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_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_refactored_stats():
gl.project_name = 'test'
gl.logdir_base = '/tmp/runs'
run_name = 'test_hessian_multibatch'
u.setup_logdir_and_event_writer(run_name=run_name)
loss_type = 'CrossEntropy'
data_width = 2
n = 4
d1 = data_width ** 2
o = 10
d = [d1, o]
model = u.SimpleFullyConnected2(d, bias=False, nonlin=False)
model = model.to(gl.device)
dataset = u.TinyMNIST(data_width=data_width, dataset_size=n, loss_type=loss_type)
stats_loader = torch.utils.data.DataLoader(dataset, batch_size=n, shuffle=False)
stats_iter = u.infinite_iter(stats_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
stats_iter = u.infinite_iter(stats_loader)
stats_data, stats_targets = next(stats_iter)
data, targets = stats_data, stats_targets
covG = autograd_lib.layer_cov_dict()
covH = autograd_lib.layer_cov_dict()
covJ = autograd_lib.layer_cov_dict()
autograd_lib.register(model)
A = {}
with autograd_lib.save_activations(A):
output = model(data)
loss = loss_fn(output, targets)
Acov = autograd_lib.ModuleDict(autograd_lib.SecondOrder)
for layer, activations in A.items():
Acov[layer].accumulate(activations)
autograd_lib.set_default_activations(A) # set activations to use by default when constructing cov matrices
autograd_lib.set_default_Acov(Acov)
# saves backprop covariances
autograd_lib.backward_accum(loss, 1, covG)
autograd_lib.backward_accum(output, autograd_lib.xent_bwd, covH)
autograd_lib.backward_accum(output, autograd_lib.identity_bwd, covJ)
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_new_setup():
torch.set_default_dtype(torch.float64)
X = torch.tensor([[-5., 0], [-2, -6]], requires_grad=True)
model: u.SimpleFullyConnected2 = u.SimpleFullyConnected2([2, 2, 2], bias=False)
model.layers[0].weight.data.copy_(X)
A = torch.tensor([[-1., 4], [3, 0]])
B = torch.tensor([[-4., 3], [2, 6]])
X = torch.tensor([[-5., 0], [-2, -6]], requires_grad=True)
#########
# computing per-example gradients
#########
activations = {}
def save_activations(layer, a, _): activations[layer] = a
with autograd_lib.module_hooks(save_activations):
Y = model(A.t())
loss = torch.sum(Y * Y) / 2
norms = {}
def compute_norms(layer, _, b):
a = activations[layer]
del activations[layer]
norms[layer] = a*a.sum(dim=0)*(b*b).sum(dim=0)
with autograd_lib.module_hooks(compute_norms):
loss.backward()
#########
# Computing higher rank Hessian approximation
#########
activations = {}
with autograd_lib.module_hooks(save_activations):
Y = model(A.t())
loss = torch.sum(Y * Y) / 2
# kfac moments: 'ij', 'kl'
# isserlis moments: 'ij', 'kl', 'il', 'ik'
# first moments: 'i', 'j', 'k', 'l'
# third moments: ...
# forth moments: ...
# moment_dict = {'Ai': Buffer, 'Bk': Buffer, 'AiAj': Buffer, 'BkBl': Buffer, 'AiBk': Buffer}
# moments_dict = MomentsDict('A', 'AA', 'B', 'BB', 'AB', 'diag')
# moments_dict = MomentsDict('i', 'ij', 'k', 'kl', 'jk', 'iikk')
moment_dict = MomentsDict(['Ai', 'Bk', 'AiAj', 'BkBl', 'AiBk', 'AiAiBkBk', 'AiAjBkBl'])
def accumulate_moments(layer, _, b):
a = activations[layer]
util.accumulate_moments(moment_dict, a, b)
with autograd_lib.module_hooks(accumulate_moments):
pass
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_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 create_toy_model():
"""
Create model from https://www.wolframcloud.com/obj/yaroslavvb/newton/linear-jacobians-and-hessians.nb
PyTorch works on transposed representation, hence to obtain Y from notebook, do model(A.T).T
"""
model: u.SimpleFullyConnected2 = u.SimpleFullyConnected2([2, 2, 2],
bias=False)
autograd_lib.register(model)
A = torch.tensor([[-1., 4], [3, 0]])
B = torch.tensor([[-4., 3], [2, 6]])
X = torch.tensor([[-5., 0], [-2, -6]], requires_grad=True)
model.layers[0].weight.data.copy_(X)
model.layers[1].weight.data.copy_(B.t())
return A, model
def init_model(B, X, A):
""" Initializes the model Y=B'XA
"""
B, X, A = u.to_pytorches(B, X, A)
n = A.shape[1]
d1, d2 = X.shape
d3 = B.shape[1]
# Do a test using Linear layers instead of matrix multiplies
model: u.SimpleFullyConnected2 = u.SimpleFullyConnected2([d1, d2, d3],
bias=False)
model.layers[0].weight.data.copy_(X)
model.layers[1].weight.data.copy_(B.t())
def eval():
return model(A.t())
return eval, model.layers[0].weight
def test_explicit_hessian():
"""Check computation of hessian of loss(B'WA) from https://github.com/yaroslavvb/kfac_pytorch/blob/master/derivation.pdf
"""
torch.set_default_dtype(torch.float64)
A = torch.tensor([[-1., 4], [3, 0]])
B = torch.tensor([[-4., 3], [2, 6]])
X = torch.tensor([[-5., 0], [-2, -6]], requires_grad=True)
Y = B.t() @ X @ A
u.check_equal(Y, [[-52, 64], [-81, -108]])
loss = torch.sum(Y * Y) / 2
hess0 = u.hessian(loss, X).reshape([4, 4])
hess1 = u.Kron(A @ A.t(), B @ B.t())
u.check_equal(loss, 12512.5)
