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visualise_sigprop.py
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visualise_sigprop.py
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"""
This script produces plots that form the base for Figure 1 and Figure 6.
"""
import math
import torch
from torch import nn
from matplotlib import pyplot as plt, gridspec
from convex_init import TraditionalInitialiser, ConvexInitialiser
from convex_modules import ConvexLinear, LazyClippedPositivity, LinearSkip
def estimate_moments(data: torch.Tensor):
mom1 = torch.mean(data, dim=0)
mom2 = data.T @ data / len(data)
return mom1, torch.diag(mom2), mom2
def normalised_moments(mixed: torch.Tensor, mean: torch.Tensor):
cov = mixed - torch.outer(mean, mean)
var = torch.diag(cov)
std = var ** .5
corr = cov / torch.outer(std, std)
return var, cov, corr
def minify_matrix(cov: torch.Tensor, factor: int = 100):
n_mini = cov.shape[0] // factor
cov_tmp = cov.reshape(factor, n_mini, factor, n_mini)
cov_blocks = torch.movedim(cov_tmp, 1, -1).reshape(-1, n_mini, n_mini)
cov_mini = cov_blocks[::factor + 1].mean(0)
return cov_mini
def plot_fancy_hist(data, bin_width: float = .5, color=None, ax=None):
fig = plt.gcf()
if ax is None:
ax = fig.gca()
low, high = data.min(), data.max()
print(data.mean(), data.median())
if low < bin_width and high > -bin_width:
min_bin_count = math.ceil(2 * max(-low, high) / bin_width)
bound = bin_width * (min_bin_count + .5)
bin_count = min(int(min_bin_count), 500)
print(-bound, bound, bin_count)
ax.hist(data, range=(-bound, bound), bins=bin_count,
density=True, color=color)
return ax
# split axis
gs = gridspec.GridSpecFromSubplotSpec(1, 2, subplot_spec=ax, wspace=0.05)
axl = fig.add_subplot(gs[0], sharey=ax)
axr = fig.add_subplot(gs[1], sharey=ax)
ax.remove()
axl.spines.right.set_visible(False)
axr.spines.left.set_visible(False)
axr.yaxis.set_visible(False)
kwargs = {"marker": [(-1, -.5), (1, .5)], "markersize": 12, "mew": 1}
kwargs.update(linestyle="none", color="k", clip_on=False)
axl.plot([1, 1], [0, 1], transform=axl.transAxes, **kwargs)
axr.plot([0, 0], [0, 1], transform=axr.transAxes, **kwargs)
if low > bin_width:
gap_bound = bin_width * math.floor(low / bin_width)
out_bound = bin_width * math.ceil(high / bin_width)
bin_count = min(int((out_bound - gap_bound) // bin_width), 500)
print(gap_bound, out_bound, bin_count)
axl.hist([], range=(-out_bound, -gap_bound))
axr.hist(data, range=(gap_bound, out_bound), bins=bin_count, density=True)
return axr
elif high < -bin_width:
gap_bound = bin_width * math.ceil(high / bin_width)
out_bound = bin_width * math.floor(low / bin_width)
bin_count = min(int((gap_bound - out_bound) // bin_width), 500)
print(gap_bound, out_bound, bin_count)
axl.hist(data, range=(out_bound, gap_bound), bins=bin_count, density=True)
axr.hist([], range=(-gap_bound, -out_bound))
return axl
return
def plot_moments(data, raw: bool = False, mini: bool = False, axes=None):
if axes is None:
_, axes = plt.subplots(ncols=3)
ax1, ax2, ax3 = axes
mean, mom2, mixed = estimate_moments(data)
var, cov, corr = normalised_moments(mixed, mean=mean)
mat, diag = (mixed, mom2) if raw else (cov, var)
if mini:
mat, corr = minify_matrix(mat), minify_matrix(corr)
diag = torch.diag(mat)
plot_fancy_hist(data.ravel(), bin_width=0.5, ax=ax1)
ax2.axis("off")
bound = diag.max()
img = ax2.imshow(mat, vmin=-bound, vmax=bound, cmap="coolwarm")
ax2.get_figure().colorbar(img, ax=ax2)
ax3.axis("off")
ax3.imshow(corr, vmin=-1, vmax=1, cmap="coolwarm")
return axes
if __name__ == "__main__":
x = torch.randn(1024, 200)
net = torch.nn.Sequential(
nn.Linear(200, 400),
nn.Sequential(nn.ReLU(), nn.Linear(400, 300)),
nn.Sequential(nn.ReLU(), nn.Linear(300, 400)),
nn.Sequential(nn.ReLU(), nn.Linear(400, 100)),
)
# regular init
init1 = TraditionalInitialiser()
initX = TraditionalInitialiser(gain=2.)
