def micro_teleportation_dot_product(network,
dataset,
nb_teleport=100,
network_descriptor='',
sampling_types=['intra_landscape'],
batch_sizes=[8, 64],
criterion=None,
device='cpu',
verbose=False,
random_data=False,
number_classes=10) -> None:
"""
This method tests the scalar product between the teleporation line and the gradient, as well as between a random
vector and the gradient for nullity. It then displays the histograms of the calculated scalar products. The
method also aggregates all relevant micro teleportation data in a dataframe.
Args:
network : the model which we wish to use to compute the micro-teleporations
dataset: the dataset that will be used to calculate the gradient and get dimensions for the
neural teleportation model
nb_teleport: The number of time the network is teleported and the scalar product calculated. An
average is then calculated.
network_descriptor: String describing the content of the network
sampling_types : Teleportation sampling types, governs how the change of basis is computed
batch_sizes: Size of the minibatch used to perform gradient calculation
criterion: the loss function used to compute the gradient
device: Device used to compute the network operations ('cpu' or 'cuda')
verbose: If true, the method will output extensive details about the calculated vectors and
aggregated data (mainly for debugging purposes)
random_data: If True, random data with random labels is used for computing the gradient.
If False, the dataset is used for computing the gradient.
number_classes: Number of classes of the classification problem.
"""
# Arbitrary precision threshold for nullity comparison
torch.set_printoptions(precision=10, sci_mode=True)
tol = 1e-2
cobs = [0.001]
hist_dir = f'images/histograms/{network_descriptor}'
if torch.cuda.is_available():
print(f'{green}Using CUDA{reset}')
network = network.cuda()
if (criterion is None):
loss_func = torch.nn.CrossEntropyLoss()
else:
loss_func = criterion
# Initialize the dataframe for data aggregation
aggregator = pd.DataFrame(columns=[
'model name', 'sampling type', 'batch size', 'COB range',
'weights vector length', 'Micro-teleportation vs Gradient',
'Micro-teleportation vs Gradient std', 'Gradient vs Random Vector',
'Gradient vs Random Vector std', 'Random Vector vs Random Vector',
'Random Vector vs Random Vector std',
'Micro-teleportation vs Random Vector',
'Micro-teleportation vs Random Vector std'
])
for sampling_type in sampling_types:
for batch_size in batch_sizes:
dataloader = torch.utils.data.DataLoader(dataset,
batch_size=batch_size)
data, target = next(iter(dataloader))
# save the initial weights for further reset
model = NeuralTeleportationModel(network=network,
input_shape=data.shape)
if torch.cuda.is_available():
model = model.cuda()
else:
model = model.cpu()
if torch.cuda.is_available():
w1 = model.get_weights().detach()
else:
w1 = model.get_weights().detach().numpy()
for cob in cobs:
angle_results = []
rand_angle_results = []
rand_rand_angle_results = []
rand_micro_angle_results = []
iterations = min(
int(len(dataloader.dataset) / dataloader.batch_size),
nb_teleport)
for _ in tqdm(range(0, iterations)):
# Get next data batch
data, target = next(iter(dataloader))
if random_data:
data, target = torch.rand(data.shape), torch.randint(
0, number_classes, target.shape)
data, target = data.to(device), target.to(device)
grad = model.get_grad(data,
target,
loss_func,
zero_grad=False)
# reset the weights for next teleportation
model.set_weights(torch.tensor(w1))
# teleport and get the new weights
model = model.random_teleport(cob_range=cob,
sampling_type=sampling_type)
if torch.cuda.is_available():
w2 = model.get_weights().detach()
else:
w2 = model.get_weights().detach().numpy()
# get teleportation vector
micro_teleport_vec = (w2 - w1)
random_vector = torch.rand(grad.shape,
dtype=torch.float) - 0.5
random_vector2 = torch.rand(grad.shape,
dtype=torch.float) - 0.5
random_vector = random_vector.to(device)
random_vector2 = random_vector2.to(device)
