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#!/usr/bin/env python3
"""exp02_neural — reduced-scale neural verification of Claims 4, 5, 6.
Real CIFAR-100 + CIFAR-100N (UCSC-REAL, human noisy labels), SmallCNN, CPU.
Optimizers: SGD, SAM (Foret et al. 2021), fSGLD (Eq 5). See specs/exp02_neural.md.
CPU only, torch/joblib. See BLOCKERS.md for the reduced-scale rationale.
"""
import os
for _v in ("OMP_NUM_THREADS", "MKL_NUM_THREADS", "OPENBLAS_NUM_THREADS", "NUMEXPR_NUM_THREADS"):
os.environ.setdefault(_v, "1")
import argparse
import hashlib
import json
import math
import pickle
import sys
import tarfile
import time
import urllib.request
import numpy as np
import torch
import torch.nn as nn
import torch.nn.functional as F
from joblib import Parallel, delayed
ROOT = os.path.dirname(os.path.abspath(__file__))
BASE = os.path.dirname(ROOT)
WORK_DIR = os.path.join(BASE, "work")
DATA_DIR = os.path.join(WORK_DIR, "data")
RESULTS_DIR = os.path.join(BASE, "results")
CIFAR100_URL = "https://www.cs.toronto.edu/~kriz/cifar-100-python.tar.gz"
CIFAR100_MD5 = "eb9058c3a382ffc7106e4002c42a8d85"
CIFAR100N_URL = "https://github.com/UCSC-REAL/cifar-10-100n/raw/main/data/CIFAR-100_human.pt"
MEAN = np.array([0.5071, 0.4865, 0.4409], dtype=np.float32)
STD = np.array([0.2673, 0.2564, 0.2762], dtype=np.float32)
BETA = 1e8
ETA_FSGLD = 0.1
SIGMA_FSGLD = BETA ** (-(1 + ETA_FSGLD) / 4.0)
WD = 5e-4
RHO_SAM = 0.05
BASE_LR = 0.1
FT_LR = 0.02
BATCH = 128
def log(msg):
print(msg, file=sys.stderr, flush=True)
# ------------------------------------------------------------------------- data
def _md5(path):
h = hashlib.md5()
with open(path, "rb") as f:
for chunk in iter(lambda: f.read(1 << 20), b""):
h.update(chunk)
return h.hexdigest()
def _download(url, path):
log(f"[data] downloading {url} -> {path}")
tmp = path + ".part"
urllib.request.urlretrieve(url, tmp)
os.replace(tmp, path)
def load_cifar100(provenance):
os.makedirs(DATA_DIR, exist_ok=True)
tar_path = os.path.join(DATA_DIR, "cifar-100-python.tar.gz")
if not os.path.exists(tar_path) or _md5(tar_path) != CIFAR100_MD5:
_download(CIFAR100_URL, tar_path)
md5ok = _md5(tar_path) == CIFAR100_MD5
log(f"[data] cifar100 tarball md5_ok={md5ok} sha256={hashlib.sha256(open(tar_path,'rb').read()).hexdigest()}")
with tarfile.open(tar_path, "r:gz") as tf:
train_raw = pickle.load(tf.extractfile("cifar-100-python/train"), encoding="latin1")
test_raw = pickle.load(tf.extractfile("cifar-100-python/test"), encoding="latin1")
train_data = np.asarray(train_raw["data"], dtype=np.uint8)
test_data = np.asarray(test_raw["data"], dtype=np.uint8)
train_fine = np.asarray(train_raw["fine_labels"], dtype=np.int64)
test_fine = np.asarray(test_raw["fine_labels"], dtype=np.int64)
struct_ok = (
train_data.shape == (50000, 3072)
and test_data.shape == (10000, 3072)
and len(np.unique(train_fine)) == 100
and train_data.min() >= 0 and train_data.max() <= 255
)
provenance["cifar100_sha256_ok"] = bool(md5ok and struct_ok)
provenance["n_train"] = int(train_data.shape[0])
provenance["n_test"] = int(test_data.shape[0])
log(f"[data] cifar100 struct_ok={struct_ok} n_train={train_data.shape[0]} n_test={test_data.shape[0]}")
return train_data, train_fine, test_data, test_fine
def load_cifar100n(provenance):
os.makedirs(DATA_DIR, exist_ok=True)
pt_path = os.path.join(DATA_DIR, "CIFAR-100_human.pt")
if not os.path.exists(pt_path):
_download(CIFAR100N_URL, pt_path)
d = torch.load(pt_path, weights_only=False)