init1(net[0].weight, net[0].bias)
for layer in net[1:]:
initX(layer[1].weight, layer[1].bias)
with torch.no_grad():
s, = nn_results = [x]
for layer in net:
s = layer(s)
nn_results.append(s)
size = (3, len(nn_results) - 1)
fig, axes = plt.subplots(*size, figsize=(size[1] * 6.4, size[0] * 4.8))
print(axes[0, 0].get_shared_y_axes())
axes[0, 0].get_shared_y_axes().join(*axes[0])
print(axes[0, 0].get_shared_y_axes())
for res, axes in zip(nn_results, axes.T):
plot_moments(res, raw=True, mini=True, axes=axes)
fig.savefig("propagation_nn.svg")
fig.show()
# icnn init
with torch.no_grad():
for layer in net[1:]:
torch.relu_(layer[1].weight)
with torch.no_grad():
s, = icnn_results = [x]
for layer in net:
s = layer(s)
icnn_results.append(s)
size = (3, len(icnn_results) - 1)
fig, axes = plt.subplots(*size, figsize=(size[1] * 6.4, size[0] * 4.8))
axes[0, 0].get_shared_y_axes().join(*axes[0])
for res, axes in zip(icnn_results, axes.T):
plot_moments(res, raw=True, mini=True, axes=axes)
fig.savefig("propagation_icnn.svg")
fig.show()
net = torch.nn.Sequential(
nn.Linear(200, 400),
nn.Sequential(nn.ReLU(), ConvexLinear(400, 300, positivity=LazyClippedPositivity())),
nn.Sequential(nn.ReLU(), ConvexLinear(300, 400, positivity=LazyClippedPositivity())),
nn.Sequential(nn.ReLU(), ConvexLinear(400, 100, positivity=LazyClippedPositivity())),
)
# principled init
initX = ConvexInitialiser()
init1(net[0].weight, net[0].bias)
for layer in net[1:]:
initX(layer[1].weight, layer[1].bias)
with torch.no_grad():
s, = ours_results = [x]
for layer in net:
s = layer(s)
ours_results.append(s)
size = (3, len(ours_results) - 1)
fig, axes = plt.subplots(*size, figsize=(size[1] * 6.4, size[0] * 4.8))
axes[0, 0].get_shared_y_axes().join(*axes[0])
for res, axes in zip(ours_results, axes.T):
plot_moments(res, raw=True, mini=True, axes=axes)
fig.savefig("propagation_icnn_init.svg")
fig.show()
# icnn rbias init
initX = ConvexInitialiser(bias_noise=0.5)
init1(net[0].weight, net[0].bias)
for layer in net[1:]:
initX(layer[1].weight, layer[1].bias)
with torch.no_grad():
s, = icnn_results = [x]
for layer in net:
s = layer(s)
icnn_results.append(s)
size = (3, len(icnn_results) - 1)
fig, axes = plt.subplots(*size, figsize=(size[1] * 6.4, size[0] * 4.8))
axes[0, 0].get_shared_y_axes().join(*axes[0])
for res, axes in zip(icnn_results, axes.T):
plot_moments(res, raw=True, mini=True, axes=axes)
fig.savefig("propagation_icnn_rbias.svg")
fig.show()
# bonus visualisation
net = LinearSkip(200, 100, nn.Sequential(
LinearSkip(200, 400, nn.Sequential(
LinearSkip(200, 300, nn.Sequential(
nn.Linear(200, 400),
nn.Sequential(nn.ReLU(), nn.Linear(400, 300))
)),
nn.Sequential(nn.ReLU(), nn.Linear(300, 400))
)),
nn.Sequential(nn.ReLU(), nn.Linear(400, 100))
))
with torch.no_grad():
for name, par in net.named_parameters():
if "residual.1.1" in name and par.ndim > 1:
print(name)
torch.relu_(par)
with torch.no_grad():
s, = skip_results = [x]
s = net.residual[0].residual[0].residual[0](s)
skip_results.append(s)
s = net.residual[0].residual[0].residual[1](s) + net.residual[0].residual[0].skip(x)
skip_results.append(s)
s = net.residual[0].residual[1](s) + net.residual[0].skip(x)
skip_results.append(s)
s = net.residual[1](s) + net.skip(x)
skip_results.append(s)
size = (3, len(skip_results) - 1)
fig, axes = plt.subplots(*size, figsize=(size[1] * 6.4, size[0] * 4.8))
axes[0, 0].get_shared_y_axes().join(*axes[0])
for res, axes in zip(skip_results, axes.T):
plot_moments(res, raw=True, mini=True, axes=axes)
fig.savefig("propagation_icnn_skip.svg")
fig.show()