def __call__(self, global_feat, labels):
global_feat = l2_norm(global_feat)
dist_mat = euclidean_dist(global_feat, global_feat)
dist_ap, dist_an = hard_example_mining(dist_mat, labels)
y = dist_an.new().resize_as_(dist_an).fill_(1)
if self.margin is not None:
loss = self.ranking_loss(dist_an, dist_ap, y)
else:
loss = self.ranking_loss(dist_an - dist_ap, y)
return loss
def main():
# for kernel_size=1, mean kron factoring works for any image size
main_vals = AttrDict(n=2,
kernel_size=1,
image_size=625,
num_channels=5,
num_layers=4,
loss='CrossEntropy',
nonlin=False)
hess_list1 = compute_hess(method='exact', **main_vals)
hess_list2 = compute_hess(method='kron', **main_vals)
value_error = max(
[u.symsqrt_dist(h1, h2) for h1, h2 in zip(hess_list1, hess_list2)])
magnitude_error = max([
u.l2_norm(h2) / u.l2_norm(h1)
for h1, h2 in zip(hess_list1, hess_list2)
])
print(value_error)
print(magnitude_error)
dimension_vals = dict(image_size=[2, 3, 4, 5, 6],
num_channels=range(2, 12),
kernel_size=[1, 2, 3, 4, 5])
for method in ['mean_kron', 'kron']: # , 'experimental_kfac']:
print()
print('=' * 10, method, '=' * 40)
for dimension in ['image_size', 'num_channels', 'kernel_size']:
value_errors = []
magnitude_errors = []
for val in dimension_vals[dimension]:
vals = AttrDict(main_vals.copy())
vals.method = method
vals[dimension] = val
vals.image_size = max(vals.image_size,
vals.kernel_size**vals.num_layers)
# print(vals)
vals_exact = AttrDict(vals.copy())
vals_exact.method = 'exact'
hess_list1 = compute_hess(**vals_exact)
hess_list2 = compute_hess(**vals)
magnitude_error = max([
u.l2_norm(h2) / u.l2_norm(h1)
for h1, h2 in zip(hess_list1, hess_list2)
])
hess_list1 = [h / u.l2_norm(h) for h in hess_list1]
hess_list2 = [h / u.l2_norm(h) for h in hess_list2]
value_error = max([
u.symsqrt_dist(h1, h2)
for h1, h2 in zip(hess_list1, hess_list2)
])
value_errors.append(value_error)
magnitude_errors.append(magnitude_error.item())
print(dimension)
print(' value: :', value_errors)
print(' magnitude :', u.format_list(magnitude_errors))
def forward(self, img):
results = []
for model, w in zip(self.models, self.weights):
if self.tta:
tta_preds = []
for trans_img in self.get_TTA(img):
feat, _ = model(trans_img)
tta_preds.append(feat)
mean_pred = torch.mean(torch.stack(tta_preds), dim=0)
results.append(l2_norm(mean_pred) * w)
else:
feat, _ = model(img)
results.append(feat * w)
if len(results) == 1:
return results[0]
if self.reduction in {'cat', 'concat'}:
return l2_norm(torch.cat(results, dim=-1))
elif self.reduction == 'mean':
return l2_norm(torch.mean(torch.stack(results), dim=0))
return torch.stack(results)
def inference(model, test_loader, tqdm=tqdm, normalize=False):
embeds = []
is_ensemble = isinstance(model, EnsembleModels)
if not is_ensemble:
model.eval()
with torch.no_grad():
for i, img in enumerate(tqdm(test_loader)):
img = img.cuda()
feat = model(img)
if not is_ensemble:
feat = feat[1]
if normalize:
feat = l2_norm(feat)
image_embeddings = feat.detach().cpu().numpy()
embeds.append(image_embeddings)
gc.collect()
return np.concatenate(embeds)
def val_epoch(model, valid_loader, criterion, valid_df, args):
model.eval()
embeds = []
bar = tqdm(valid_loader)
with torch.no_grad():
for image, target in bar:
image, target = image.cuda(), target.cuda()
feat, _ = model(image)
feat = l2_norm(feat)
embeds.append(feat.detach().cpu().numpy())
embeds = np.concatenate(embeds)
preds, _ = search_similiar_images(embeds, valid_df)
_, val_f1_score = row_wise_f1_score(valid_df.target, preds)
return val_f1_score
def main():
attemp_count = 0
