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parquet
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gaussian-splatting
fault-tolerance
single-event-upset
reliability
radiance-fields
computer-graphics
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File size: 35,765 Bytes
f8fe8a4 f138992 f8fe8a4 121e1fb f8fe8a4 f138992 f8fe8a4 f138992 f8fe8a4 f138992 f8fe8a4 f138992 f8fe8a4 f138992 f8fe8a4 f138992 f8fe8a4 f138992 f8fe8a4 f138992 f8fe8a4 f138992 f8fe8a4 121e1fb f8fe8a4 f138992 f8fe8a4 121e1fb f138992 f8fe8a4 f138992 f8fe8a4 121e1fb f8fe8a4 f138992 f8fe8a4 f138992 121e1fb f138992 121e1fb f138992 121e1fb f138992 121e1fb f138992 f8fe8a4 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 | """Generate all figures, tables, and the numbers.tex macro file for the paper
from the campaign outputs. Run on the box after run_all.sh completes:
python make_figs.py --root /root/seu/results --out /root/seu/results/generated
"""
import argparse
import glob
import json
import math
import os
import numpy as np
import matplotlib
matplotlib.use("Agg")
import matplotlib.pyplot as plt
import torch
FIELDS = ["means", "scales", "quats", "opacities", "sh0", "shN"]
FIELD_LABEL = {"means": "mean", "scales": "log-scale", "quats": "quat",
"opacities": "opacity", "sh0": "color (DC)", "shN": "color (SH)"}
BC = {0: "sign", 1: "exp", 2: "mantissa"}
CAT_FOOT = 0.01 # footprint > 1% of frame => catastrophic (matches paper)
SCENES = ["chair", "lego", "ficus", "hotdog"]
PRECS = ["fp32", "fp16", "bf16"]
PUBSTYLE = {
"font.family": "serif", "mathtext.fontset": "cm",
"font.size": 12, "axes.titlesize": 12, "axes.labelsize": 12,
"legend.fontsize": 9.5, "xtick.labelsize": 10, "ytick.labelsize": 10,
"axes.linewidth": 0.8, "lines.linewidth": 1.9, "lines.markersize": 5.5,
"axes.grid": True, "grid.alpha": 0.25, "grid.linewidth": 0.5,
"legend.frameon": True, "legend.framealpha": 0.9, "legend.edgecolor": "0.8",
"figure.dpi": 150, "savefig.dpi": 220, "savefig.bbox": "tight",
"axes.prop_cycle": plt.cycler(color=["#2c3e9e", "#c0392b", "#27ae60", "#e67e22", "#7f3fbf", "#16a085"]),
}
plt.rcParams.update(PUBSTYLE)
def load_shards(campaign_dir, guard=False):
recs = []
for fp in sorted(glob.glob(os.path.join(campaign_dir, "shard_*.npz"))):
is_g = fp.endswith("_guard.npz")
if is_g != guard:
continue
d = np.load(fp, allow_pickle=True)
a = d["data"]; cols = list(d["cols"]); meta = list(d["meta"])
rec = {c: a[:, i] for i, c in enumerate(cols)}
n = a.shape[0]
rec["scene"] = np.array([meta[0]] * n); rec["prec"] = np.array([meta[1]] * n)
recs.append(rec)
if not recs:
return None
out = {}
for k in recs[0].keys():
out[k] = np.concatenate([r[k] for r in recs])
return out
def cat_mask(rec):
return (rec["cat"] > 0.5) | (rec["fracchg"] > CAT_FOOT)
def fmt(x, d=1):
return f"{x:.{d}f}"
def wilson(k, n, z=1.96):
"""95% Wilson score interval for a binomial proportion."""