# PyTorch autograd computes Hessian with respect to row-vectorized parameters, whereas
# autograd_lib uses math convention and does column-vectorized.
# Commuting order of Kronecker product switches between two representations
u.check_equal(hess1.commute(), hess0)
# Do a test using Linear layers instead of matrix multiplies
model: u.SimpleFullyConnected2 = u.SimpleFullyConnected2([2, 2, 2], bias=False)
model.layers[0].weight.data.copy_(X)
# Transpose to match previous results, layers treat dim0 as batch dimension
u.check_equal(model.layers[0](A.t()).t(), [[5, -20], [-16, -8]]) # XA = (A'X0)'
model.layers[1].weight.data.copy_(B.t())
u.check_equal(model(A.t()).t(), Y)
Y = model(A.t()).t() # transpose to data-dimension=columns
loss = torch.sum(Y * Y) / 2
loss.backward()
u.check_equal(model.layers[0].weight.grad, [[-2285, -105], [-1490, -1770]])
G = B @ Y @ A.t()
u.check_equal(model.layers[0].weight.grad, G)
u.check_equal(hess0, u.Kron(B @ B.t(), A @ A.t()))
# compute newton step
u.check_equal(u.Kron([email protected](), [email protected]()).pinv() @ u.vec(G), u.v2c([-5, -2, 0, -6]))
# compute Newton step using factored representation
autograd_lib.add_hooks(model)
Y = model(A.t())
n = 2
loss = torch.sum(Y * Y) / 2
autograd_lib.backprop_hess(Y, hess_type='LeastSquares')
autograd_lib.compute_hess(model, method='kron', attr_name='hess_kron', vecr_order=False, loss_aggregation='sum')
param = model.layers[0].weight
hess2 = param.hess_kron
print(hess2)
u.check_equal(hess2, [[425, 170, -75, -30], [170, 680, -30, -120], [-75, -30, 225, 90], [-30, -120, 90, 360]])
# Gradient test
model.zero_grad()
loss.backward()
u.check_close(u.vec(G).flatten(), u.Vec(param.grad))
# Newton step test
# Method 0: PyTorch native autograd
newton_step0 = param.grad.flatten() @ torch.pinverse(hess0)
newton_step0 = newton_step0.reshape(param.shape)
u.check_equal(newton_step0, [[-5, 0], [-2, -6]])
# Method 1: colummn major order
ihess2 = hess2.pinv()
u.check_equal(ihess2.LL, [[1/16, 1/48], [1/48, 17/144]])
u.check_equal(ihess2.RR, [[2/45, -(1/90)], [-(1/90), 1/36]])
u.check_equal(torch.flatten(hess2.pinv() @ u.vec(G)), [-5, -2, 0, -6])
newton_step1 = (ihess2 @ u.Vec(param.grad)).matrix_form()
# Method2: row major order
ihess2_rowmajor = ihess2.commute()
newton_step2 = ihess2_rowmajor @ u.Vecr(param.grad)
newton_step2 = newton_step2.matrix_form()
u.check_equal(newton_step0, newton_step1)
u.check_equal(newton_step0, newton_step2)
def _test_explicit_hessian_refactored():
"""Check computation of hessian of loss(B'WA) from https://github.com/yaroslavvb/kfac_pytorch/blob/master/derivation.pdf
"""
torch.set_default_dtype(torch.float64)
A = torch.tensor([[-1., 4], [3, 0]])
B = torch.tensor([[-4., 3], [2, 6]])
X = torch.tensor([[-5., 0], [-2, -6]], requires_grad=True)
Y = B.t() @ X @ A
u.check_equal(Y, [[-52, 64], [-81, -108]])
loss = torch.sum(Y * Y) / 2
hess0 = u.hessian(loss, X).reshape([4, 4])
hess1 = u.Kron(A @ A.t(), B @ B.t())
u.check_equal(loss, 12512.5)
# Do a test using Linear layers instead of matrix multiplies
model: u.SimpleFullyConnected2 = u.SimpleFullyConnected2([2, 2, 2], bias=False)
model.layers[0].weight.data.copy_(X)
# Transpose to match previous results, layers treat dim0 as batch dimension
u.check_equal(model.layers[0](A.t()).t(), [[5, -20], [-16, -8]]) # XA = (A'X0)'
model.layers[1].weight.data.copy_(B.t())
u.check_equal(model(A.t()).t(), Y)
Y = model(A.t()).t() # transpose to data-dimension=columns
loss = torch.sum(Y * Y) / 2
loss.backward()
u.check_equal(model.layers[0].weight.grad, [[-2285, -105], [-1490, -1770]])
G = B @ Y @ A.t()
u.check_equal(model.layers[0].weight.grad, G)
autograd_lib.register(model)
activations_dict = autograd_lib.ModuleDict() # todo(y): make save_activations ctx manager automatically create A
with autograd_lib.save_activations(activations_dict):
Y = model(A.t())
Acov = autograd_lib.ModuleDict(autograd_lib.SecondOrderCov)
for layer, activations in activations_dict.items():
print(layer, activations)
Acov[layer].accumulate(activations, activations)
autograd_lib.set_default_activations(activations_dict)
autograd_lib.set_default_Acov(Acov)
B = autograd_lib.ModuleDict(autograd_lib.SymmetricFourthOrderCov)
autograd_lib.backward_accum(Y, "identity", B, retain_graph=False)
print(B[model.layers[0]])
autograd_lib.backprop_hess(Y, hess_type='LeastSquares')
autograd_lib.compute_hess(model, method='kron', attr_name='hess_kron', vecr_order=False, loss_aggregation='sum')
param = model.layers[0].weight
hess2 = param.hess_kron
print(hess2)
u.check_equal(hess2, [[425, 170, -75, -30], [170, 680, -30, -120], [-75, -30, 225, 90], [-30, -120, 90, 360]])
# Gradient test
model.zero_grad()
loss.backward()
u.check_close(u.vec(G).flatten(), u.Vec(param.grad))
# Newton step test
# Method 0: PyTorch native autograd
newton_step0 = param.grad.flatten() @ torch.pinverse(hess0)
newton_step0 = newton_step0.reshape(param.shape)
u.check_equal(newton_step0, [[-5, 0], [-2, -6]])
# Method 1: colummn major order
ihess2 = hess2.pinv()