noisy = np.asarray(d["noisy_label"], dtype=np.int64)
clean = np.asarray(d["clean_label"], dtype=np.int64)
provenance["cifar100n_len"] = int(len(noisy))
noise_rate = float(np.mean(noisy != clean))
provenance["cifar100n_noise_rate"] = noise_rate
log(f"[data] cifar100n len={len(noisy)} noise_rate={noise_rate:.4f}")
return noisy, clean
def preprocess(data_u8):
imgs = data_u8.reshape(-1, 3, 32, 32).astype(np.float32) / 255.0
imgs = (imgs - MEAN.reshape(1, 3, 1, 1)) / STD.reshape(1, 3, 1, 1)
return imgs.astype(np.float32)
def get_subset_indices(n_subset, seed_tag):
path = os.path.join(WORK_DIR, f"exp02_subset_indices_{seed_tag}_{n_subset}.npy")
if os.path.exists(path):
return np.load(path)
idx = np.random.default_rng(0).choice(50000, n_subset, replace=False)
np.save(path, idx)
return idx
# ------------------------------------------------------------------------- augmentation
def augment_batch(x_np):
# x_np: (B,3,32,32) float32, pad=4 random crop + random horizontal flip
B = x_np.shape[0]
padded = np.pad(x_np, ((0, 0), (0, 0), (4, 4), (4, 4)), mode="reflect")
out = np.empty_like(x_np)
for i in range(B):
top = np.random.randint(0, 9)
left = np.random.randint(0, 9)
crop = padded[i, :, top:top + 32, left:left + 32]
if np.random.rand() < 0.5:
crop = crop[:, :, ::-1]
out[i] = crop
return np.ascontiguousarray(out)
# ------------------------------------------------------------------------- model
class SmallCNN(nn.Module):
def __init__(self, n_classes=100):
super().__init__()
self.c1 = nn.Conv2d(3, 32, 3, padding=1)
self.b1 = nn.BatchNorm2d(32)
self.c2 = nn.Conv2d(32, 64, 3, padding=1)
self.b2 = nn.BatchNorm2d(64)
self.c3 = nn.Conv2d(64, 128, 3, padding=1)
self.b3 = nn.BatchNorm2d(128)
self.c4 = nn.Conv2d(128, 128, 3, padding=1)
self.b4 = nn.BatchNorm2d(128)
self.pool = nn.MaxPool2d(2)
self.gap = nn.AdaptiveAvgPool2d(4)
self.fc1 = nn.Linear(128 * 16, 256)
self.fc2 = nn.Linear(256, n_classes)
def forward(self, x):
x = F.relu(self.b1(self.c1(x)))
x = self.pool(F.relu(self.b2(self.c2(x))))
x = self.pool(F.relu(self.b3(self.c3(x))))
x = F.relu(self.b4(self.c4(x)))
x = self.gap(x).flatten(1)
x = F.relu(self.fc1(x))
return self.fc2(x)
# ------------------------------------------------------------------------- optimizers
def lr_at(epoch, base_lr, milestones):
lr = base_lr
for m in milestones:
if epoch >= m:
lr *= 0.1
return lr
def sgd_step(model, opt, xb, yb):
opt.zero_grad()
out = model(xb)
loss = F.cross_entropy(out, yb)
loss.backward()
opt.step()
return loss.item(), 1
def sam_step(model, opt, xb, yb, rho):
# first pass: compute grad at theta
opt.zero_grad()
out = model(xb)
loss1 = F.cross_entropy(out, yb)
loss1.backward()
params = [p for p in model.parameters() if p.grad is not None]
with torch.no_grad():
grad_norm = torch.norm(torch.stack([p.grad.norm(2) for p in params])) + 1e-12
eps_list = []
for p in params:
e = p.grad * (rho / grad_norm)
p.add_(e)
eps_list.append(e)
# second pass: grad at theta+eps, used for the real update
opt.zero_grad()
out2 = model(xb)
loss2 = F.cross_entropy(out2, yb)
loss2.backward()
with torch.no_grad():
for p, e in zip(params, eps_list):
p.sub_(e)
opt.step()
return loss1.item(), 2
def fsgld_step(model, params, lam, sigma, beta, wd, xb, yb):
with torch.no_grad():
eps_list = [torch.randn_like(p) * sigma for p in params]
for p, e in zip(params, eps_list):
p.add_(e)
for p in params:
if p.grad is not None:
p.grad = None
out = model(xb)