while os.path.exists(f"{args.logdir}{attemp_count:02d}"):
attemp_count += 1
logdir = f"{args.logdir}{attemp_count:02d}"
run_name = os.path.basename(logdir)
gl.event_writer = SummaryWriter(logdir)
print(f"Logging to {run_name}")
u.seed_random(1)
try:
# os.environ['WANDB_SILENT'] = 'true'
if args.wandb:
wandb.init(project='curv_train_tiny', name=run_name)
wandb.tensorboard.patch(tensorboardX=False)
wandb.config['train_batch'] = args.train_batch_size
wandb.config['stats_batch'] = args.stats_batch_size
wandb.config['method'] = args.method
except Exception as e:
print(f"wandb crash with {e}")
# data_width = 4
# targets_width = 2
d1 = args.data_width**2
d2 = 10
d3 = args.targets_width**2
o = d3
n = args.stats_batch_size
d = [d1, d2, d3]
model = u.SimpleFullyConnected(d, nonlin=args.nonlin)
optimizer = torch.optim.SGD(model.parameters(), lr=0.1, momentum=0.9)
dataset = u.TinyMNIST(data_width=args.data_width,
targets_width=args.targets_width,
dataset_size=args.dataset_size)
train_loader = torch.utils.data.DataLoader(
dataset,
batch_size=args.train_batch_size,
shuffle=False,
drop_last=True)
train_iter = u.infinite_iter(train_loader)
stats_loader = torch.utils.data.DataLoader(
dataset,
batch_size=args.stats_batch_size,
shuffle=False,
drop_last=True)
stats_iter = u.infinite_iter(stats_loader)
def capture_activations(module, input, _output):
if skip_forward_hooks:
return
assert gl.backward_idx == 0 # no need to forward-prop on Hessian computation
assert not hasattr(
module, 'activations'
), "Seeing activations from previous forward, call util.zero_grad to clear"
assert len(input) == 1, "this works for single input layers only"
setattr(module, "activations", input[0].detach())
def capture_backprops(module: nn.Module, _input, output):
if skip_backward_hooks:
return
assert len(output) == 1, "this works for single variable layers only"
if gl.backward_idx == 0:
assert not hasattr(
module, 'backprops'
), "Seeing results of previous autograd, call util.zero_grad to clear"
setattr(module, 'backprops', [])
assert gl.backward_idx == len(module.backprops)
module.backprops.append(output[0])
def save_grad(param: nn.Parameter) -> Callable[[torch.Tensor], None]:
"""Hook to save gradient into 'param.saved_grad', so it can be accessed after model.zero_grad(). Only stores gradient
if the value has not been set, call util.zero_grad to clear it."""
def save_grad_fn(grad):
if not hasattr(param, 'saved_grad'):
setattr(param, 'saved_grad', grad)
return save_grad_fn
for layer in model.layers:
layer.register_forward_hook(capture_activations)
layer.register_backward_hook(capture_backprops)
layer.weight.register_hook(save_grad(layer.weight))
def loss_fn(data, targets):
err = data - targets.view(-1, data.shape[1])
assert len(data) == len(targets)
return torch.sum(err * err) / 2 / len(data)
gl.token_count = 0
for step in range(args.stats_steps):
data, targets = next(stats_iter)
skip_forward_hooks = False
skip_backward_hooks = False
# get gradient values
gl.backward_idx = 0
u.zero_grad(model)
output = model(data)
loss = loss_fn(output, targets)
loss.backward(retain_graph=True)
print("loss", loss.item())
# get Hessian values
skip_forward_hooks = True
id_mat = torch.eye(o)
u.log_scalars({'loss': loss.item()})
# o = 0
for out_idx in range(o):
model.zero_grad()
# backprop to get section of batch output jacobian for output at position out_idx
output = model(
data
) # opt: using autograd.grad means I don't have to zero_grad
ei = id_mat[out_idx]
bval = torch.stack([ei] * n)
gl.backward_idx = out_idx + 1
output.backward(bval)
skip_backward_hooks = True #