u.check_equal(ihess2.LL, [[1/16, 1/48], [1/48, 17/144]])
u.check_equal(ihess2.RR, [[2/45, -(1/90)], [-(1/90), 1/36]])
u.check_equal(torch.flatten(hess2.pinv() @ u.vec(G)), [-5, -2, 0, -6])
newton_step1 = (ihess2 @ u.Vec(param.grad)).matrix_form()
# Method2: row major order
ihess2_rowmajor = ihess2.commute()
newton_step2 = ihess2_rowmajor @ u.Vecr(param.grad)
newton_step2 = newton_step2.matrix_form()
u.check_equal(newton_step0, newton_step1)
u.check_equal(newton_step0, newton_step2)
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=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='/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=5,
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('--train_batch_size', type=int, default=64)
parser.add_argument('--stats_batch_size', type=int, default=10000)
parser.add_argument('--lr', type=float, default=1e-3)
parser.add_argument('--weight_decay', type=float, default=1e-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=1)
parser.add_argument('--lmb', type=float, default=1e-3)
parser.add_argument('--uniform',
type=int,
default=0,
help="all layers same size")
parser.add_argument('--redundancy',
type=int,
default=0,
help="duplicate all layers this many times")
args = parser.parse_args()
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)
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
if args.redundancy:
model = u.RedundantFullyConnected2(d,
nonlin=args.nonlin,
bias=args.bias,
dropout=args.dropout,
redundancy=args.redundancy)
else:
model = u.SimpleFullyConnected2(d,
nonlin=args.nonlin,
bias=args.bias,
dropout=args.dropout)
model = model.to(gl.device)
try:
# os.environ['WANDB_SILENT'] = 'true'
if args.wandb:
wandb.init(project='train_ciresan', 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['redundancy'] = args.redundancy
except Exception as e:
print(f"wandb crash with {e}")
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()
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
model.eval()
if args.swa:
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)
model.skip_forward_hooks = False
model.skip_backward_hooks = False
# get gradient values
with u.timeit("backprop_g"):
gl.backward_idx = 0
u.clear_backprops(model)
output = model(data)
loss = loss_fn(output, targets)
loss.backward(retain_graph=True)
u.log_scalar(loss=loss.item())
# get Hessian values
hessian_activations = []
hessian_backprops = []
hessians = [] # list of Hessians in Kronecker form
model.skip_forward_hooks = True
for (i, layer) in enumerate(model.layers):
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[0] * n
assert B_t.shape == (n, d[i + 1])
G = (B_t, A_t)
# g = G.sum(dim=0, keepdim=True) / n # average gradient
g = u.kron_sum(G) / n
assert g.shape == (1, d[i] * d[i + 1])
s.sparsity = torch.sum(layer.output <= 0) / layer.output.numel()
s.mean_activation = torch.mean(A_t)
s.mean_backprop = torch.mean(B_t)
# empirical Fisher
with u.timeit(f'sigma-{i}'):
# efisher = u.kron_cov(G) # G.t() @ G / n
sigma = u.kron_sigma(G, g) # efisher - g.t() @ g
s.sigma_l2 = u.kron_sym_l2_norm(sigma)
s.sigma_erank = u.kron_trace(
sigma) / s.sigma_l2 # torch.trace(sigma)/s.sigma_l2
#############################
# Hessian stats
#############################
# this is a pair of left/right Kronecker fctors
H = hessians[i]
with u.timeit(f"invH-{i}"):
invH = u.kron_inverse(H)
with u.timeit(f"H_l2-{i}"):
s.H_l2 = u.kron_sym_l2_norm(H)
s.iH_l2 = u.kron_sym_l2_norm(invH)
with u.timeit(f"norms-{i}"):
s.H_fro = u.kron_fro_norm(H)
s.invH_fro = u.kron_fro_norm(invH)
s.grad_fro = u.kron_fro_norm(g) # g.flatten().norm()
s.param_fro = layer.weight.data.flatten().norm()
u.kron_nan_check(H)
with u.timeit(f"pinvH-{i}"):
pinvH = u.kron_pinv(H)
def kron_curv_direction(dd: torch.Tensor):
"""Curvature in direction dd, using factored form"""
# dd @ H @ dd.t(), computed by kron_quadratic_form(H, dd)
return u.to_python_scalar(
u.kron_quadratic_form(H, dd) / (dd.flatten().norm()**2))
def kron_loss_direction(dd: torch.Tensor, eps):
"""loss improvement if we take step eps in direction dd"""
# kron_matmul(dd, g) = dd @ g.t()
return u.to_python_scalar(eps * (u.kron_matmul(dd, g)) -
0.5 * eps**2 *
u.kron_quadratic_form(H, dd))
with u.timeit(f'curv-{i}'):
s.grad_curv = kron_curv_direction(g)
s.step_openai = 1 / s.grad_curv if s.grad_curv else 999
s.step_max = 2 / s.H_l2
s.step_min = torch.tensor(2) / u.kron_trace(H)
s.regret_gradient = kron_loss_direction(g, s.step_openai)
with u.timeit(f"batch-{i}"):
# torch.trace(H @ sigma) # (g @ H @ g.t())
s.batch_openai = u.kron_trace_matmul(
H, sigma) / u.kron_quadratic_form(H, g)
s.diversity = torch.norm(G, "fro")**2 / torch.norm(g)**2
# torch.trace(H)
s.H_erank = u.kron_trace(H) / s.H_l2
s.batch_jain_simple = 1 + s.H_erank
u.log_scalars(u.nest_stats(layer.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 test_hessian_multibatch():
"""Test that Kronecker-factored computations still work when splitting work over batches."""
