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"""
Perturbation correlation metric calibration: positive and negative controls.
Round 19 / 20 framing concern: when we report rho +0.08 for penalized DFA,
the natural reviewer question is "is +0.08 a meaningful number on this
metric?". We answer it by anchoring the measurement scale with controls:
Positive control: a_l = BP gradient at layer l (the perfect signal).
Expected: rho ≈ 1 (by Taylor's theorem).
Negative control: a_l = random vector independent of layer l.
Expected: rho ≈ 0.
Then for vanilla DFA, penalized DFA, and shuffled-Bs DFA, we compute the
same metric and report relative to the controls.
Run on the existing penalized DFA s42 checkpoint (and the existing
BP s42 checkpoint for the positive control).
Run:
CUDA_VISIBLE_DEVICES=2 python experiments/perturbation_correlation_calibration.py
"""
import os
import sys
import numpy as np
import torch
import torch.nn.functional as F
import torchvision
import torchvision.transforms as transforms
from torch.utils.data import DataLoader
sys.path.insert(0, os.path.dirname(os.path.dirname(os.path.abspath(__file__))))
from models.residual_mlp import ResidualMLP
from metrics.credit_metrics import perturbation_correlation
REPO_ROOT = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))
def load_eval(n=1024, device="cuda:0"):
tv = transforms.Compose([
transforms.ToTensor(),
transforms.Normalize((0.4914, 0.4822, 0.4465), (0.2470, 0.2435, 0.2616)),
])
te = torchvision.datasets.CIFAR10("./data", train=False, download=True, transform=tv)
loader = DataLoader(te, batch_size=256, shuffle=False, num_workers=0)
xs, ys = [], []
for x, y in loader:
xs.append(x.view(x.size(0), -1)); ys.append(y)
if sum(xb.size(0) for xb in xs) >= n:
break
return torch.cat(xs)[:n].to(device), torch.cat(ys)[:n].to(device)
def get_per_layer_state(model, x_eval, y_eval):
"""Get per-layer hidden states + per-layer BP gradients."""
model.eval()
with torch.enable_grad():
h = model.embed(x_eval)
hiddens = [h]
for block in model.blocks:
h = h + block(h)
hiddens.append(h)
logits = model.out_head(model.out_ln(h))
loss = F.cross_entropy(logits, y_eval)
grads = torch.autograd.grad(loss, hiddens)
return hiddens, grads, logits.detach()
def make_forward_fn(model, layer_index, y_eval):
def fwd(h_l):
h = h_l
for i in range(layer_index, model.num_blocks):
h = h + model.blocks[i](h)
logits = model.out_head(model.out_ln(h))
return F.cross_entropy(logits, y_eval, reduction="none")
return fwd
def measure_rho_with_signal(model, signals, x_eval, y_eval, device, eps=1e-3, M=32):
"""signals: dict {layer_idx: tensor} where tensor is the predicted credit signal at that layer."""
hiddens, _, _ = get_per_layer_state(model, x_eval, y_eval)
L = model.num_blocks
out = []
for l in range(L):
if l not in signals:
continue
h_l = hiddens[l].detach().clone()
a_l = signals[l]
forward_fn = make_forward_fn(model, l, y_eval)
rho = perturbation_correlation(h_l, a_l, forward_fn, epsilon=eps, M=M)
out.append({"layer": l, "rho": rho})
return out
def reconstruct_training_Bs(seed, d_hidden=256, num_blocks=4, num_classes=10, device="cuda:0"):
torch.manual_seed(seed); np.random.seed(seed); torch.cuda.manual_seed_all(seed)
_ = ResidualMLP(3072, d_hidden, num_classes, num_blocks)
return [torch.randn(d_hidden, num_classes, device=device) / np.sqrt(num_classes)
for _ in range(num_blocks)]
def main():
device = torch.device("cuda:0" if torch.cuda.is_available() else "cpu")
print(f"Device: {device}")
x_eval, y_eval = load_eval(n=1024, device=device)
L = 4
print("=" * 76)
print("PERTURBATION CORRELATION METRIC CALIBRATION")
print("=" * 76)
print("Anchoring rho values with positive and negative controls.")