for (i, layer) in enumerate(model.layers):
s = AttrDefault(str, {}) # dictionary-like object for layer stats
#############################
# Gradient stats
#############################
A_t = layer.activations
assert A_t.shape == (n, d[i])
# add factor of n because backprop takes loss averaged over batch, while we need per-example loss
B_t = layer.backprops[0] * n
assert B_t.shape == (n, d[i + 1])
G = u.khatri_rao_t(B_t, A_t) # batch loss Jacobian
assert G.shape == (n, d[i] * d[i + 1])
g = G.sum(dim=0, keepdim=True) / n # average gradient
assert g.shape == (1, d[i] * d[i + 1])
if args.autograd_check:
u.check_close(B_t.t() @ A_t / n, layer.weight.saved_grad)
u.check_close(g.reshape(d[i + 1], d[i]),
layer.weight.saved_grad)
# empirical Fisher
efisher = G.t() @ G / n
sigma = efisher - g.t() @ g
# u.dump(sigma, f'/tmp/sigmas/{step}-{i}')
s.sigma_l2 = u.l2_norm(sigma)
#############################
# Hessian stats
#############################
A_t = layer.activations
Bh_t = [layer.backprops[out_idx + 1] for out_idx in range(o)]
Amat_t = torch.cat([A_t] * o, dim=0)
Bmat_t = torch.cat(Bh_t, dim=0)
assert Amat_t.shape == (n * o, d[i])
assert Bmat_t.shape == (n * o, d[i + 1])
Jb = u.khatri_rao_t(Bmat_t,
Amat_t) # batch Jacobian, in row-vec format
H = Jb.t() @ Jb / n
pinvH = u.pinv(H)
s.hess_l2 = u.l2_norm(H)
s.invhess_l2 = u.l2_norm(pinvH)
s.hess_fro = H.flatten().norm()
s.invhess_fro = pinvH.flatten().norm()
s.jacobian_l2 = u.l2_norm(Jb)
s.grad_fro = g.flatten().norm()
s.param_fro = layer.weight.data.flatten().norm()
u.nan_check(H)
if args.autograd_check:
model.zero_grad()
output = model(data)
loss = loss_fn(output, targets)
H_autograd = u.hessian(loss, layer.weight)
H_autograd = H_autograd.reshape(d[i] * d[i + 1],
d[i] * d[i + 1])
u.check_close(H, H_autograd)
# u.dump(sigma, f'/tmp/sigmas/H-{step}-{i}')
def loss_direction(dd: torch.Tensor, eps):
"""loss improvement if we take step eps in direction dd"""
return u.to_python_scalar(eps * (dd @ g.t()) -
0.5 * eps**2 * dd @ H @ dd.t())
def curv_direction(dd: torch.Tensor):
"""Curvature in direction dd"""
return u.to_python_scalar(dd @ H @ dd.t() /
dd.flatten().norm()**2)
s.regret_newton = u.to_python_scalar(g @ u.pinv(H) @ g.t() / 2)
s.grad_curv = curv_direction(g)
ndir = g @ u.pinv(H) # newton direction
s.newton_curv = curv_direction(ndir)
setattr(layer.weight, 'pre',
u.pinv(H)) # save Newton preconditioner
s.step_openai = 1 / s.grad_curv if s.grad_curv else 999
s.newton_fro = ndir.flatten().norm(
) # frobenius norm of Newton update
s.regret_gradient = loss_direction(g, s.step_openai)
u.log_scalars(u.nest_stats(layer.name, s))
# gradient steps
for i in range(args.train_steps):
optimizer.zero_grad()
data, targets = next(train_iter)
model.zero_grad()
output = model(data)
loss = loss_fn(output, targets)
loss.backward()
u.log_scalar(train_loss=loss.item())
if args.method != 'newton':
optimizer.step()
else:
for (layer_idx, layer) in enumerate(model.layers):
param: torch.nn.Parameter = layer.weight
param_data: torch.Tensor = param.data
param_data.copy_(param_data - 0.1 * param.grad)
if layer_idx != 1: # only update 1 layer with Newton, unstable otherwise
continue
u.nan_check(layer.weight.pre)
u.nan_check(param.grad.flatten())
u.nan_check(u.v2r(param.grad.flatten()) @ layer.weight.pre)
param_new_flat = u.v2r(param_data.flatten()) - u.v2r(
param.grad.flatten()) @ layer.weight.pre
u.nan_check(param_new_flat)
param_data.copy_(param_new_flat.reshape(param_data.shape))
gl.token_count += data.shape[0]
gl.event_writer.close()
def test_hessian():
"""Tests of Hessian computation."""