loss = F.cross_entropy(out, yb)
loss.backward()
with torch.no_grad():
for p, e in zip(params, eps_list):
p.sub_(e)
for p in params:
g = p.grad + wd * p
xi = torch.randn_like(p)
p.add_(-lam * g + math.sqrt(2 * lam / beta) * xi)
return loss.item(), 1
# ------------------------------------------------------------------------- train / eval
def make_optimizer(name, model):
if name == "SGD":
return torch.optim.SGD(model.parameters(), lr=BASE_LR, momentum=0.9, weight_decay=WD)
if name == "SAM":
return torch.optim.SGD(model.parameters(), lr=BASE_LR, momentum=0.9, weight_decay=WD)
return None
def set_lr(opt, lr):
for g in opt.param_groups:
g["lr"] = lr
def run_epochs(model, optimizer_name, train_x, train_y, epochs, milestones, base_lr,
batch_size, measure_timing=False, warmup_steps=10, timing_steps=50):
n = train_x.shape[0]
torch_opt = make_optimizer(optimizer_name, model) if optimizer_name in ("SGD", "SAM") else None
params = [p for p in model.parameters()]
s_per_iter = None
all_times = []
step_times = []
last_loss = None
global_step = 0
for epoch in range(epochs):
lr = lr_at(epoch, base_lr, milestones)
if torch_opt is not None:
set_lr(torch_opt, lr)
perm = np.random.permutation(n)
model.train()
for start in range(0, n, batch_size):
idx = perm[start:start + batch_size]
xb_np = augment_batch(train_x[idx])
xb = torch.from_numpy(xb_np)
yb = torch.from_numpy(train_y[idx])
t0 = time.time() if measure_timing else None
if optimizer_name == "SGD":
loss, _ = sgd_step(model, torch_opt, xb, yb)
elif optimizer_name == "SAM":
loss, _ = sam_step(model, torch_opt, xb, yb, RHO_SAM)
else:
loss, _ = fsgld_step(model, params, lr, SIGMA_FSGLD, BETA, WD, xb, yb)
if measure_timing:
dt = time.time() - t0
global_step += 1
all_times.append(dt)
if global_step > warmup_steps and len(step_times) < timing_steps:
step_times.append(dt)
last_loss = loss
if measure_timing and not step_times:
step_times = all_times # run too short to clear warmup; fall back to all steps
if measure_timing and step_times:
s_per_iter = float(np.mean(step_times))
return last_loss, s_per_iter
@torch.no_grad()
def evaluate(model, test_x, test_y, batch_size=256):
model.eval()
correct = 0
n = test_x.shape[0]
for start in range(0, n, batch_size):
xb = torch.from_numpy(test_x[start:start + batch_size])
yb = torch.from_numpy(test_y[start:start + batch_size])
out = model(xb)
pred = out.argmax(1)
correct += (pred == yb).sum().item()
return correct / n
# ------------------------------------------------------------------------- flatness
def hvp(loss, params, v):
grads = torch.autograd.grad(loss, params, create_graph=True)
flat_grad = torch.cat([g.reshape(-1) for g in grads])
flat_v = torch.cat([vi.reshape(-1) for vi in v])
gv = (flat_grad * flat_v).sum()
hv = torch.autograd.grad(gv, params, retain_graph=True)
return [h.detach() for h in hv]
def compute_flatness(model, x_batch, y_batch, m_hutch, top_iters, tol=1e-4):
model.eval()
params = [p for p in model.parameters() if p.requires_grad]
x = torch.from_numpy(x_batch)
y = torch.from_numpy(y_batch)
def get_loss():
out = model(x)
return F.cross_entropy(out, y)
# Hutchinson trace
traces = []
for _ in range(m_hutch):
v = [torch.randint(0, 2, p.shape, dtype=torch.float32) * 2 - 1 for p in params]
loss = get_loss()
hv = hvp(loss, params, v)
t = sum((vi * hi).sum().item() for vi, hi in zip(v, hv))
traces.append(t)
hess_trace = float(np.mean(traces))
# power iteration for top eigenvalue
v = [torch.randn_like(p) for p in params]
