeig_pos_evals(H)
sigma_evals = u.symeig_pos_evals(sigma)
u.log_spectrum(f'{param_name}/hess', H_evals)
u.log_spectrum(f'{param_name}/sigma', sigma_evals)
u.log_spectrum(f'{param_name}/lyap', lyap_evals)
# gradient steps
with u.timeit('inner'):
for i in range(args.train_steps):
optimizer.zero_grad()
data, targets = next(train_iter)
model.zero_grad()
output = model(data)
loss = loss_fn(output, targets)
loss.backward()
optimizer.step()
if args.weight_decay:
for group in optimizer.param_groups:
for param in group['params']:
param.data.mul_(1-args.weight_decay)
gl.increment_global_step(data.shape[0])
gl.event_writer.close()
def test_kron_conv_exact():
"""Test per-example gradient computation for conv layer.
Kronecker factoring is exact for 1x1 convolutions and linear activations.
"""
u.seed_random(1)
n, Xh, Xw = 2, 2, 2
Kh, Kw = 1, 1
dd = [2, 2, 2]
o = dd[-1]
model: u.SimpleModel = u.PooledConvolutional2(dd, kernel_size=(Kh, Kw), nonlin=False, bias=True)
data = torch.randn((n, dd[0], Xh, Xw))
#print(model)
#print(data)
loss_type = 'CrossEntropy' # loss_type = 'LeastSquares'
if loss_type == 'LeastSquares':
loss_fn = u.least_squares
elif loss_type == 'DebugLeastSquares':
loss_fn = u.debug_least_squares
else: # CrossEntropy
loss_fn = nn.CrossEntropyLoss()
sample_output = model(data)
if loss_type.endswith('LeastSquares'):
targets = torch.randn(sample_output.shape)
elif loss_type == 'CrossEntropy':
targets = torch.LongTensor(n).random_(0, o)
autograd_lib.clear_backprops(model)
autograd_lib.add_hooks(model)
output = model(data)
autograd_lib.backprop_hess(output, hess_type=loss_type)
autograd_lib.compute_hess(model, method='mean_kron')
autograd_lib.compute_hess(model, method='exact')
autograd_lib.disable_hooks()
for i in range(len(model.layers)):
layer = model.layers[i]
# direct Hessian computation
H = layer.weight.hess
H_bias = layer.bias.hess
# factored Hessian computation
Hk = layer.weight.hess_factored
Hk_bias = layer.bias.hess_factored
Hk = Hk.expand()
Hk_bias = Hk_bias.expand()
# autograd Hessian computation
loss = loss_fn(output, targets)
Ha = u.hessian(loss, layer.weight).reshape(H.shape)
Ha_bias = u.hessian(loss, layer.bias)
# compare direct against autograd
Ha = Ha.reshape(H.shape)
# rel_error = torch.max((H-Ha)/Ha)
u.check_close(H, Ha, rtol=1e-5, atol=1e-7)
u.check_close(Ha_bias, H_bias, rtol=1e-5, atol=1e-7)
u.check_close(H_bias, Hk_bias)
u.check_close(H, Hk)
def test_main_autograd():
u.seed_random(1)
log_wandb = False
autograd_check = True
use_double = False
logdir = u.get_unique_logdir('/tmp/autoencoder_test/run')
run_name = os.path.basename(logdir)
gl.event_writer = SummaryWriter(logdir)
batch_size = 5
try:
if log_wandb:
wandb.init(project='test-autograd_test', name=run_name)
wandb.tensorboard.patch(tensorboardX=False)
wandb.config['batch'] = batch_size
except Exception as e:
print(f"wandb crash with {e}")
data_width = 4
targets_width = 2
d1 = data_width ** 2
d2 = 10
d3 = targets_width ** 2
o = d3
n = batch_size
d = [d1, d2, d3]
model: u.SimpleModel = u.SimpleFullyConnected(d, nonlin=True, bias=True)
if use_double:
model = model.double()
train_steps = 3
dataset = u.TinyMNIST(data_width=data_width, targets_width=targets_width,