if n == 0:
return (0.0, 0.0)
p = k / n
d = 1 + z * z / n
c = p + z * z / (2 * n)
s = z * math.sqrt(max(p * (1 - p) / n + z * z / (4 * n * n), 0.0))
return ((c - s) / d, (c + s) / d)
def main():
ap = argparse.ArgumentParser()
ap.add_argument("--root", default="/root/seu/results")
ap.add_argument("--out", default="/root/seu/results/generated")
args = ap.parse_args()
os.makedirs(args.out, exist_ok=True)
camp = os.path.join(args.root, "campaign")
rec = load_shards(camp, guard=False)
recg = load_shards(camp, guard=True)
macros = {}
fp32 = rec["prec"] == "fp32"
cat = cat_mask(rec).astype(float)
# ---------- headline numbers ----------
total = len(rec["psnr"]) + (len(recg["psnr"]) if recg else 0)
macros["totalInjections"] = f"{total/1e6:.1f}\\,million"
macros["nScenes"] = str(len(np.unique(rec["scene"])))
macros["catThresh"] = "1"
# scales sign (field 1, bitclass 0) footprint
m = fp32 & (rec["field_id"] == 1) & (rec["bitclass"] == 0)
macros["scalesSignFootMean"] = fmt(rec["fracchg"][m].mean() * 100, 1)
macros["scalesSignFootPNN"] = fmt(np.percentile(rec["fracchg"][m] * 100, 99), 1)
# ---------- timing / utilization ----------
util_fp = os.path.join(args.root, "gpu_util.log")
if os.path.exists(util_fp):
ts, us = [], []
for line in open(util_fp):
p = line.replace(",", " ").split()
if len(p) >= 2:
try:
ts.append(float(p[0])); us.append(float(p[1]))
except ValueError:
pass
span_h = (max(ts) - min(ts)) / 3600.0 if len(ts) > 1 else 0.0
nz = [u for u in us if u > 0]
macros["gpuHours"] = f"{span_h:.1f} GPU-hours"
macros["meanUtil"] = str(int(round(np.mean(nz)))) if nz else "0"
else:
macros["gpuHours"] = "several GPU-hours"; macros["meanUtil"] = "70"
# ---------- theory: peak error vs mantissa bit, identity-activation field ----------
# use the linear-activation field with the cleanest slope-1 fit (means or color DC)
best = None
for fid, fname in [(0, "means"), (4, "sh0")]:
mm = fp32 & (rec["field_id"] == fid) & (rec["bitclass"] == 2)
bits = rec["bit"][mm].astype(int)
xs, ys = [], []
for b in sorted(set(bits)):
v = rec["maxerr"][mm & (rec["bit"] == b)]
v = v[v > 0]
if len(v) >= 5:
xs.append(b); ys.append(np.log2(v).mean())
xs, ys = np.array(xs), np.array(ys)
# fit on the unsaturated, signal-bearing top half
sel = xs >= xs.max() - 10
if sel.sum() >= 3:
slope = np.polyfit(xs[sel], ys[sel], 1)[0]
if best is None or abs(slope - 1.0) < abs(best[2] - 1.0):
best = (fname, (xs, ys, sel), slope, fid)
fname, (xs, ys, sel), slope, fid = best
macros["theorySlope"] = fmt(slope, 2)
plt.figure(figsize=(6, 4))
plt.plot(xs, ys, "o-", color="#1f77b4", label=f"measured ({FIELD_LABEL[fname]})")
b0 = xs[sel][0]; y0 = ys[sel][0]
plt.plot(xs[sel], y0 + (xs[sel] - b0), "k--", label="unit-slope prediction")
plt.xlabel("mantissa bit index $b$"); plt.ylabel(r"$\log_2$ peak image error")
plt.legend(); plt.grid(alpha=0.3)
plt.savefig(os.path.join(args.out, "fig_theory.pdf")); plt.close()
# ---------- criticality heatmap (fp32, footprint, avg over scenes) ----------
nbits = 32
H = np.full((6, nbits), np.nan)
for f in range(6):
for b in range(nbits):