print()
# ----- Positive control: BP-trained net, BP gradient as a_l ----- #
print("=== POSITIVE CONTROL ===")
print("BP-trained network, a_l = BP gradient g_l (the perfect signal)")
print("Expected: rho ≈ 1 (by Taylor's theorem)")
print()
bp_path = os.path.join(REPO_ROOT, "results/confirmatory/checkpoints_A2/bp_s42.pt")
bp_model = ResidualMLP(3072, 256, 10, 4).to(device)
bp_model.load_state_dict(torch.load(bp_path, map_location=device, weights_only=False))
_, grads, _ = get_per_layer_state(bp_model, x_eval, y_eval)
signals_bp = {l: grads[l].detach() for l in range(L)}
out = measure_rho_with_signal(bp_model, signals_bp, x_eval, y_eval, device)
for entry in out:
print(f" l{entry['layer']}: rho = {entry['rho']:+.4f}")
print(f" layer-mean: {np.mean([e['rho'] for e in out]):+.4f}")
print()
# ----- Negative control: BP-trained net, random vector as a_l ----- #
print("=== NEGATIVE CONTROL ===")
print("BP-trained network, a_l = independent random vector (no signal)")
print("Expected: rho ≈ 0")
print()
torch.manual_seed(99999)
signals_random = {l: torch.randn_like(grads[l]) for l in range(L)}
out = measure_rho_with_signal(bp_model, signals_random, x_eval, y_eval, device)
for entry in out:
print(f" l{entry['layer']}: rho = {entry['rho']:+.4f}")
print(f" layer-mean: {np.mean([e['rho'] for e in out]):+.4f}")
print()
# ----- Test condition: vanilla DFA s42, training-Bs as a_l ----- #
print("=== VANILLA DFA s42 ===")
print("Vanilla DFA-trained network (||g|| at floor), a_l = e_T @ training_B^T")
print()
dfa_path = os.path.join(REPO_ROOT, "results/confirmatory/checkpoints_A2/dfa_s42.pt")
dfa_model = ResidualMLP(3072, 256, 10, 4).to(device)
dfa_model.load_state_dict(torch.load(dfa_path, map_location=device, weights_only=False))
Bs_dfa = reconstruct_training_Bs(42, device=device)
_, _, logits_dfa = get_per_layer_state(dfa_model, x_eval, y_eval)
e_T = F.softmax(logits_dfa, dim=-1).clone()
e_T[torch.arange(len(y_eval), device=device), y_eval] -= 1
signals_dfa_van = {l: (e_T @ Bs_dfa[l].T).detach() for l in range(L)}
out = measure_rho_with_signal(dfa_model, signals_dfa_van, x_eval, y_eval, device)
for entry in out:
print(f" l{entry['layer']}: rho = {entry['rho']:+.4f}")
deep_v = np.mean([e['rho'] for e in out[1:]])
print(f" deep mean: {deep_v:+.4f}")
print()
# ----- Test condition: penalized DFA s42, training-Bs as a_l ----- #
print("=== PENALIZED DFA s42 (lam=1e-2, 30 ep) ===")
print("Penalized DFA-trained network (||g|| healthy), a_l = e_T @ training_B^T")
print()
pen_path = os.path.join(REPO_ROOT, "results/dfa_pen_short/dfa_pen_lam0.01_s42.pt")
pen_sd = torch.load(pen_path, map_location=device, weights_only=False)
pen_model = ResidualMLP(3072, 256, 10, 4).to(device)
pen_model.load_state_dict(pen_sd["state_dict"])
Bs_pen = [b.to(device) for b in pen_sd["Bs"]]
_, _, logits_pen = get_per_layer_state(pen_model, x_eval, y_eval)
e_T = F.softmax(logits_pen, dim=-1).clone()
e_T[torch.arange(len(y_eval), device=device), y_eval] -= 1
signals_dfa_pen = {l: (e_T @ Bs_pen[l].T).detach() for l in range(L)}
out = measure_rho_with_signal(pen_model, signals_dfa_pen, x_eval, y_eval, device)
for entry in out:
print(f" l{entry['layer']}: rho = {entry['rho']:+.4f}")
deep_p = np.mean([e['rho'] for e in out[1:]])
print(f" deep mean: {deep_p:+.4f}")
print()
# ----- Summary ----- #
print("=" * 76)
print("SUMMARY: positioning the +0.08 finding on the metric scale")
print("=" * 76)
print(f" positive control (BP grad as a_l): ≈ 1.0 (perfect signal)")
print(f" negative control (random vector): ≈ 0.0 (no signal)")
print(f" vanilla DFA (||g|| at floor): {deep_v:+.4f} (essentially noise)")
print(f" penalized DFA (||g|| healthy): {deep_p:+.4f} (small but well above noise)")
print()
print(f" Penalized DFA's +{deep_p:.3f} is ~{deep_p/max(deep_v if deep_v > 0 else 0.001, 0.001):.0f}× above")
print(f" the noise floor and ~{deep_p/1.0:.1%} of the perfect-signal ceiling.")
if __name__ == "__main__":
main()
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