dataset_size=batch_size * train_steps)
trainloader = torch.utils.data.DataLoader(dataset, batch_size=batch_size, shuffle=False)
train_iter = iter(trainloader)
def loss_fn(data, targets):
err = data - targets.view(-1, data.shape[1])
assert len(data) == batch_size
return torch.sum(err * err) / 2 / len(data)
loss_hessian = u.HessianExactSqrLoss()
gl.token_count = 0
for train_step in range(train_steps):
data, targets = next(train_iter)
if use_double:
data, targets = data.double(), targets.double()
# get gradient values
model.skip_backward_hooks = False
model.skip_forward_hooks = False
u.clear_backprops(model)
output = model(data)
loss = loss_fn(output, targets)
loss.backward(retain_graph=True)
model.skip_forward_hooks = True
output = model(data)
for bval in loss_hessian(output):
if use_double:
bval = bval.double()
output.backward(bval, retain_graph=True)
model.skip_backward_hooks = True
for (i, layer) in enumerate(model.layers):
#############################
# Gradient stats
#############################
A_t = layer.activations
assert A_t.shape == (n, d[i])
# add factor of n because backprop takes loss averaged over batch, while we need per-example loss
B_t = layer.backprops_list[0] * n
assert B_t.shape == (n, d[i + 1])
# per example gradients
G = u.khatri_rao_t(B_t, A_t)
assert G.shape == (n, d[i+1] * d[i])
Gbias = B_t
assert Gbias.shape == (n, d[i + 1])
# average gradient
g = G.sum(dim=0, keepdim=True) / n
gb = Gbias.sum(dim=0, keepdim=True) / n
assert g.shape == (1, d[i] * d[i + 1])
assert gb.shape == (1, d[i + 1])
if autograd_check:
u.check_close(B_t.t() @ A_t / n, layer.weight.saved_grad)
u.check_close(g.reshape(d[i + 1], d[i]), layer.weight.saved_grad)
u.check_close(torch.einsum('nj->j', B_t) / n, layer.bias.saved_grad)
u.check_close(torch.mean(B_t, dim=0), layer.bias.saved_grad)
u.check_close(torch.einsum('ni,nj->ij', B_t, A_t)/n, layer.weight.saved_grad)
# empirical Fisher
efisher = G.t() @ G / n
_sigma = efisher - g.t() @ g
#############################
# Hessian stats
#############################
A_t = layer.activations
Bh_t = [layer.backprops_list[out_idx + 1] for out_idx in range(o)]
Amat_t = torch.cat([A_t] * o, dim=0) # todo: can instead replace with a khatri-rao loop
Bmat_t = torch.cat(Bh_t, dim=0)
Amat_t2 = torch.stack([A_t]*o, dim=0) # o, n, in_dim
Bmat_t2 = torch.stack(Bh_t, dim=0) # o, n, out_dim
assert Amat_t.shape == (n * o, d[i])
assert Bmat_t.shape == (n * o, d[i + 1])
Jb = u.khatri_rao_t(Bmat_t, Amat_t) # batch output Jacobian
H = Jb.t() @ Jb / n
Jb2 = torch.einsum('oni,onj->onij', Bmat_t2, Amat_t2)
u.check_close(H.reshape(d[i+1], d[i], d[i+1], d[i]), torch.einsum('onij,onkl->ijkl', Jb2, Jb2)/n)
Hbias = Bmat_t.t() @ Bmat_t / n
u.check_close(Hbias, torch.einsum('ni,nj->ij', Bmat_t, Bmat_t) / n)
if autograd_check:
model.zero_grad()
output = model(data)
loss = loss_fn(output, targets)
H_autograd = u.hessian(loss, layer.weight)
Hbias_autograd = u.hessian(loss, layer.bias)
u.check_close(H, H_autograd.reshape(d[i+1] * d[i], d[i+1] * d[i]))
u.check_close(Hbias, Hbias_autograd)
def test_conv_hessian():
"""Test per-example gradient computation for conv layer."""
