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#!/usr/bin/env python3
"""Prove the convolutional local eligibility matches exact BP when instructed."""
import os
import sys
import torch
import torch.nn.functional as F
sys.path.insert(0, os.path.dirname(os.path.dirname(os.path.abspath(__file__))))
from sdil.conv import (CIFARLocalResNet, CIFARSDILResNet, ConvSDILConfig,
conv_local_step, simultaneous_conv_node_perturbation)
def architecture_checks():
expected = {
8: (7, 74810),
20: (19, 268346),
32: (31, 461882),
56: (55, 848954),
}
for depth, (hidden, parameters) in expected.items():
net = CIFARLocalResNet(depth=depth)
assert net.n_hidden == hidden
assert net.n_forward_parameters == parameters
assert len(net.blocks) == 3 * ((depth - 2) // 6)
assert len(net.W) + 1 == depth
for depth in (7, 9, 21):
try:
CIFARLocalResNet(depth=depth)
except ValueError:
pass
else:
raise AssertionError(f"invalid depth {depth} was accepted")
x = torch.arange(2 * 3 * 8 * 8, dtype=torch.float32).reshape(2, 3, 8, 8)
shortcut = CIFARLocalResNet._option_a_shortcut(x, 6, 2)
assert tuple(shortcut.shape) == (2, 6, 4, 4)
assert torch.count_nonzero(shortcut[:, 0]) == 0
assert torch.count_nonzero(shortcut[:, -2:]) == 0
assert torch.equal(shortcut[:, 1:4], x[:, :, ::2, ::2])
def exact_local_gradient_check():
torch.manual_seed(123)
batch = 3
x = torch.randn(batch, 3, 32, 32)
y = torch.tensor([0, 3, 8])
local = CIFARLocalResNet(depth=8, base_width=4, seed=19)
bp = CIFARLocalResNet(depth=8, base_width=4, seed=19)
parameters = local.W + [local.W_out, local.b_out]
for parameter in parameters:
parameter.requires_grad_(True)
forward = local.forward(x, return_cache=True)
for hidden in forward["hiddens"]:
hidden.retain_grad()
loss = F.cross_entropy(forward["logits"], y)
loss.backward()
# .backward() differentiated a batch-mean loss. Multiplying hidden grads
# by B recovers the per-example convention consumed by the local rule.
teaching = [-batch * hidden.grad for hidden in forward["hiddens"]]
output_error = (torch.softmax(forward["logits"].detach(), dim=1)
- F.one_hot(y, local.n_classes))
directions, out_direction, bias_direction = local.local_ascent_directions(
teaching, output_error, forward)
relative_errors = []
for direction, parameter in zip(directions, local.W):
absolute = (direction + parameter.grad).abs().max()
scale = parameter.grad.abs().max().clamp_min(1e-12)
relative_errors.append(float(absolute / scale))
output_abs = float((out_direction + local.W_out.grad).abs().max())
bias_abs = float((bias_direction + local.b_out.grad).abs().max())
assert max(relative_errors) < 3e-5
assert output_abs < 2e-6 and bias_abs < 2e-6
for parameter in parameters:
parameter.requires_grad_(False)
eta = 0.017
local.apply_ascent(directions, out_direction, bias_direction, eta)
bp_loss = bp.bp_step(x, y, eta)
assert abs(float(loss.detach()) - bp_loss) < 1e-7
parameter_differences = [
float((left - right).abs().max())
for left, right in zip(
local.W + [local.W_out, local.b_out],
bp.W + [bp.W_out, bp.b_out])]
assert max(parameter_differences) < 2e-7
return {
"max_relative_local_gradient_error": max(relative_errors),
"output_absolute_error": output_abs,
"post_update_parameter_max_error": max(parameter_differences),
}
def perturbation_checks():
net = CIFARLocalResNet(depth=8, base_width=4, seed=3)
x = torch.randn(2, 3, 32, 32)
clean = net.forward(x)
perturbations = [torch.zeros_like(hidden) for hidden in clean["hiddens"]]
perturbed = net.forward(x, perturbations=perturbations)
assert torch.equal(clean["logits"], perturbed["logits"])
perturbations[0] = torch.ones_like(perturbations[0]) * 0.01
changed = net.forward(x, perturbations=perturbations)
assert not torch.equal(clean["logits"], changed["logits"])
try:
net.forward(x, perturbations=perturbations[:-1])
except ValueError:
pass
else:
raise AssertionError("short perturbation list was accepted")
def perturbation_estimator_check():
"""Antithetic finite differences equal the simultaneous hidden JVP."""