# Normalized scalar products & angles calculations
dot_prod = normalized_dot_product(grad, micro_teleport_vec)
angle = np.degrees(torch.acos(dot_prod).cpu())
rand_dot_prod = normalized_dot_product(grad, random_vector)
rand_angle = np.degrees(torch.acos(rand_dot_prod).cpu())
rand_rand_dot_prod = normalized_dot_product(
random_vector2, random_vector)
rand_rand_angle = np.degrees(
torch.acos(rand_rand_dot_prod).cpu())
rand_micro_dot_prod = normalized_dot_product(
random_vector2, micro_teleport_vec)
rand_micro_angle = np.degrees(
torch.acos(rand_micro_dot_prod).cpu())
# Perpendicularity assertion
failed = (not torch.allclose(
dot_prod, torch.tensor([0.0]).to(device), atol=tol))
rand_failed = (not torch.allclose(rand_dot_prod,
torch.tensor(
[0.0]).to(device),
atol=tol))
target_angle = 90.0
angle_results.append(angle)
rand_angle_results.append(rand_angle)
rand_rand_angle_results.append(rand_rand_angle)
rand_micro_angle_results.append(rand_micro_angle)
angle_results = np.array(angle_results)
rand_angle_results = np.array(rand_angle_results)
rand_rand_angle_results = np.array(rand_rand_angle_results)
rand_micro_angle_results = np.array(rand_micro_angle_results)
# Append resuslts to dataframe for further ploting
aggregator = aggregator.append(
{
'model name':
network_descriptor,
'sampling type':
sampling_type,
'batch size':
batch_size,
'COB range':
cob,
'weights vector length':
len(w1),
'Micro-teleportation vs Gradient':
angle_results.mean(),
'Micro-teleportation vs Gradient std':
angle_results.std(),
'Gradient vs Random Vector':
rand_angle_results.mean(),
'Gradient vs Random Vector std':
rand_angle_results.std(),
'Random Vector vs Random Vector':
rand_rand_angle_results.mean(),
'Random Vector vs Random Vector std':
rand_rand_angle_results.std(),
'Micro-teleportation vs Random Vector':
rand_micro_angle_results.mean(),
'Micro-teleportation vs Random Vector std':
rand_micro_angle_results.std()
},
ignore_index=True)
print(
f'The angle between the gradient and a micro-teleporation vector is: '
f'{red * failed}'
f'{np.round(angle_results.mean(), abs(int(np.log10(tol))))}',
f' (!=0 => FAILED!)' * failed,
f'{reset}',
f' using {sampling_type} sampling type',
f', the delta in angle is {angle - target_angle}°\n',
f'The angle between the gradient and a random vector is: ',
f'{red * rand_failed}{rand_angle_results.mean()}',
f' (FAILED!)' * rand_failed,
f'{reset}',
f', the delta in angle is {rand_angle - target_angle}°\n',
sep='')
if verbose:
print(aggregator.iloc[aggregator.last_valid_index()])
if torch.cuda.is_available():
print(f'w1: {w1}',
f'nans: {torch.sum(torch.isnan(w1))}',
f'max: {torch.max(w1)}',
f'min: {torch.min(w1)}',
sep='\n')
print(f'w2: {w2}',
f' nans: {torch.sum(torch.isnan(w2))}',
f'max: {torch.max(w2)}',
f'min: {torch.min(w2)}',
sep='\n')
else:
print(f'w1: {w1}',
f'nans: {np.sum(np.isnan(w1))}',
f'max: {np.max(w1)}',
f'min: {np.min(w1)}',
sep='\n')
print(f'w2: {w2}',
f' nans: {np.sum(np.isnan(w2))}',
f'max: {np.max(w2)}',
f'min: {np.min(w2)}',
sep='\n')
if not np.isnan(
aggregator.loc[aggregator.last_valid_index(),
'Micro-teleportation vs Gradient']):
delta = 0.25
x_min = 90 - delta
x_max = 90 + delta
figsize = (10.0, 10.0)
fig, (ax0, ax1, ax2, ax3) = plt.subplots(4,
1,
figsize=figsize)
if random_data:
fig.suptitle(
f'{network_descriptor} on Random Data and batch size of {batch_size}'
)
else:
fig.suptitle(
f'{network_descriptor} on CIFAR-10 and batch size of {batch_size}'
)
bin_height, bin_boundary = np.histogram(
np.array(angle_results))
width = bin_boundary[1] - bin_boundary[0]
bin_height = bin_height / float(max(bin_height))
ax0.bar(bin_boundary[:-1],
bin_height,
width=np.maximum(width, 0.01))
ax0.legend(['Micro-teleportation\n vs \n Gradient'])
ax0.set_xlim(x_min, x_max)
ax0.set_yticks([])
bin_height, bin_boundary = np.histogram(
np.array(rand_micro_angle_results))
width = bin_boundary[1] - bin_boundary[0]
bin_height = bin_height / float(max(bin_height))
ax1.bar(bin_boundary[:-1],
bin_height,
width=np.maximum(width, 0.1),