u.seed_random(1)
# torch.set_default_dtype(torch.float64)
gl.project_name = 'test'
gl.logdir_base = '/tmp/runs'
run_name = 'test_hessian_multibatch'
u.setup_logdir_and_event_writer(run_name=run_name)
loss_type = 'CrossEntropy'
data_width = 2
n = 4
d1 = data_width ** 2
o = 10
d = [d1, o]
model = u.SimpleFullyConnected2(d, bias=False, nonlin=False)
model = model.to(gl.device)
dataset = u.TinyMNIST(data_width=data_width, dataset_size=n, loss_type=loss_type)
stats_loader = torch.utils.data.DataLoader(dataset, batch_size=n, shuffle=False)
stats_iter = u.infinite_iter(stats_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
stats_iter = u.infinite_iter(stats_loader)
stats_data, stats_targets = next(stats_iter)
data, targets = stats_data, stats_targets
# Capture Hessian and gradient stats
autograd_lib.enable_hooks()
autograd_lib.clear_backprops(model)
output = model(data)
loss = loss_fn(output, targets)
loss.backward(retain_graph=True)
layer = model.layers[0]
autograd_lib.clear_hess_backprops(model)
autograd_lib.backprop_hess(output, hess_type=loss_type)
autograd_lib.disable_hooks()
# compute Hessian using direct method, compare against PyTorch autograd
hess0 = u.hessian(loss, layer.weight)
autograd_lib.compute_hess(model)
hess1 = layer.weight.hess
u.check_close(hess0.reshape(hess1.shape), hess1, atol=1e-8, rtol=1e-6)
# compute Hessian using factored method. Because Hessian depends on examples for cross entropy, factoring is not exact, raise tolerance
autograd_lib.compute_hess(model, method='kron', attr_name='hess2', vecr_order=True)
hess2 = layer.weight.hess2
u.check_close(hess1, hess2, atol=1e-3, rtol=1e-1)
# compute Hessian using multibatch
# restart iterators
dataset = u.TinyMNIST(data_width=data_width, dataset_size=n, loss_type=loss_type)
assert n % 2 == 0
stats_loader = torch.utils.data.DataLoader(dataset, batch_size=n//2, shuffle=False)
stats_iter = u.infinite_iter(stats_loader)
autograd_lib.compute_cov(model, loss_fn, stats_iter, batch_size=n//2, steps=2)
cov: autograd_lib.LayerCov = layer.cov
hess2: u.Kron = hess2.commute() # get back into AA x BB order
u.check_close(cov.H.value(), hess2)
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():
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_factored_stats_golden_values():
"""Test stats from values generated by non-factored version"""
u.seed_random(1)
u.install_pdb_handler()
torch.set_default_dtype(torch.float32)
parser = argparse.ArgumentParser(description='PyTorch MNIST Example')
args = parser.parse_args()
logdir = u.create_local_logdir('/temp/runs/factored_test')
run_name = os.path.basename(logdir)
gl.event_writer = SummaryWriter(logdir)
print('logging to ', logdir)
loss_type = 'LeastSquares'
args.data_width = 2
args.dataset_size = 5
args.stats_batch_size = 5
d1 = args.data_width**2
args.stats_batch_size = args.dataset_size
args.stats_steps = 1
n = args.stats_batch_size
o = 10
d = [d1, o]
model = u.SimpleFullyConnected2(d, bias=False, nonlin=0)
model = model.to(gl.device)
print(model)
dataset = u.TinyMNIST(data_width=args.data_width,
dataset_size=args.dataset_size,
loss_type=loss_type)
stats_loader = torch.utils.data.DataLoader(
dataset, batch_size=args.stats_batch_size, shuffle=False)
stats_iter = u.infinite_iter(stats_loader)
stats_data, stats_targets = next(stats_iter)
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
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()
data, targets = stats_data, stats_targets
# Capture Hessian and gradient stats
autograd_lib.enable_hooks()
autograd_lib.clear_backprops(model)
with u.timeit("backprop_g"):
output = model(data)
loss = loss_fn(output, targets)
loss.backward(retain_graph=True)
autograd_lib.clear_hess_backprops(model)
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)
autograd_lib.compute_hess(model, method='kron', attr_name='hess2')
autograd_lib.compute_stats_factored(model)
params = list(model.parameters())
assert len(params) == 1
new_values = params[0].stats
golden_values = torch.load('test/factored.pt')
for valname in new_values:
print("Checking ", valname)
if valname == 'sigma_l2':
u.check_close(new_values[valname],
golden_values[valname],
atol=1e-2) # sigma is approximate
elif valname == 'sigma_erank':
u.check_close(new_values[valname],
golden_values[valname],
atol=0.11) # 1.0 vs 1.1
elif valname in ['rho', 'step_div_1_adjusted', 'batch_jain_full']:
continue # lyapunov stats weren't computed correctly in golden set
elif valname in ['batch_openai']:
continue # batch sizes depend on sigma which is approximate
elif valname in ['noise_variance_pinv']:
pass # went from 0.22 to 0.014 after kron factoring (0.01 with full centering, 0.3 with no centering)
elif valname in ['sparsity']:
pass # had a bug in old calc (using integer arithmetic)
else:
u.check_close(new_values[valname],
golden_values[valname],
rtol=1e-4,
atol=1e-6,
label=valname)
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=0, help='skip all stats collection')
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('--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=0)
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('--stats_num_batches', type=int, default=1)
parser.add_argument('--run_name', type=str, default='noname')
parser.add_argument('--launch_blocking', type=int, default=0)
parser.add_argument('--sampled', type=int, default=0)
parser.add_argument('--curv', type=str, default='kfac',
help='decomposition to use for curvature estimates: zero_order, kfac, isserlis or full')
parser.add_argument('--log_spectra', type=int, default=0)
u.seed_random(1)
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
d = [784, 2500, 2000, 1500, 1000, 500, 10]
# number of samples per datapoint. Used to normalize kfac
model = u.SimpleFullyConnected2(d, nonlin=args.nonlin, bias=args.bias, dropout=args.dropout)
model = model.to(gl.device)
autograd_lib.register(model)
assert args.dataset_size >= args.stats_batch_size
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=True,
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_eval_loader = torch.utils.data.DataLoader(test_dataset, batch_size=args.stats_batch_size, shuffle=False,