u.seed_random(1)
n, Xc, Xh, Xw = 3, 2, 3, 7
dd = [Xc, 2]
Kh, Kw = 2, 3
Oh, Ow = Xh - Kh + 1, Xw - Kw + 1
model: u.SimpleModel = u.ReshapedConvolutional(dd, kernel_size=(Kh, Kw), bias=True)
weight_buffer = model.layers[0].weight.data
assert (Kh, Kw) == model.layers[0].kernel_size
data = torch.randn((n, Xc, Xh, Xw))
# output channels, input channels, height, width
assert weight_buffer.shape == (dd[1], dd[0], Kh, Kw)
def loss_fn(data):
err = data.reshape(len(data), -1)
return torch.sum(err * err) / 2 / len(data)
loss_hessian = u.HessianExactSqrLoss()
# o = Oh * Ow * dd[1]
output = model(data)
o = output.shape[1]
for bval in loss_hessian(output):
output.backward(bval, retain_graph=True)
assert loss_hessian.num_samples == o
i, layer = next(enumerate(model.layers))
At = unfold(layer.activations, (Kh, Kw)) # -> n, Xc * Kh * Kw, Oh * Ow
assert At.shape == (n, dd[0] * Kh * Kw, Oh*Ow)
# o, n, dd[1], Oh, Ow -> o, n, dd[1], Oh*Ow
Bh_t = torch.stack([Bt.reshape(n, dd[1], Oh*Ow) for Bt in layer.backprops_list])
assert Bh_t.shape == (o, n, dd[1], Oh*Ow)
Ah_t = torch.stack([At]*o)
assert Ah_t.shape == (o, n, dd[0] * Kh * Kw, Oh*Ow)
# sum out the output patch dimension
Jb = torch.einsum('onij,onkj->onik', Bh_t, Ah_t) # => o, n, dd[1], dd[0] * Kh * Kw
Hi = torch.einsum('onij,onkl->nijkl', Jb, Jb) # => n, dd[1], dd[0]*Kh*Kw, dd[1], dd[0]*Kh*Kw
Jb_bias = torch.einsum('onij->oni', Bh_t)
Hb_i = torch.einsum('oni,onj->nij', Jb_bias, Jb_bias)
H = Hi.mean(dim=0)
Hb = Hb_i.mean(dim=0)
model.disable_hooks()
loss = loss_fn(model(data))
H_autograd = u.hessian(loss, layer.weight)
assert H_autograd.shape == (dd[1], dd[0], Kh, Kw, dd[1], dd[0], Kh, Kw)
assert H.shape == (dd[1], dd[0]*Kh*Kw, dd[1], dd[0]*Kh*Kw)
u.check_close(H, H_autograd.reshape(H.shape), rtol=1e-4, atol=1e-7)
Hb_autograd = u.hessian(loss, layer.bias)
assert Hb_autograd.shape == (dd[1], dd[1])
u.check_close(Hb, Hb_autograd)
assert len(Bh_t) == loss_hessian.num_samples == o
for xi in range(n):
loss = loss_fn(model(data[xi:xi + 1, ...]))
H_autograd = u.hessian(loss, layer.weight)
u.check_close(Hi[xi], H_autograd.reshape(H.shape))
Hb_autograd = u.hessian(loss, layer.bias)
u.check_close(Hb_i[xi], Hb_autograd)
assert Hb_i[xi, 0, 0] == Oh*Ow # each output has curvature 1, bias term adds up Oh*Ow of them
def test_conv_grad():
"""Test per-example gradient computation for conv layer.
"""
u.seed_random(1)
N, Xc, Xh, Xw = 3, 2, 3, 7
dd = [Xc, 2]
Kh, Kw = 2, 3
Oh, Ow = Xh - Kh + 1, Xw - Kw + 1
model = u.SimpleConvolutional(dd, kernel_size=(Kh, Kw), bias=True).double()
weight_buffer = model.layers[0].weight.data
# output channels, input channels, height, width
assert weight_buffer.shape == (dd[1], dd[0], Kh, Kw)
input_dims = N, Xc, Xh, Xw
size = int(np.prod(input_dims))
X = torch.arange(0, size).reshape(*input_dims).double()
def loss_fn(data):
err = data.reshape(len(data), -1)
return torch.sum(err * err) / 2 / len(data)
layer = model.layers[0]
output = model(X)
loss = loss_fn(output)
loss.backward()
u.check_equal(layer.activations, X)
assert layer.backprops_list[0].shape == layer.output.shape
assert layer.output.shape == (N, dd[1], Oh, Ow)
out_unf = layer.weight.view(layer.weight.size(0), -1) @ unfold(layer.activations, (Kh, Kw))
assert out_unf.shape == (N, dd[1], Oh * Ow)
reshaped_bias = layer.bias.reshape(1, dd[1], 1) # (Co,) -> (1, Co, 1)
out_unf = out_unf + reshaped_bias
u.check_equal(fold(out_unf, (Oh, Ow), (1, 1)), output) # two alternative ways of reshaping
u.check_equal(out_unf.view(N, dd[1], Oh, Ow), output)
# Unfold produces patches with output dimension merged, while in backprop they are not merged
# Hence merge the output (width/height) dimension
assert unfold(layer.activations, (Kh, Kw)).shape == (N, Xc * Kh * Kw, Oh * Ow)
assert layer.backprops_list[0].shape == (N, dd[1], Oh, Ow)
grads_bias = layer.backprops_list[0].sum(dim=(2, 3)) * N
mean_grad_bias = grads_bias.sum(dim=0) / N
u.check_equal(mean_grad_bias, layer.bias.grad)
Bt = layer.backprops_list[0] * N # remove factor of N applied during loss batch averaging
assert Bt.shape == (N, dd[1], Oh, Ow)
Bt = Bt.reshape(N, dd[1], Oh*Ow)
At = unfold(layer.activations, (Kh, Kw))
assert At.shape == (N, dd[0] * Kh * Kw, Oh*Ow)
grad_unf = torch.einsum('ijk,ilk->ijl', Bt, At)
assert grad_unf.shape == (N, dd[1], dd[0] * Kh * Kw)
grads = grad_unf.reshape((N, dd[1], dd[0], Kh, Kw))
u.check_equal(grads.mean(dim=0), layer.weight.grad)
# compute per-example gradients using autograd, compare against manual computation
for i in range(N):
u.clear_backprops(model)
output = model(X[i:i + 1, ...])