norm = math.sqrt(sum((vi ** 2).sum().item() for vi in v))
v = [vi / norm for vi in v]
lam_prev = 0.0
lam_top = 0.0
for it in range(top_iters):
loss = get_loss()
hv = hvp(loss, params, v)
norm = math.sqrt(sum((hi ** 2).sum().item() for hi in hv))
if norm < 1e-12:
break
v = [hi / norm for hi in hv]
loss = get_loss()
hv2 = hvp(loss, params, v)
lam_top = sum((vi * hi).sum().item() for vi, hi in zip(v, hv2))
if abs(lam_top - lam_prev) < tol:
lam_prev = lam_top
break
lam_prev = lam_top
return hess_trace, float(lam_top)
# ------------------------------------------------------------------------- checkpointed units
def ckpt_path(prefix, name):
return os.path.join(WORK_DIR, f"{prefix}_{name}.json")
def load_ckpt(path):
with open(path) as f:
return json.load(f)
def save_ckpt(path, obj):
tmp = path + ".tmp"
with open(tmp, "w") as f:
json.dump(obj, f)
os.replace(tmp, path)
def scratch_unit(prefix, optimizer_name, seed, train_x, train_y, test_x, test_y, epochs, milestones,
warmup_steps=10, timing_steps=50):
path = ckpt_path(prefix, f"scratch_{optimizer_name}_{seed}")
if os.path.exists(path):
log(f"[scratch] skip existing {optimizer_name} seed={seed}")
return load_ckpt(path)
torch.set_num_threads(1)
torch.manual_seed(seed)
np.random.seed(seed)
t0 = time.time()
model = SmallCNN()
last_loss, s_per_iter = run_epochs(model, optimizer_name, train_x, train_y, epochs, milestones,
BASE_LR, BATCH, measure_timing=True,
warmup_steps=warmup_steps, timing_steps=timing_steps)
test_acc = evaluate(model, test_x, test_y)
model_path = os.path.join(WORK_DIR, f"{prefix}_scratchmodel_{optimizer_name}_{seed}.pt")
torch.save(model.state_dict(), model_path)
row = {"optimizer": optimizer_name, "seed": seed, "test_acc": test_acc,
"train_loss": last_loss, "s_per_iter": s_per_iter}
save_ckpt(path, row)
log(f"[scratch] {optimizer_name} seed={seed} acc={test_acc:.4f} s_per_iter={s_per_iter:.4f} wall={time.time()-t0:.1f}s")
return row
def ablation_unit(prefix, eta, seed, train_x, train_y, test_x, test_y, epochs, milestones):
tag = f"{eta:.3f}".replace("-", "m")
path = ckpt_path(prefix, f"ablation_eta{tag}_{seed}")
if os.path.exists(path):
log(f"[ablation] skip existing eta={eta} seed={seed}")
return load_ckpt(path)
torch.set_num_threads(1)
torch.manual_seed(seed)
np.random.seed(seed)
t0 = time.time()
sigma = BETA ** (-(1 + eta) / 4.0)
model = SmallCNN()
params = [p for p in model.parameters()]
n = train_x.shape[0]
for epoch in range(epochs):
lam = lr_at(epoch, BASE_LR, milestones)
perm = np.random.permutation(n)
model.train()
for start in range(0, n, BATCH):
idx = perm[start:start + BATCH]
xb = torch.from_numpy(augment_batch(train_x[idx]))
yb = torch.from_numpy(train_y[idx])
fsgld_step(model, params, lam, sigma, BETA, WD, xb, yb)
test_acc = evaluate(model, test_x, test_y)
row = {"eta": eta, "seed": seed, "test_acc": test_acc}
save_ckpt(path, row)
log(f"[ablation] eta={eta} seed={seed} acc={test_acc:.4f} wall={time.time()-t0:.1f}s")
return row
def pretrain_unit(prefix, seed, train_x, clean_y, epochs, milestones):
path = os.path.join(WORK_DIR, f"{prefix}_pretrain_seed{seed}.pt")
if os.path.exists(path):
log(f"[pretrain] skip existing seed={seed}")
return path
torch.set_num_threads(1)
torch.manual_seed(seed)
np.random.seed(seed)
t0 = time.time()
model = SmallCNN()
run_epochs(model, "SGD", train_x, clean_y, epochs, milestones, BASE_LR, BATCH)
torch.save(model.state_dict(), path)