torch.manual_seed(3)
batch = 2
net = CIFARSDILResNet(
depth=8, base_width=2, seed=4, dtype=torch.float64)
x = torch.randn(batch, 3, 32, 32, dtype=torch.float64)
y = torch.tensor([2, 7])
parameters = net.W + [net.W_out, net.b_out]
for parameter in parameters:
parameter.requires_grad_(True)
clean = net.forward(x, return_cache=True)
for hidden in clean["hiddens"]:
hidden.retain_grad()
F.cross_entropy(clean["logits"], y).backward()
generator = torch.Generator(device="cpu").manual_seed(99)
targets, diagnostics = simultaneous_conv_node_perturbation(
net, x, y, clean, sigma=1e-6, n_directions=1,
generator=generator, return_diagnostics=True)
directions = diagnostics["directions"][0]
finite_difference = diagnostics["directional_derivatives"][0]
exact = sum(
(batch * hidden.grad * direction).flatten(1).sum(dim=1)
for hidden, direction in zip(clean["hiddens"], directions))
relative = (finite_difference - exact).abs() / exact.abs().clamp_min(1e-12)
assert float(relative.max()) < 2e-6
for target, direction in zip(targets, directions):
expected = -finite_difference[:, None, None, None] * direction
assert torch.equal(target, expected)
for parameter in parameters:
parameter.requires_grad_(False)
return float(relative.max())
def apical_learning_checks():
torch.manual_seed(11)
net = CIFARSDILResNet(depth=8, base_width=2, seed=6)
x = torch.randn(8, 3, 32, 32)
y = torch.arange(8) % 10
clean = net.forward(x, return_cache=True)
output_signal = (torch.softmax(clean["logits"], dim=1)
- F.one_hot(y, 10))
prediction, _, _ = net.apical_components(
output_signal, clean["hiddens"], use_residual=True)
targets = [torch.randn_like(value) * 0.01 for value in prediction]
before = sum(float((target - value).square().sum())
for target, value in zip(targets, prediction))
net.calibrate_apical(output_signal, prediction, targets, eta=0.1)
after_prediction, _, _ = net.apical_components(
output_signal, clean["hiddens"], use_residual=True)
after = sum(float((target - value).square().sum())
for target, value in zip(targets, after_prediction))
assert after < before
predictor_net = CIFARSDILResNet(depth=8, base_width=2, seed=8)
hiddens = [torch.randn(64, *shape) for shape in predictor_net.hidden_shapes]
initial = predictor_net.predictor_step(hiddens, eta=0.1, nuisance_scale=0.5)
final = initial
for _ in range(60):
final = predictor_net.predictor_step(hiddens, eta=0.1, nuisance_scale=0.5)
assert final < initial * 1e-3
weights_before = [weight.clone() for weight in net.W]
result = conv_local_step(
net, x[:2], y[:2],
ConvSDILConfig(
eta=1e-3, eta_A=1e-3, momentum=0.0, weight_decay=0.0,
pert_every=1),
step=0, generator=torch.Generator(device="cpu").manual_seed(7))
assert result["did_perturb"] and result["calibration"] is not None
assert torch.isfinite(torch.tensor(list(
value for key, value in result.items()
if isinstance(value, float) and key != "predictor_mse"))).all()
assert any(not torch.equal(before_weight, after_weight)
for before_weight, after_weight in zip(weights_before, net.W))
assert all(not parameter.requires_grad
for parameter in net.W + [net.W_out, net.b_out])
return {"apical_mse_ratio": after / before,
"predictor_mse_ratio": final / initial}
def main():
architecture_checks()
perturbation_checks()
report = exact_local_gradient_check()
report["perturbation_jvp_max_relative_error"] = perturbation_estimator_check()
report.update(apical_learning_checks())
print(report)
print("ALL CONVOLUTIONAL LOCAL-ELIGIBILITY CHECKS PASSED")
if __name__ == "__main__":
main()
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