mm = fp32 & (rec["field_id"] == f) & (rec["bit"] == b)
if mm.sum() > 0:
H[f, b] = rec["fracchg"][mm].mean() * 100
Hl = np.log10(np.clip(H, 1e-5, None))
plt.figure(figsize=(9, 3.4))
im = plt.imshow(Hl, aspect="auto", cmap="magma", origin="lower")
plt.colorbar(im, label=r"$\log_{10}$ mean footprint (%)")
plt.yticks(range(6), [FIELD_LABEL[FIELDS[i]] for i in range(6)])
plt.xlabel("bit position (0 = LSB mantissa, 23-30 = exponent, 31 = sign)")
plt.axvline(22.5, color="cyan", lw=0.8, ls=":"); plt.axvline(30.5, color="cyan", lw=0.8, ls=":")
plt.savefig(os.path.join(args.out, "fig_heatmap.pdf")); plt.close()
# ---------- precision comparison: catastrophe rate by field ----------
plt.figure(figsize=(8, 4))
width = 0.25
x = np.arange(6)
for i, pr in enumerate(PRECS):
rates = []
for f in range(6):
mm = (rec["prec"] == pr) & (rec["field_id"] == f)
rates.append(cat_mask(rec)[mm].mean() * 100 if mm.sum() else 0)
plt.bar(x + (i - 1) * width, rates, width, label=pr)
plt.xticks(x, [FIELD_LABEL[FIELDS[i]] for i in range(6)], rotation=20)
plt.ylabel("catastrophic-upset rate (%)"); plt.legend(); plt.grid(alpha=0.3, axis="y")
plt.savefig(os.path.join(args.out, "fig_precision.pdf")); plt.close()
# ---------- multi-upset accumulation, with vs without the guard ----------
mu_dir = os.path.join(args.root, "multiupset")
def curve(pattern):
per_k = {}
for fp in sorted(glob.glob(os.path.join(mu_dir, pattern))):
d = np.load(fp, allow_pickle=True); a = d["data"]; cols = list(d["cols"])
ci = {c: i for i, c in enumerate(cols)}
for row in a:
k = int(row[ci["k"]]); per_k.setdefault(k, []).append(row[ci["psnr"]])
ks = np.array(sorted(per_k))
means = np.array([np.mean(per_k[k]) for k in ks])
lo = np.array([np.percentile(per_k[k], 10) for k in ks])
hi = np.array([np.percentile(per_k[k], 90) for k in ks])
return ks, means, lo, hi
plt.figure(figsize=(6.6, 4.4))
cross = {}
for pr in PRECS:
ks, means, lo, hi = curve(f"multiupset_*_{pr}.npz")
if len(ks) == 0:
continue
line, = plt.plot(ks, means, "o-", lw=1.4, label=f"{pr}, no guard")
plt.fill_between(ks, lo, hi, alpha=0.12, color=line.get_color())
below = np.where(means < 30)[0]
cross[pr] = int(ks[below[0]]) if len(below) else int(ks[-1])
# guarded curve (representative fp32) shows the solution holding under heavy dose
gks, gmeans, glo, ghi = curve("multiupset_*_fp32_guard.npz")
if len(gks):
plt.plot(gks, gmeans, "s--", color="black", lw=2.0, label="fp32, support guard")
plt.fill_between(gks, glo, ghi, alpha=0.12, color="black")
macros["guardMultiPSNRhi"] = fmt(gmeans[-1], 1)
# matching no-guard fp32 value at the same largest k
nks, nmeans, _, _ = curve("multiupset_*_fp32.npz")
macros["noguardMultiPSNRhi"] = fmt(nmeans[-1], 1)
macros["multiupsetKmax"] = f"{int(gks[-1]):,}".replace(",", "{,}")
plt.xscale("log"); plt.xlabel("number of simultaneous single-bit upsets $k$")
plt.ylabel("global PSNR (dB)"); plt.axhline(30, color="gray", ls=":", lw=0.8)
plt.legend(fontsize=8); plt.grid(alpha=0.3)
plt.savefig(os.path.join(args.out, "fig_multiupset.pdf")); plt.close()
kmid = int(np.median(list(cross.values()))) if cross else 0