log(f"[pretrain] seed={seed} wall={time.time()-t0:.1f}s")
return path
def finetune_unit(prefix, optimizer_name, seed, pretrain_path, train_x, noisy_y, test_x, test_y,
epochs, milestones):
path = ckpt_path(prefix, f"finetune_{optimizer_name}_{seed}")
if os.path.exists(path):
log(f"[finetune] skip existing {optimizer_name} seed={seed}")
return load_ckpt(path)
torch.set_num_threads(1)
torch.manual_seed(seed + 1000)
np.random.seed(seed + 1000)
t0 = time.time()
model = SmallCNN()
model.load_state_dict(torch.load(pretrain_path))
run_epochs(model, optimizer_name, train_x, noisy_y, epochs, milestones, FT_LR, BATCH)
test_acc = evaluate(model, test_x, test_y)
row = {"optimizer": optimizer_name, "seed": seed, "test_acc": test_acc}
save_ckpt(path, row)
log(f"[finetune] {optimizer_name} seed={seed} acc={test_acc:.4f} wall={time.time()-t0:.1f}s")
return row
def flatness_unit(prefix, optimizer_name, model_path, x_batch, y_batch, m_hutch, top_iters):
path = ckpt_path(prefix, f"flatness_{optimizer_name}")
if os.path.exists(path):
log(f"[flatness] skip existing {optimizer_name}")
return load_ckpt(path)
torch.set_num_threads(1)
t0 = time.time()
model = SmallCNN()
model.load_state_dict(torch.load(model_path))
hess_trace, lam_top = compute_flatness(model, x_batch, y_batch, m_hutch, top_iters)
row = {"optimizer": optimizer_name, "hess_trace": hess_trace, "lambda_top": lam_top}
save_ckpt(path, row)
log(f"[flatness] {optimizer_name} trace={hess_trace:.4f} lam_top={lam_top:.4f} wall={time.time()-t0:.1f}s")
return row
# ------------------------------------------------------------------------- main
def main():
parser = argparse.ArgumentParser()
parser.add_argument("--toy", action="store_true")
args = parser.parse_args()
toy = args.toy
os.makedirs(WORK_DIR, exist_ok=True)
os.makedirs(RESULTS_DIR, exist_ok=True)
job_cores = int(os.environ.get("JOB_CORES", 4))
prefix = "exp02_toy" if toy else "exp02"
t_start = time.time()
provenance = {}
train_u8, train_fine, test_u8, test_fine = load_cifar100(provenance)
noisy_label, clean_label = load_cifar100n(provenance)
seeds = [0, 1] if toy else [0, 1, 2]
n_subset = 400 if toy else 15000
epochs_scratch = 2 if toy else 30
epochs_ft = 2 if toy else 15
epochs_pretrain = 2 if toy else 15
milestones_scratch = [1] if toy else [15, 25]
milestones_ft = [1] if toy else [10]
m_hutch = 4 if toy else 100
top_iters = 5 if toy else 100
flat_batch = 100 if toy else 2000
warmup_steps = 1 if toy else 10
timing_steps = 3 if toy else 50
etas = [-0.5, 0.1, 0.5, 0.9, 1.5]
subset_tag = "toy" if toy else "full"
sub_idx = get_subset_indices(n_subset, subset_tag)
train_x_all = preprocess(train_u8)
test_x_all = preprocess(test_u8)
train_x = train_x_all[sub_idx]
train_noisy_y = noisy_label[sub_idx].astype(np.int64)
train_clean_y = clean_label[sub_idx].astype(np.int64)
test_x = test_x_all
test_y = test_fine.astype(np.int64)
# ---- scratch (Claims 4, 6b) ----
scratch_jobs = [(opt, s) for opt in ("SGD", "SAM", "fSGLD") for s in seeds]
scratch_rows = Parallel(n_jobs=job_cores)(
delayed(scratch_unit)(prefix, opt, s, train_x, train_noisy_y, test_x, test_y,
epochs_scratch, milestones_scratch,
warmup_steps=warmup_steps, timing_steps=timing_steps)
for opt, s in scratch_jobs
)
def summarize(rows, key="test_acc"):
accs = [r[key] for r in rows]
return {"acc_mean": float(np.mean(accs)), "acc_std": float(np.std(accs))}
scratch_summary = {}
for opt in ("SGD", "SAM", "fSGLD"):
rows = [r for r in scratch_rows if r["optimizer"] == opt]