u.seed_random(1)
batch_size = 500
data_width = 4
targets_width = 4
d1 = data_width ** 2
d2 = 10
d3 = targets_width ** 2
o = d3
N = batch_size
d = [d1, d2, d3]
dataset = u.TinyMNIST(data_width=data_width, targets_width=targets_width, dataset_size=batch_size)
trainloader = torch.utils.data.DataLoader(dataset, batch_size=batch_size, shuffle=False)
train_iter = iter(trainloader)
data, targets = next(train_iter)
def loss_fn(data, targets):
assert len(data) == len(targets)
err = data - targets.view(-1, data.shape[1])
return torch.sum(err * err) / 2 / len(data)
u.seed_random(1)
model: u.SimpleModel = u.SimpleFullyConnected(d, nonlin=False, bias=True)
# backprop hessian and compare against autograd
hessian_backprop = u.HessianExactSqrLoss()
output = model(data)
for bval in hessian_backprop(output):
output.backward(bval, retain_graph=True)
i, layer = next(enumerate(model.layers))
A_t = layer.activations
Bh_t = layer.backprops_list
H, Hb = u.hessian_from_backprops(A_t, Bh_t, bias=True)
model.disable_hooks()
H_autograd = u.hessian(loss_fn(model(data), targets), layer.weight)
u.check_close(H, H_autograd.reshape(d[i + 1] * d[i], d[i + 1] * d[i]),
rtol=1e-4, atol=1e-7)
Hb_autograd = u.hessian(loss_fn(model(data), targets), layer.bias)
u.check_close(Hb, Hb_autograd, rtol=1e-4, atol=1e-7)
# check first few per-example Hessians
Hi, Hb_i = u.per_example_hess(A_t, Bh_t, bias=True)
u.check_close(H, Hi.mean(dim=0))
u.check_close(Hb, Hb_i.mean(dim=0), atol=2e-6, rtol=1e-5)
for xi in range(5):
loss = loss_fn(model(data[xi:xi + 1, ...]), targets[xi:xi + 1])
H_autograd = u.hessian(loss, layer.weight)
u.check_close(Hi[xi], H_autograd.reshape(d[i + 1] * d[i], d[i + 1] * d[i]))
Hbias_autograd = u.hessian(loss, layer.bias)
u.check_close(Hb_i[i], Hbias_autograd)
# get subsampled Hessian
u.seed_random(1)
model = u.SimpleFullyConnected(d, nonlin=False)
hessian_backprop = u.HessianSampledSqrLoss(num_samples=1)
output = model(data)
for bval in hessian_backprop(output):
output.backward(bval, retain_graph=True)
model.disable_hooks()
i, layer = next(enumerate(model.layers))
H_approx1 = u.hessian_from_backprops(layer.activations, layer.backprops_list)
# get subsampled Hessian with more samples
u.seed_random(1)
model = u.SimpleFullyConnected(d, nonlin=False)
hessian_backprop = u.HessianSampledSqrLoss(num_samples=o)
output = model(data)
for bval in hessian_backprop(output):
output.backward(bval, retain_graph=True)
model.disable_hooks()
i, layer = next(enumerate(model.layers))
H_approx2 = u.hessian_from_backprops(layer.activations, layer.backprops_list)
assert abs(u.l2_norm(H) / u.l2_norm(H_approx1) - 1) < 0.08, abs(u.l2_norm(H) / u.l2_norm(H_approx1) - 1) # 0.0612
assert abs(u.l2_norm(H) / u.l2_norm(H_approx2) - 1) < 0.03, abs(u.l2_norm(H) / u.l2_norm(H_approx2) - 1) # 0.0239
assert u.kl_div_cov(H_approx1, H) < 0.3, u.kl_div_cov(H_approx1, H) # 0.222
assert u.kl_div_cov(H_approx2, H) < 0.2, u.kl_div_cov(H_approx2, H) # 0.1233
def compute_layer_stats(layer):
refreeze = False
if hasattr(layer, 'frozen') and layer.frozen:
u.unfreeze(layer)
refreeze = True
s = AttrDefault(str, {})
n = args.stats_batch_size
param = u.get_param(layer)
_d = len(param.flatten()) # dimensionality of parameters
layer_idx = model.layers.index(layer)
# TODO: get layer type, include it in name
assert layer_idx >= 0
assert stats_data.shape[0] == n
def backprop_loss():
model.zero_grad()
output = model(
stats_data) # use last saved data batch for backprop
loss = compute_loss(output, stats_targets)
loss.backward()
return loss, output
def backprop_output():
model.zero_grad()
output = model(stats_data)
output.backward(gradient=torch.ones_like(output))
return output
# per-example gradients, n, d
_loss, _output = backprop_loss()
At = layer.data_input
Bt = layer.grad_output * n
G = u.khatri_rao_t(At, Bt)
g = G.sum(dim=0, keepdim=True) / n
u.check_close(g, u.vec(param.grad).t())
s.diversity = torch.norm(G, "fro")**2 / g.flatten().norm()**2
s.grad_fro = g.flatten().norm()
s.param_fro = param.data.flatten().norm()
pos_activations = torch.sum(layer.data_output > 0)