color='g')
ax1.set_xlim(x_min, x_max)
ax1.legend(['Micro-teleportation\n vs \n Random Vector'])
ax1.set_yticks([])
bin_height, bin_boundary = np.histogram(
np.array(rand_angle_results))
width = bin_boundary[1] - bin_boundary[0]
bin_height = bin_height / float(max(bin_height))
ax2.bar(bin_boundary[:-1],
bin_height,
width=np.maximum(width, 0.1),
color='g')
ax2.set_xlim(x_min, x_max)
ax2.legend(['Gradient\n vs \n Random Vector'])
ax2.set_yticks([])
bin_height, bin_boundary = np.histogram(
np.array(rand_rand_angle_results))
width = bin_boundary[1] - bin_boundary[0]
bin_height = bin_height / float(max(bin_height))
ax3.bar(bin_boundary[:-1],
bin_height,
width=np.maximum(width, 0.1),
color='g')
ax3.set_xlim(x_min, x_max)
ax3.legend(['Random Vector\n vs \n Random Vector'])
ax3.set_yticks([])
plt.xlabel('Angle in degrees')
Path(hist_dir).mkdir(parents=True, exist_ok=True)
plt.savefig(
f'{hist_dir}/{network_descriptor}_'
f'_cob_{cob}_iter_{iterations}_batch_size_{batch_size}.png'
)
plt.show()
if random_data:
fig.savefig(
f"{network_descriptor}-RandomData-batchsize_{batch_size}.pdf",
bbox_inches='tight')
else:
fig.savefig(
f"{network_descriptor}-cifar10-batchsize_{batch_size}.pdf",
bbox_inches='tight')
else:
print(red)
print(aggregator.iloc[aggregator.last_valid_index()])
print(reset)
def dot_product_between_teleportation(network,
dataset,
network_descriptor=None,
nb_teleport=100,
device='cpu') -> None:
"""
This method tests the scalar product between the initial and teleported set of weights and plots the results with
respect to the order of magnitude of the change of basis of the teleportation
Args:
network : the model which we want to use to compute the teleportations
dataset : the model which we want to use to size the teleportation model
network_descriptor: String describing the content of the network
nb_teleport: Number of times the micro-teleportation for statistical (mean, variance, etc)
calculation
device: Device used to compute the network operations ('cpu' or 'cuda')
"""
series_dir = f'images/series_dot_prod_vs_cob/{network_descriptor}'
if torch.cuda.is_available():
print(f'{green}Using CUDA{reset}')
network = network.cuda()
if network_descriptor is None:
network_descriptor = network.__name__
# Prepare the range of COB to test
cobs = np.linspace(0.00001, 0.999, 40)
dataloader = torch.utils.data.DataLoader(dataset, batch_size=16)
data, target = next(iter(dataloader))
model = NeuralTeleportationModel(network=network, input_shape=data.shape)
if torch.cuda.is_available():
model = model.cuda()
else:
model = model.cpu()
w1 = model.get_weights().detach().to(device)
dot_product_results = []
angles = []
for cob in cobs:
dot_product_result = 0
angle = 0
for _ in tqdm(range(0, nb_teleport)):
# reset the weights
model.set_weights(w1)
# teleport and get the new weights
model.random_teleport(cob_range=cob,
sampling_type='intra_landscape')
w2 = model.get_weights().detach().to(device)
# cos(theta) = (w1 w2)/(||w1|| ||w2||)
dot_product_result += normalized_dot_product(w1, w2)
angle += np.degrees(
torch.acos(normalized_dot_product(w1, w2)).cpu())
dot_product_result /= nb_teleport
angle /= nb_teleport
dot_product_results.append(dot_product_result.item())
angles.append(angle.item())
plt.plot(cobs, dot_product_results)
plt.title(f'Scalar product between original and \nteleported weights with '
f'respect to COB\'s order of magnitude\n{network_descriptor}')
plt.ylabel('Scalar product')
plt.xlabel('change of basis')
Path(series_dir).mkdir(parents=True, exist_ok=True)
plt.savefig(
f'{series_dir}/dot_product_vs_cob_{network_descriptor}_Samp_type_intra_landscape'
)
plt.show()
plt.plot(cobs, angles)
plt.title(f'Angle between original and \nteleported weights with '
f'respect to COB\'s order of magnitude\n{network_descriptor}')
plt.ylabel('Theta')
plt.xlabel('change of basis')
Path(series_dir).mkdir(parents=True, exist_ok=True)
plt.savefig(
f'{series_dir}/angle_vs_cob_{network_descriptor}_Samp_type_intra_landscape'
)
plt.show()