drop_last=False)
train_eval_loader = torch.utils.data.DataLoader(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
lr = optimizer.param_groups[0]['lr']
print('token_count', gl.token_count)
if last_outer:
u.log_scalars({"time/outer": 1000 * (time.perf_counter() - last_outer)})
print(f'time: {time.perf_counter() - last_outer:.2f}')
last_outer = time.perf_counter()
with u.timeit("validate"):
val_accuracy, val_loss = validate(model, test_eval_loader, f'test (epoch {epoch})')
train_accuracy, train_loss = validate(model, train_eval_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)
def mom_update(buffer, val):
buffer *= 0.9
buffer += val * 0.1
if not args.skip_stats:
# number of samples passed through
n = args.stats_batch_size * args.stats_num_batches
# quanti
forward_stats = defaultdict(lambda: AttrDefault(float))
hessians = defaultdict(lambda: AttrDefault(float))
jacobians = defaultdict(lambda: AttrDefault(float))
fishers = defaultdict(lambda: AttrDefault(float)) # empirical fisher/gradient
quad_fishers = defaultdict(lambda: AttrDefault(float)) # gradient statistics that depend on fisher (4th order moments)
train_regrets = defaultdict(list)
test_regrets1 = defaultdict(list)
test_regrets2 = defaultdict(list)
train_regrets_opt = defaultdict(list)
test_regrets_opt = defaultdict(list)
cosines = defaultdict(list)
dot_products = defaultdict(list)
hessians_histograms = defaultdict(lambda: AttrDefault(u.MyList))
jacobians_histograms = defaultdict(lambda: AttrDefault(u.MyList))
fishers_histograms = defaultdict(lambda: AttrDefault(u.MyList))
quad_fishers_histograms = defaultdict(lambda: AttrDefault(u.MyList))
current = None
current_histograms = None
for i in range(args.stats_num_batches):
activations = {}
backprops = {}
def save_activations(layer, A, _):
activations[layer] = A
forward_stats[layer].AA += torch.einsum("ni,nj->ij", A, A)
print('forward')
with u.timeit("stats_forward"):
with autograd_lib.module_hook(save_activations):
data, targets = next(stats_iter)
output = model(data)
loss = loss_fn(output, targets) * len(output)
def compute_stats(layer, _, B):
A = activations[layer]
if current == fishers:
backprops[layer] = B
# about 27ms per layer
with u.timeit('compute_stats'):
current[layer].BB += torch.einsum("ni,nj->ij", B, B) # TODO(y): index consistency
current[layer].diag += torch.einsum("ni,nj->ij", B * B, A * A)
current[layer].BA += torch.einsum("ni,nj->ij", B, A)
current[layer].a += torch.einsum("ni->i", A)
current[layer].b += torch.einsum("nk->k", B)
current[layer].norm2 += ((A * A).sum(dim=1) * (B * B).sum(dim=1)).sum()
# compute curvatures in direction of all gradiennts
if current is fishers:
assert args.stats_num_batches == 1, "not tested on more than one stats step, currently reusing aggregated moments"
hess = hessians[layer]
jac = jacobians[layer]
Bh, Ah = B @ hess.BB / n, A @ forward_stats[layer].AA / n
Bj, Aj = B @ jac.BB / n, A @ forward_stats[layer].AA / n
norms = ((A * A).sum(dim=1) * (B * B).sum(dim=1))
current[layer].min_norm2 = min(norms)
current[layer].median_norm2 = torch.median(norms)
current[layer].max_norm2 = max(norms)
norms2_hess = ((Ah * A).sum(dim=1) * (Bh * B).sum(dim=1))
norms2_jac = ((Aj * A).sum(dim=1) * (Bj * B).sum(dim=1))
current[layer].norm += norms.sum()
current_histograms[layer].norms.extend(torch.sqrt(norms))
current[layer].curv_hess += (skip_nans(norms2_hess / norms)).sum()
current_histograms[layer].curv_hess.extend(skip_nans(norms2_hess / norms))
current[layer].curv_hess_max += (skip_nans(norms2_hess / norms)).max()
current[layer].curv_hess_median += (skip_nans(norms2_hess / norms)).median()
current_histograms[layer].curv_jac.extend(skip_nans(norms2_jac / norms))
current[layer].curv_jac += (skip_nans(norms2_jac / norms)).sum()
current[layer].curv_jac_max += (skip_nans(norms2_jac / norms)).max()
current[layer].curv_jac_median += (skip_nans(norms2_jac / norms)).median()
current[layer].a_sparsity += torch.sum(A <= 0).float() / A.numel()
current[layer].b_sparsity += torch.sum(B <= 0).float() / B.numel()
current[layer].mean_activation += torch.mean(A)
current[layer].mean_activation2 += torch.mean(A*A)
current[layer].mean_backprop = torch.mean(B)
current[layer].mean_backprop2 = torch.mean(B*B)
current[layer].norms_hess += torch.sqrt(norms2_hess).sum()
current_histograms[layer].norms_hess.extend(torch.sqrt(norms2_hess))
current[layer].norms_jac += norms2_jac.sum()
current_histograms[layer].norms_jac.extend(torch.sqrt(norms2_jac))
normalized_moments = copy.copy(hessians[layer])
normalized_moments.AA = forward_stats[layer].AA
normalized_moments = u.divide_attributes(normalized_moments, n)
train_regrets_ = autograd_lib.offset_losses(A, B, alpha=lr, offset=0, m=normalized_moments,
approx=args.curv)
test_regrets1_ = autograd_lib.offset_losses(A, B, alpha=lr, offset=1, m=normalized_moments,
approx=args.curv)
test_regrets2_ = autograd_lib.offset_losses(A, B, alpha=lr, offset=2, m=normalized_moments,
approx=args.curv)
test_regrets_opt_ = autograd_lib.offset_losses(A, B, alpha=None, offset=2,
m=normalized_moments, approx=args.curv)
train_regrets_opt_ = autograd_lib.offset_losses(A, B, alpha=None, offset=0,
m=normalized_moments, approx=args.curv)
cosines_ = autograd_lib.offset_cosines(A, B)
train_regrets[layer].extend(train_regrets_)
test_regrets1[layer].extend(test_regrets1_)
test_regrets2[layer].extend(test_regrets2_)
train_regrets_opt[layer].extend(train_regrets_opt_)
test_regrets_opt[layer].extend(test_regrets_opt_)
cosines[layer].extend(cosines_)
dot_products[layer].extend(autograd_lib.offset_dotprod(A, B))
# statistics of the form g.Sigma.g
elif current == quad_fishers:
hess = hessians[layer]
sigma = fishers[layer]
jac = jacobians[layer]
Bs, As = B @ sigma.BB / n, A @ forward_stats[layer].AA / n
Bh, Ah = B @ hess.BB / n, A @ forward_stats[layer].AA / n
Bj, Aj = B @ jac.BB / n, A @ forward_stats[layer].AA / n
norms = ((A * A).sum(dim=1) * (B * B).sum(dim=1))
norms2_hess = ((Ah * A).sum(dim=1) * (Bh * B).sum(dim=1))
norms2_jac = ((Aj * A).sum(dim=1) * (Bj * B).sum(dim=1))
norms_sigma = ((As * A).sum(dim=1) * (Bs * B).sum(dim=1))
