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"""
Frozen-init identity check (supporting measurement for the depth-utility ladder).
Quantifies how close a randomly-initialized, frozen ResidualMLP block stack is to
the identity map. This grounds the footnote explaining why the k=0 rung of the
ladder (all blocks frozen at init) already sits well above chance: the trained
embedding + readout are composed with a fixed, near-norm-preserving random feature
map, i.e. effectively a trained (near-)linear classifier on pixels.
Reports, at random init, on a CIFAR-10 test batch (mean over seeds):
- per-block residual ratio ||f_l(h_l)|| / ||h_l|| (median over batch)
- whole-stack deviation ||h_L - h_0|| / ||h_0|| (median over batch)
- whole-stack direction cos(h_L, h_0) (median over batch)
Usage:
CUDA_VISIBLE_DEVICES=2 python experiments/frozen_init_identity_check.py
"""
import os, sys, json
import numpy as np
import torch
import torch.nn.functional as F
import torchvision
import torchvision.transforms as transforms
sys.path.insert(0, os.path.dirname(os.path.dirname(os.path.abspath(__file__))))
from models.residual_mlp import ResidualMLP
def main():
d_hidden, L, C, n = 256, 4, 10, 256
seeds = [42, 123, 456]
tf = transforms.Compose([transforms.ToTensor(),
transforms.Normalize((0.4914, 0.4822, 0.4465),
(0.2470, 0.2435, 0.2616))])
ds = torchvision.datasets.CIFAR10('./data', train=False, download=True, transform=tf)
x = torch.stack([ds[i][0] for i in range(n)]).view(n, -1)
per_block, rel_dev, cos_dev = [], [], []
seed_rows = {}
for seed in seeds:
torch.manual_seed(seed); np.random.seed(seed)
m = ResidualMLP(32 * 32 * 3, d_hidden, C, L).eval()
with torch.no_grad():
h0 = m.embed(x); h = h0; ratios = []
for blk in m.blocks:
f = blk(h)
ratios.append(float((f.norm(dim=-1) / h.norm(dim=-1)).median()))
h = h + f
rel = float(((h - h0).norm(dim=-1) / h0.norm(dim=-1)).median())
cos = float(F.cosine_similarity(h, h0, dim=-1).median())
per_block.append(ratios); rel_dev.append(rel); cos_dev.append(cos)
seed_rows[str(seed)] = {'per_block_ratio': ratios, 'rel_dev': rel, 'cos': cos}
print(f"seed {seed}: per-block ||f||/||h|| = "
f"{['%.4f' % r for r in ratios]} "
f"||h_L-h_0||/||h_0|| = {rel:.3f} cos(h_L,h_0) = {cos:.4f}", flush=True)
pb = np.array(per_block)
summary = {
'config': {'d_hidden': d_hidden, 'L': L, 'num_classes': C, 'batch': n,
'dataset': 'cifar10-test', 'seeds': seeds},
'per_seed': seed_rows,
'per_block_ratio_mean': pb.mean(0).tolist(),
'per_block_ratio_grand_mean': float(pb.mean()),
'rel_dev_mean': float(np.mean(rel_dev)),
'rel_dev_std': float(np.std(rel_dev, ddof=1)),
'cos_mean': float(np.mean(cos_dev)),
'cos_std': float(np.std(cos_dev, ddof=1)),
}
print(f"\nMEAN over {len(seeds)} seeds: "
f"per-block ratio ≈ {summary['per_block_ratio_grand_mean']:.3f}, "
f"||h_L-h_0||/||h_0|| = {summary['rel_dev_mean']:.3f} ± {summary['rel_dev_std']:.3f}, "
f"cos = {summary['cos_mean']:.4f} ± {summary['cos_std']:.4f}", flush=True)
out = 'results/depth_ladder/frozen_init_identity.json'
os.makedirs(os.path.dirname(out), exist_ok=True)
with open(out, 'w') as f:
json.dump(summary, f, indent=2)
print(f"Saved -> {out}", flush=True)
if __name__ == '__main__':
main()
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