neg_activations = torch.sum(layer.data_output <= 0)
s.a_sparsity = neg_activations.float() / (
pos_activations + neg_activations) # 1 sparsity means all 0's
activation_size = len(layer.data_output.flatten())
s.a_magnitude = torch.sum(layer.data_output) / activation_size
_output = backprop_output()
B2t = layer.grad_output
J = u.khatri_rao_t(At, B2t) # batch output Jacobian
H = J.t() @ J / n
s.hessian_l2 = u.l2_norm(H)
s.jacobian_l2 = u.l2_norm(J)
J1 = J.sum(dim=0) / n # single output Jacobian
s.J1_l2 = J1.norm()
# newton decrement
def loss_direction(direction, eps):
"""loss improvement if we take step eps in direction dir"""
return u.to_python_scalar(eps * (direction @ g.t()) - 0.5 *
eps**2 * direction @ H @ direction.t())
s.regret_newton = u.to_python_scalar(g @ u.pinv(H) @ g.t() / 2)
# TODO: gradient diversity is stuck at 1
# TODO: newton/gradient angle
# TODO: newton step magnitude
s.grad_curvature = u.to_python_scalar(
g @ H @ g.t()) # curvature in direction of g
s.step_openai = u.to_python_scalar(
s.grad_fro**2 / s.grad_curvature) if s.grad_curvature else 999
s.regret_gradient = loss_direction(g, s.step_openai)
if refreeze:
u.freeze(layer)
return s
def test_l2_norm():
mat = torch.tensor([[1, 1], [0, 1]]).float()
u.check_equal(u.l2_norm(mat), 0.5 * (1 + math.sqrt(5)))
ii = torch.eye(5)
u.check_equal(u.l2_norm(ii), 1)
def compute_layer_stats(layer):
stats = AttrDefault(str, {})
n = stats_batch_size
param = u.get_param(layer)
d = len(param.flatten())
layer_idx = model.layers.index(layer)
assert layer_idx >= 0
assert stats_data.shape[0] == n
def backprop_loss():
model.zero_grad()
output = model(
stats_data) # use last saved data batch for backprop
loss = compute_loss(output, stats_targets)
loss.backward()
return loss, output
def backprop_output():
model.zero_grad()
output = model(stats_data)
output.backward(gradient=torch.ones_like(output))
return output
# per-example gradients, n, d
loss, output = backprop_loss()
At = layer.data_input
Bt = layer.grad_output * n
G = u.khatri_rao_t(At, Bt)
g = G.sum(dim=0, keepdim=True) / n
u.check_close(g, u.vec(param.grad).t())
stats.diversity = torch.norm(G, "fro")**2 / g.flatten().norm()**2
stats.gradient_norm = g.flatten().norm()
stats.parameter_norm = param.data.flatten().norm()
pos_activations = torch.sum(layer.data_output > 0)
neg_activations = torch.sum(layer.data_output <= 0)
stats.sparsity = pos_activations.float() / (pos_activations +
neg_activations)
output = backprop_output()
At2 = layer.data_input
u.check_close(At, At2)
B2t = layer.grad_output
J = u.khatri_rao_t(At, B2t)
H = J.t() @ J / n
model.zero_grad()
output = model(stats_data) # use last saved data batch for backprop
loss = compute_loss(output, stats_targets)
hess = u.hessian(loss, param)
hess = hess.transpose(2, 3).transpose(0, 1).reshape(d, d)
u.check_close(hess, H)
u.check_close(hess, H)
stats.hessian_norm = u.l2_norm(H)
stats.jacobian_norm = u.l2_norm(J)
Joutput = J.sum(dim=0) / n
stats.jacobian_sensitivity = Joutput.norm()
# newton decrement
stats.loss_newton = u.to_python_scalar(g @ u.pinv(H) @ g.t() / 2)
u.check_close(stats.loss_newton, loss)
# do line-search to find optimal step
def line_search(directionv, start, end, steps=10):
"""Takes steps between start and end, returns steps+1 loss entries"""
param0 = param.data.clone()
param0v = u.vec(param0).t()
losses = []
for i in range(steps + 1):
output = model(
stats_data) # use last saved data batch for backprop
loss = compute_loss(output, stats_targets)
losses.append(loss)
offset = start + i * ((end - start) / steps)
param1v = param0v + offset * directionv
param1 = u.unvec(param1v.t(), param.data.shape[0])
param.data.copy_(param1)
output = model(
stats_data) # use last saved data batch for backprop
loss = compute_loss(output, stats_targets)
losses.append(loss)
param.data.copy_(param0)
return losses
# try to take a newton step
gradv = g
line_losses = line_search(-gradv @ u.pinv(H), 0, 2, steps=10)
u.check_equal(line_losses[0], loss)
u.check_equal(line_losses[6], 0)
assert line_losses[5] > line_losses[6]
assert line_losses[7] > line_losses[6]
return stats