current[layer].norm += norms.sum() # TODO(y) remove, redundant with norm2 above
current[layer].curv_sigma += (skip_nans(norms_sigma / norms)).sum()
current[layer].curv_sigma_max = skip_nans(norms_sigma / norms).max()
current[layer].curv_sigma_median = skip_nans(norms_sigma / norms).median()
current[layer].curv_hess += skip_nans(norms2_hess / norms).sum()
current[layer].curv_hess_max += skip_nans(norms2_hess / norms).max()
current[layer].lyap_hess_mean += skip_nans(norms_sigma / norms2_hess).mean()
current[layer].lyap_hess_max = max(skip_nans(norms_sigma/norms2_hess))
current[layer].lyap_jac_mean += skip_nans(norms_sigma / norms2_jac).mean()
current[layer].lyap_jac_max = max(skip_nans(norms_sigma/norms2_jac))
print('backward')
with u.timeit("backprop_H"):
with autograd_lib.module_hook(compute_stats):
current = hessians
current_histograms = hessians_histograms
autograd_lib.backward_hessian(output, loss='CrossEntropy', sampled=args.sampled,
retain_graph=True) # 600 ms
current = jacobians
current_histograms = jacobians_histograms
autograd_lib.backward_jacobian(output, sampled=args.sampled, retain_graph=True) # 600 ms
current = fishers
current_histograms = fishers_histograms
model.zero_grad()
loss.backward(retain_graph=True) # 60 ms
current = quad_fishers
current_histograms = quad_fishers_histograms
model.zero_grad()
loss.backward() # 60 ms
print('summarize')
for (i, layer) in enumerate(model.layers):
stats_dict = {'hessian': hessians, 'jacobian': jacobians, 'fisher': fishers}
# evaluate stats from
# https://app.wandb.ai/yaroslavvb/train_ciresan/runs/425pu650?workspace=user-yaroslavvb
for stats_name in stats_dict:
s = AttrDict()
stats = stats_dict[stats_name][layer]
for key in forward_stats[layer]:
# print(f'copying {key} in {stats_name}, {layer}')
try:
assert stats[key] == float()
except:
f"Trying to overwrite {key} in {stats_name}, {layer}"
stats[key] = forward_stats[layer][key]
diag: torch.Tensor = stats.diag / n
# jacobian:
# curv in direction of gradient goes down to roughly 0.3-1
# maximum curvature goes up to 1000-2000
#
# Hessian:
# max curv goes down to 1, in direction of gradient 0.0001
s.diag_l2 = torch.max(diag) # 40 - 3000 smaller than kfac l2 for jac
s.diag_fro = torch.norm(
diag) # jacobian grows to 0.5-1.5, rest falls, layer-5 has phase transition, layer-4 also
s.diag_trace = diag.sum() # jacobian grows 0-1000 (first), 0-150 (last). Almost same as kfac_trace (771 vs 810 kfac). Jacobian has up/down phase transition
s.diag_average = diag.mean()
# normalize for mean loss
BB = stats.BB / n
AA = stats.AA / n
# A_evals, _ = torch.symeig(AA) # averaging 120ms per hit, 90 hits
# B_evals, _ = torch.symeig(BB)
# s.kfac_l2 = torch.max(A_evals) * torch.max(B_evals) # 60x larger than diag_l2. layer0/hess has down/up phase transition. layer5/jacobian has up/down phase transition
s.kfac_trace = torch.trace(AA) * torch.trace(BB) # 0/hess down/up tr, 5/jac sharp phase transition
s.kfac_fro = torch.norm(stats.AA) * torch.norm(
stats.BB) # 0/hess has down/up tr, 5/jac up/down transition
# s.kfac_erank = s.kfac_trace / s.kfac_l2 # first layer has 25, rest 15, all layers go down except last, last noisy
# s.kfac_erank_fro = s.kfac_trace / s.kfac_fro / max(stats.BA.shape)
s.diversity = (stats.norm2 / n) / u.norm_squared(
stats.BA / n) # gradient diversity. Goes up 3x. Bottom layer has most diversity. Jacobian diversity much less noisy than everythingelse
# discrepancy of KFAC based on exact values of diagonal approximation
# average difference normalized by average diagonal magnitude
diag_kfac = torch.einsum('ll,ii->li', BB, AA)
s.kfac_error = (torch.abs(diag_kfac - diag)).mean() / torch.mean(diag.abs())
u.log_scalars(u.nest_stats(f'layer-{i}/{stats_name}', s))
# openai batch size stat
s = AttrDict()
hess = hessians[layer]
jac = jacobians[layer]
fish = fishers[layer]
quad_fish = quad_fishers[layer]
# the following check passes, but is expensive
# if args.stats_num_batches == 1:
# u.check_close(fisher[layer].BA, layer.weight.grad)
def trsum(A, B):
return (A * B).sum() # computes tr(AB')
grad = fishers[layer].BA / n
s.grad_fro = torch.norm(grad)
# get norms
s.lyap_hess_max = quad_fish.lyap_hess_max
s.lyap_hess_ave = quad_fish.lyap_hess_sum / n
s.lyap_jac_max = quad_fish.lyap_jac_max
s.lyap_jac_ave = quad_fish.lyap_jac_sum / n
s.hess_trace = hess.diag.sum() / n
s.jac_trace = jac.diag.sum() / n
# Version 1 of Jain stochastic rates, use Hessian for curvature
b = args.train_batch_size
s.hess_curv = trsum((hess.BB / n) @ grad @ (hess.AA / n), grad) / trsum(grad, grad)
s.jac_curv = trsum((jac.BB / n) @ grad @ (jac.AA / n), grad) / trsum(grad, grad)
# compute gradient noise statistics
# fish.BB has /n factor twice, hence don't need extra /n on fish.AA
# after sampling, hess_noise,jac_noise became 100x smaller, but normalized is unaffected
s.hess_noise = (trsum(hess.AA / n, fish.AA / n) * trsum(hess.BB / n, fish.BB / n))
s.jac_noise = (trsum(jac.AA / n, fish.AA / n) * trsum(jac.BB / n, fish.BB / n))
s.hess_noise_centered = s.hess_noise - trsum(hess.BB / n @ grad, grad @ hess.AA / n)
s.jac_noise_centered = s.jac_noise - trsum(jac.BB / n @ grad, grad @ jac.AA / n)
s.openai_gradient_noise = (fish.norms_hess / n) / trsum(hess.BB / n @ grad, grad @ hess.AA / n)
s.mean_norm = torch.sqrt(fish.norm2) / n
s.min_norm = torch.sqrt(fish.min_norm2)
s.median_norm = torch.sqrt(fish.median_norm2)
s.max_norm = torch.sqrt(fish.max_norm2)
s.enorms = u.norm_squared(grad)
s.a_sparsity = fish.a_sparsity
s.b_sparsity = fish.b_sparsity
s.mean_activation = fish.mean_activation
s.msr_activation = torch.sqrt(fish.mean_activation2)
s.mean_backprop = fish.mean_backprop
s.msr_backprop = torch.sqrt(fish.mean_backprop2)
s.norms_centered = fish.norm2 / n - u.norm_squared(grad)
s.norms_hess = fish.norms_hess / n
s.norms_jac = fish.norms_jac / n
s.hess_curv_grad = fish.curv_hess / n # phase transition, hits minimum loss in layer 1, then starts going up. Other layers take longer to reach minimum. Decreases with depth.
s.hess_curv_grad_max = fish.curv_hess_max # phase transition, hits minimum loss in layer 1, then starts going up. Other layers take longer to reach minimum. Decreases with depth.