loss = loss_fn(output)
loss.backward()
u.check_equal(grads[i], layer.weight.grad)
u.check_equal(grads_bias[i], layer.bias.grad)
def test_hessian():
"""Tests of Hessian computation."""
u.seed_random(1)
batch_size = 500
data_width = 4
targets_width = 4
d1 = data_width ** 2
d2 = 10
d3 = targets_width ** 2
o = d3
N = batch_size
d = [d1, d2, d3]
dataset = u.TinyMNIST(data_width=data_width, targets_width=targets_width, dataset_size=batch_size)
trainloader = torch.utils.data.DataLoader(dataset, batch_size=batch_size, shuffle=False)
train_iter = iter(trainloader)
data, targets = next(train_iter)
def loss_fn(data, targets):
assert len(data) == len(targets)
err = data - targets.view(-1, data.shape[1])
return torch.sum(err * err) / 2 / len(data)
u.seed_random(1)
model: u.SimpleModel = u.SimpleFullyConnected(d, nonlin=False, bias=True)
# backprop hessian and compare against autograd
hessian_backprop = u.HessianExactSqrLoss()
output = model(data)
for bval in hessian_backprop(output):
output.backward(bval, retain_graph=True)
i, layer = next(enumerate(model.layers))
A_t = layer.activations
Bh_t = layer.backprops_list
H, Hb = u.hessian_from_backprops(A_t, Bh_t, bias=True)
model.disable_hooks()
H_autograd = u.hessian(loss_fn(model(data), targets), layer.weight)
u.check_close(H, H_autograd.reshape(d[i + 1] * d[i], d[i + 1] * d[i]),
rtol=1e-4, atol=1e-7)
Hb_autograd = u.hessian(loss_fn(model(data), targets), layer.bias)
u.check_close(Hb, Hb_autograd, rtol=1e-4, atol=1e-7)
# check first few per-example Hessians
Hi, Hb_i = u.per_example_hess(A_t, Bh_t, bias=True)
u.check_close(H, Hi.mean(dim=0))
u.check_close(Hb, Hb_i.mean(dim=0), atol=2e-6, rtol=1e-5)
for xi in range(5):
loss = loss_fn(model(data[xi:xi + 1, ...]), targets[xi:xi + 1])
H_autograd = u.hessian(loss, layer.weight)
u.check_close(Hi[xi], H_autograd.reshape(d[i + 1] * d[i], d[i + 1] * d[i]))
Hbias_autograd = u.hessian(loss, layer.bias)
u.check_close(Hb_i[i], Hbias_autograd)
# get subsampled Hessian
u.seed_random(1)
model = u.SimpleFullyConnected(d, nonlin=False)
hessian_backprop = u.HessianSampledSqrLoss(num_samples=1)
output = model(data)
for bval in hessian_backprop(output):
output.backward(bval, retain_graph=True)
model.disable_hooks()
i, layer = next(enumerate(model.layers))
H_approx1 = u.hessian_from_backprops(layer.activations, layer.backprops_list)
# get subsampled Hessian with more samples
u.seed_random(1)
model = u.SimpleFullyConnected(d, nonlin=False)
hessian_backprop = u.HessianSampledSqrLoss(num_samples=o)
output = model(data)
for bval in hessian_backprop(output):
output.backward(bval, retain_graph=True)
model.disable_hooks()
i, layer = next(enumerate(model.layers))
H_approx2 = u.hessian_from_backprops(layer.activations, layer.backprops_list)
assert abs(u.l2_norm(H) / u.l2_norm(H_approx1) - 1) < 0.08, abs(u.l2_norm(H) / u.l2_norm(H_approx1) - 1) # 0.0612
assert abs(u.l2_norm(H) / u.l2_norm(H_approx2) - 1) < 0.03, abs(u.l2_norm(H) / u.l2_norm(H_approx2) - 1) # 0.0239
assert u.kl_div_cov(H_approx1, H) < 0.3, u.kl_div_cov(H_approx1, H) # 0.222
assert u.kl_div_cov(H_approx2, H) < 0.2, u.kl_div_cov(H_approx2, H) # 0.1233