s = summarize(rows)
s["s_per_iter"] = float(np.mean([r["s_per_iter"] for r in rows]))
scratch_summary[opt] = s
efficiency = {
"sam_over_fsgld_s_per_iter": scratch_summary["SAM"]["s_per_iter"] / scratch_summary["fSGLD"]["s_per_iter"],
"sam_over_sgd": scratch_summary["SAM"]["s_per_iter"] / scratch_summary["SGD"]["s_per_iter"],
"fsgld_over_sgd": scratch_summary["fSGLD"]["s_per_iter"] / scratch_summary["SGD"]["s_per_iter"],
}
# ---- ablation (Claim 6a) ----
ablation_jobs = [(eta, s) for eta in etas for s in seeds]
ablation_rows = Parallel(n_jobs=job_cores)(
delayed(ablation_unit)(prefix, eta, s, train_x, train_noisy_y, test_x, test_y,
epochs_scratch, milestones_scratch)
for eta, s in ablation_jobs
)
ablation_summary = []
for eta in etas:
rows = [r for r in ablation_rows if abs(r["eta"] - eta) < 1e-9]
s = summarize(rows)
s["eta"] = eta
ablation_summary.append(s)
# ---- fine-tuning (Claim 5) ----
Parallel(n_jobs=job_cores)(
delayed(pretrain_unit)(prefix, s, train_x, train_clean_y, epochs_pretrain, milestones_scratch)
for s in seeds
)
ft_jobs = [(opt, s) for opt in ("SGD", "SAM", "fSGLD") for s in seeds]
finetune_rows = Parallel(n_jobs=job_cores)(
delayed(finetune_unit)(prefix, opt, s,
os.path.join(WORK_DIR, f"{prefix}_pretrain_seed{s}.pt"),
train_x, train_noisy_y, test_x, test_y, epochs_ft, milestones_ft)
for opt, s in ft_jobs
)
finetune_summary = {}
for opt in ("SGD", "SAM", "fSGLD"):
rows = [r for r in finetune_rows if r["optimizer"] == opt]
finetune_summary[opt] = summarize(rows)
# ---- flatness (Claim 6b), seed-0 scratch models, fixed clean batch ----
flat_idx = np.random.default_rng(0).choice(train_x.shape[0], min(flat_batch, train_x.shape[0]), replace=False)
flat_x = train_x[flat_idx]
flat_y = train_clean_y[flat_idx]
flatness_rows = Parallel(n_jobs=job_cores)(
delayed(flatness_unit)(prefix, opt,
os.path.join(WORK_DIR, f"{prefix}_scratchmodel_{opt}_0.pt"),
flat_x, flat_y, m_hutch, top_iters)
for opt in ("SGD", "SAM", "fSGLD")
)
results = {
"scratch": scratch_rows,
"scratch_summary": scratch_summary,
"efficiency": efficiency,
"ablation": ablation_rows,
"ablation_summary": ablation_summary,
"finetune": finetune_rows,
"finetune_summary": finetune_summary,
"flatness": flatness_rows,
"provenance": provenance,
"meta": {
"scale": ("REDUCED/toy: SmallCNN 0.5M params, tiny subset, few epochs, CPU; see BLOCKERS.md"
if toy else
"REDUCED: SmallCNN 0.5M params, 15k subset, 30 epochs, CPU; see BLOCKERS.md"),
"beta": BETA, "eta": ETA_FSGLD, "sigma": SIGMA_FSGLD,
"n_seeds": len(seeds), "epochs_scratch": epochs_scratch,
},
}
out_path = os.path.join(RESULTS_DIR, "exp02.json")
with open(out_path, "w") as f:
json.dump(results, f, indent=2)
print(f"exp02_neural: {'TOY' if toy else 'FULL'} run complete in {time.time()-t_start:.2f}s")
print(f" scratch: SGD={scratch_summary['SGD']['acc_mean']:.4f} "
f"SAM={scratch_summary['SAM']['acc_mean']:.4f} fSGLD={scratch_summary['fSGLD']['acc_mean']:.4f}")
print(f" s_per_iter: SGD={scratch_summary['SGD']['s_per_iter']:.4f} "
f"SAM={scratch_summary['SAM']['s_per_iter']:.4f} fSGLD={scratch_summary['fSGLD']['s_per_iter']:.4f}")
print(f" efficiency: {efficiency}")
print(f" finetune: SGD={finetune_summary['SGD']['acc_mean']:.4f} "
f"SAM={finetune_summary['SAM']['acc_mean']:.4f} fSGLD={finetune_summary['fSGLD']['acc_mean']:.4f}")
print(f" provenance: {provenance}")
print(f" results -> {out_path}")
if __name__ == "__main__":
main()