s.hess_curv_grad_median = fish.curv_hess_median # phase transition, hits minimum loss in layer 1, then starts going up. Other layers take longer to reach minimum. Decreases with depth.
s.sigma_curv_grad = quad_fish.curv_sigma / n
s.sigma_curv_grad_max = quad_fish.curv_sigma_max
s.sigma_curv_grad_median = quad_fish.curv_sigma_median
s.band_bottou = 0.5 * lr * s.sigma_curv_grad / s.hess_curv_grad
s.band_bottou_stoch = 0.5 * lr * quad_fish.curv_ratio / n
s.band_yaida = 0.25 * lr * s.mean_norm**2
s.band_yaida_centered = 0.25 * lr * s.norms_centered
s.jac_curv_grad = fish.curv_jac / n # this one has much lower variance than jac_curv. Reaches peak at 10k steps, also kfac error reaches peak there. Decreases with depth except for last layer.
s.jac_curv_grad_max = fish.curv_jac_max # this one has much lower variance than jac_curv. Reaches peak at 10k steps, also kfac error reaches peak there. Decreases with depth except for last layer.
s.jac_curv_grad_median = fish.curv_jac_median # this one has much lower variance than jac_curv. Reaches peak at 10k steps, also kfac error reaches peak there. Decreases with depth except for last layer.
# OpenAI gradient noise statistics
s.hess_noise_normalized = s.hess_noise_centered / (fish.norms_hess / n)
s.jac_noise_normalized = s.jac_noise / (fish.norms_jac / n)
train_regrets_, test_regrets1_, test_regrets2_, train_regrets_opt_, test_regrets_opt_, cosines_, dot_products_ = (torch.stack(r[layer]) for r in (train_regrets, test_regrets1, test_regrets2, train_regrets_opt, test_regrets_opt, cosines, dot_products))
s.train_regret = train_regrets_.median() # use median because outliers make it hard to see the trend
s.test_regret1 = test_regrets1_.median()
s.test_regret2 = test_regrets2_.median()
s.test_regret_opt = test_regrets_opt_.median()
s.train_regret_opt = train_regrets_opt_.median()
s.mean_dot_product = torch.mean(dot_products_)
s.median_dot_product = torch.median(dot_products_)
a = [1, 2, 3]
s.median_cosine = cosines_.median()
s.mean_cosine = cosines_.mean()
# get learning rates
L1 = s.hess_curv_grad / n
L2 = s.jac_curv_grad / n
diversity = (fish.norm2 / n) / u.norm_squared(grad)
robust_diversity = (fish.norm2 / n) / fish.median_norm2
dotprod_diversity = fish.median_norm2 / s.median_dot_product
s.lr1 = 2 / (L1 * diversity)
s.lr2 = 2 / (L2 * diversity)
s.lr3 = 2 / (L2 * robust_diversity)
s.lr4 = 2 / (L2 * dotprod_diversity)
hess_A = u.symeig_pos_evals(hess.AA / n)
hess_B = u.symeig_pos_evals(hess.BB / n)
fish_A = u.symeig_pos_evals(fish.AA / n)
fish_B = u.symeig_pos_evals(fish.BB / n)
jac_A = u.symeig_pos_evals(jac.AA / n)
jac_B = u.symeig_pos_evals(jac.BB / n)
u.log_scalars({f'layer-{i}/hessA_erank': erank(hess_A)})
u.log_scalars({f'layer-{i}/hessB_erank': erank(hess_B)})
u.log_scalars({f'layer-{i}/fishA_erank': erank(fish_A)})
u.log_scalars({f'layer-{i}/fishB_erank': erank(fish_B)})
u.log_scalars({f'layer-{i}/jacA_erank': erank(jac_A)})
u.log_scalars({f'layer-{i}/jacB_erank': erank(jac_B)})
gl.event_writer.add_histogram(f'layer-{i}/hist_hess_eig', u.outer(hess_A, hess_B).flatten(), gl.get_global_step())
gl.event_writer.add_histogram(f'layer-{i}/hist_fish_eig', u.outer(hess_A, hess_B).flatten(), gl.get_global_step())
gl.event_writer.add_histogram(f'layer-{i}/hist_jac_eig', u.outer(hess_A, hess_B).flatten(), gl.get_global_step())
s.hess_l2 = max(hess_A) * max(hess_B)
s.jac_l2 = max(jac_A) * max(jac_B)
s.fish_l2 = max(fish_A) * max(fish_B)
s.hess_trace = hess.diag.sum() / n
s.jain1_sto = 1/(s.hess_trace + 2 * s.hess_l2)
s.jain1_det = 1/s.hess_l2
s.jain1_lr = (1 / b) * (1/s.jain1_sto) + (b - 1) / b * (1/s.jain1_det)
s.jain1_lr = 2 / s.jain1_lr
s.regret_ratio = (
train_regrets_opt_ / test_regrets_opt_).median() # ratio between train and test regret, large means overfitting
u.log_scalars(u.nest_stats(f'layer-{i}', s))
# compute stats that would let you bound rho
if i == 0: # only compute this once, for output layer
hhh = hessians[model.layers[-1]].BB / n
fff = fishers[model.layers[-1]].BB / n
d = fff.shape[0]
L = u.lyapunov_spectral(hhh, 2 * fff, cond=1e-8)
L_evals = u.symeig_pos_evals(L)
Lcheap = fff @ u.pinv(hhh, cond=1e-8)
Lcheap_evals = u.eig_real(Lcheap)
u.log_scalars({f'mismatch/rho': d/erank(L_evals)})
u.log_scalars({f'mismatch/rho_cheap': d/erank(Lcheap_evals)})
u.log_scalars({f'mismatch/diagonalizability': erank(L_evals)/erank(Lcheap_evals)}) # 1 means diagonalizable
u.log_spectrum(f'mismatch/sigma', u.symeig_pos_evals(fff), loglog=False)
u.log_spectrum(f'mismatch/hess', u.symeig_pos_evals(hhh), loglog=False)
u.log_spectrum(f'mismatch/lyapunov', L_evals, loglog=True)
u.log_spectrum(f'mismatch/lyapunov_cheap', Lcheap_evals, loglog=True)
gl.event_writer.add_histogram(f'layer-{i}/hist_grad_norms', u.to_numpy(fishers_histograms[layer].norms.value()), gl.get_global_step())
gl.event_writer.add_histogram(f'layer-{i}/hist_grad_norms_hess', u.to_numpy(fishers_histograms[layer].norms_hess.value()), gl.get_global_step())
gl.event_writer.add_histogram(f'layer-{i}/hist_curv_jac', u.to_numpy(fishers_histograms[layer].curv_jac.value()), gl.get_global_step())
gl.event_writer.add_histogram(f'layer-{i}/hist_curv_hess', u.to_numpy(fishers_histograms[layer].curv_hess.value()), gl.get_global_step())
gl.event_writer.add_histogram(f'layer-{i}/hist_cosines', u.to_numpy(cosines[layer]), gl.get_global_step())
if args.log_spectra:
with u.timeit('spectrum'):
# 2/alpha
# s.jain1_lr = (1 / b) * s.jain1_sto + (b - 1) / b * s.jain1_det
# s.jain1_lr = 1 / s.jain1_lr
# hess.diag_trace, jac.diag_trace
# Version 2 of Jain stochastic rates, use Jacobian squared for curvature
s.jain2_sto = s.lyap_jac_max * s.jac_trace / s.lyap_jac_ave
s.jain2_det = s.jac_l2
s.jain2_lr = (1 / b) * s.jain2_sto + (b - 1) / b * s.jain2_det
s.jain2_lr = 1 / s.jain2_lr
u.log_spectrum(f'layer-{i}/hess_A', hess_A)
u.log_spectrum(f'layer-{i}/hess_B', hess_B)
u.log_spectrum(f'layer-{i}/hess_AB', u.outer(hess_A, hess_B).flatten())
u.log_spectrum(f'layer-{i}/jac_A', jac_A)
u.log_spectrum(f'layer-{i}/jac_B', jac_B)
u.log_spectrum(f'layer-{i}/fish_A', fish_A)
u.log_spectrum(f'layer-{i}/fish_B', fish_B)
u.log_scalars({f'layer-{i}/trace_ratio': fish_B.sum()/hess_B.sum()})
L = torch.eig(u.lyapunov_spectral(hess.BB, 2*fish.BB, cond=1e-8))[0]
L = L[:, 0] # extract real part
L = L.sort()[0]
L = torch.flip(L, [0])
L_cheap = torch.eig(fish.BB @ u.pinv(hess.BB, cond=1e-8))[0]
L_cheap = L_cheap[:, 0] # extract real part
L_cheap = L_cheap.sort()[0]
L_cheap = torch.flip(L_cheap, [0])
d = len(hess_B)
u.log_spectrum(f'layer-{i}/Lyap', L)
u.log_spectrum(f'layer-{i}/Lyap_cheap', L_cheap)
u.log_scalars({f'layer-{i}/dims': d})
u.log_scalars({f'layer-{i}/L_erank': erank(L)})
u.log_scalars({f'layer-{i}/L_cheap_erank': erank(L_cheap)})
u.log_scalars({f'layer-{i}/rho': d/erank(L)})
u.log_scalars({f'layer-{i}/rho_cheap': d/erank(L_cheap)})
model.train()
with u.timeit('train'):
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.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 test_factored_hessian():
""""Simple test to ensure Hessian computation is working.
In a linear neural network with squared loss, Newton step will converge in one step.
Compute stats after minimizing, pass sanity checks.
"""
u.seed_random(1)
loss_type = 'LeastSquares'
data_width = 2
n = 5
d1 = data_width ** 2
o = 10
d = [d1, o]
model = u.SimpleFullyConnected2(d, bias=False, nonlin=False)
model = model.to(gl.device)
print(model)
dataset = u.TinyMNIST(data_width=data_width, dataset_size=n, loss_type=loss_type)
stats_loader = torch.utils.data.DataLoader(dataset, batch_size=n, shuffle=False)
stats_iter = u.infinite_iter(stats_loader)
stats_data, stats_targets = next(stats_iter)
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
data, targets = stats_data, stats_targets
# Capture Hessian and gradient stats
autograd_lib.enable_hooks()
autograd_lib.clear_backprops(model)
output = model(data)
loss = loss_fn(output, targets)
print(loss)
loss.backward(retain_graph=True)
layer = model.layers[0]
autograd_lib.clear_hess_backprops(model)
autograd_lib.backprop_hess(output, hess_type=loss_type)
autograd_lib.disable_hooks()
# compute Hessian using direct method, compare against PyTorch autograd
hess0 = u.hessian(loss, layer.weight)
autograd_lib.compute_hess(model)
hess1 = layer.weight.hess
print(hess1)
u.check_close(hess0.reshape(hess1.shape), hess1, atol=1e-9, rtol=1e-6)
# compute Hessian using factored method
autograd_lib.compute_hess(model, method='kron', attr_name='hess2', vecr_order=True)
# s.regret_newton = vecG.t() @ pinvH.commute() @ vecG.t() / 2 # TODO(y): figure out why needed transposes
hess2 = layer.weight.hess2
u.check_close(hess1, hess2, atol=1e-9, rtol=1e-6)
# Newton step in regular notation
g1 = layer.weight.grad.flatten()
newton1 = hess1 @ g1
g2 = u.Vecr(layer.weight.grad)
newton2 = g2 @ hess2
u.check_close(newton1, newton2, atol=1e-9, rtol=1e-6)
# compute regret in factored notation, compare against actual drop in loss
regret1 = g1 @ hess1.pinverse() @ g1 / 2
regret2 = g2 @ hess2.pinv() @ g2 / 2
u.check_close(regret1, regret2)
current_weight = layer.weight.detach().clone()
param: torch.nn.Parameter = layer.weight
# param.data.sub_((hess1.pinverse() @ g1).reshape(param.shape))
# output = model(data)
# loss = loss_fn(output, targets)
# print("result 1", loss)
# param.data.sub_((hess1.pinverse() @ u.vec(layer.weight.grad)).reshape(param.shape))
# output = model(data)
# loss = loss_fn(output, targets)
# print("result 2", loss)
# param.data.sub_((u.vec(layer.weight.grad).t() @ hess1.pinverse()).reshape(param.shape))
# output = model(data)
# loss = loss_fn(output, targets)
# print("result 3", loss)
#
del layer.weight.grad
output = model(data)
loss = loss_fn(output, targets)
loss.backward()
param.data.sub_(u.unvec(hess1.pinverse() @ u.vec(layer.weight.grad), layer.weight.shape[0]))
output = model(data)
loss = loss_fn(output, targets)
print("result 4", loss)
# param.data.sub_((g1 @ hess1.pinverse() @ g1).reshape(param.shape))
print(loss)
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.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='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
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()