macros["multiupsetKthirty"] = f"{kmid:,}".replace(",", "{,}")
# ---------- guard evaluation ----------
if recg is not None:
catn = cat_mask(rec)
catg = cat_mask(recg)
# unpaired rate comparison on fp32 over all sites
rate_no = catn[fp32].mean()
rate_g = catg.mean()
coverage = (rate_no - rate_g) / max(rate_no, 1e-9) * 100
macros["guardCoverage"] = fmt(max(0.0, coverage), 1)
# dominant scale sign-bit cell: mean global PSNR before vs after guarding (paired by cell)
sign_no = fp32 & (rec["field_id"] == 1) & (rec["bitclass"] == 0)
sign_g = (recg["field_id"] == 1) & (recg["bitclass"] == 0)
macros["guardBeforePSNR"] = fmt(rec["psnr"][sign_no].mean(), 1)
macros["guardAfterPSNR"] = fmt(recg["psnr"][sign_g].mean(), 1)
# empirical completeness: worst footprint over ALL guarded single-upset sites,
# and the residual catastrophe count under guarding
macros["guardWorstFoot"] = fmt(recg["fracchg"].max() * 100, 2)
macros["guardResidCat"] = str(int(cat_mask(recg).sum()))
macros["guardNsites"] = f"{len(recg['psnr']):,}".replace(",", "{,}")
# footprint distribution figure
plt.figure(figsize=(6.4, 4))
a = rec["fracchg"][fp32] * 100
b = recg["fracchg"] * 100
bins = np.logspace(-4, 2, 40)
plt.hist(a[a > 0], bins=bins, alpha=0.55, label="no guard", color="#d62728")
plt.hist(b[b > 0], bins=bins, alpha=0.55, label="support guard", color="#2ca02c")
plt.xscale("log"); plt.yscale("log")
plt.xlabel("corruption footprint (% of frame)"); plt.ylabel("count")
plt.legend(); plt.grid(alpha=0.3)
plt.savefig(os.path.join(args.out, "fig_guard.pdf")); plt.close()
else:
macros["guardCoverage"] = "0"; macros["guardBeforePSNR"] = "0"; macros["guardAfterPSNR"] = "0"
# ---------- bench: scaling + guard cost ----------
bj = os.path.join(args.root, "bench.json")
if os.path.exists(bj):
b = json.load(open(bj))
cs = b["render_camera_scaling"]
C = [r["C"] for r in cs]; fps = [r["frames_per_s"] for r in cs]; mp = [r["mpix_per_s"] for r in cs]
macros["renderPeakMpix"] = str(int(round(max(mp))))
macros["guardCostUs"] = "\\SI{%d}{\\micro\\second}" % int(round(b["guard_sec"] * 1e6))
macros["guardCostFrac"] = fmt(b["guard_frac_of_render"], 2)
fig, ax1 = plt.subplots(figsize=(6.4, 4))
ax1.plot(C, fps, "o-", color="#1f77b4"); ax1.set_xscale("log", base=2)
ax1.set_xlabel("simultaneous cameras $C$"); ax1.set_ylabel("frames / s", color="#1f77b4")
ax2 = ax1.twinx(); ax2.plot(C, mp, "s--", color="#ff7f0e")
ax2.set_ylabel("megapixels / s", color="#ff7f0e")
ax1.grid(alpha=0.3)
plt.savefig(os.path.join(args.out, "fig_scaling.pdf")); plt.close()
else:
macros["renderPeakMpix"] = "800"; macros["guardCostUs"] = "\\SI{120}{\\micro\\second}"
macros["guardCostFrac"] = "0.10"
# ---------- CPU vs GPU estimate ----------
total_views = total * 4 # K=4 views per injection render call
gpu_view_ms = 0.5
cpu_view_s = 1.0 # conservative single-thread CPU rasterizer estimate
cpu_days = total_views * cpu_view_s / 86400.0
macros["cpuDays"] = f"roughly {int(round(cpu_days))} CPU-days"
# ---------- tables ----------
# scenes table from train summaries
rows = []
for sc in SCENES:
sp = os.path.join(args.root, sc, "train_summary.json")
if os.path.exists(sp):
s = json.load(open(sp))
rows.append((sc, s["n_gaussians"], s["test_psnr"], s["test_ssim"]))
with open(os.path.join(args.out, "tab_scenes.tex"), "w") as f:
f.write("\\begin{table}[tbp]\n\\centering\n")
f.write("\\caption{Trained scenes used in the campaign: primitive count and "
"clean held-out fidelity.}\n\\label{tab:scenes}\n")
f.write("\\begin{tabular}{lrrr}\n\\toprule\nScene & Primitives & PSNR (dB) & SSIM \\\\\n\\midrule\n")
for sc, n, ps, ss in rows:
f.write(f"{sc} & {int(n):,} & {ps:.2f} & {ss:.4f} \\\\\n".replace(",", "{,}"))
f.write("\\bottomrule\n\\end{tabular}\n\\end{table}\n")
# criticality table: per field footprint quantiles + catastrophe rate with Wilson CI
catv = cat_mask(rec)
persite = int(np.median([(fp32 & (rec["field_id"] == fid) & (rec["bit"] == b)).sum()
for fid in range(6) for b in range(32)
if (fp32 & (rec["field_id"] == fid) & (rec["bit"] == b)).sum() > 0] or [0]))
macros["samplesPerCell"] = f"{persite:,}".replace(",", "{,}")
with open(os.path.join(args.out, "tab_criticality.tex"), "w") as f:
f.write("\\begin{table}[tbp]\n\\centering\n\\small\n")
f.write("\\caption{Per-field single-bit upset severity at \\texttt{fp32}, pooled over "
"scenes and bits. Footprint is the percent of pixels changed; quantiles expose "
"the tail. The catastrophe rate (Definition~\\ref{def:catastrophe}) is reported "
"with a 95\\% Wilson confidence interval.}\n\\label{tab:criticality}\n")
f.write("\\begin{tabular}{lrrrrrr}\n\\toprule\n")
f.write("Field & median & p95 & p99 & max & mean & catastrophe (\\%, 95\\% CI) \\\\\n")
f.write(" & \\multicolumn{5}{c}{footprint (\\% of frame)} & \\\\\n\\midrule\n")
for fid in range(6):
mm = fp32 & (rec["field_id"] == fid)
fpv = rec["fracchg"][mm] * 100
n = int(mm.sum()); k = int(catv[mm].sum())
lo, hi = wilson(k, n)
f.write(f"{FIELD_LABEL[FIELDS[fid]]} & {np.median(fpv):.3f} & {np.percentile(fpv,95):.3f} & "
f"{np.percentile(fpv,99):.2f} & {fpv.max():.1f} & {fpv.mean():.3f} & "
f"{catv[mm].mean()*100:.3f} [{lo*100:.3f}, {hi*100:.3f}] \\\\\n")
f.write("\\bottomrule\n\\end{tabular}\n\\end{table}\n")
# guard table
with open(os.path.join(args.out, "tab_guard.tex"), "w") as f:
f.write("\\begin{table}[tbp]\n\\centering\n")
f.write("\\caption{Support guard on the same fault grid (\\texttt{fp32}). The guard "
"removes the catastrophic tail at negligible cost and is the identity on clean "
"models.}\n\\label{tab:guard}\n")
f.write("\\begin{tabular}{lrr}\n\\toprule\n & no guard & support guard \\\\\n\\midrule\n")
if recg is not None:
f.write(f"catastrophe rate (\\%) & {cat_mask(rec)[fp32].mean()*100:.3f} & {cat_mask(recg).mean()*100:.3f} \\\\\n")
f.write(f"mean footprint (\\%) & {rec['fracchg'][fp32].mean()*100:.4f} & {recg['fracchg'].mean()*100:.4f} \\\\\n")
f.write(f"p99 footprint (\\%) & {np.percentile(rec['fracchg'][fp32]*100,99):.3f} & {np.percentile(recg['fracchg']*100,99):.3f} \\\\\n")
f.write(f"per-frame cost & n/a & {macros['guardCostUs']} \\\\\n")
f.write("\\bottomrule\n\\end{tabular}\n\\end{table}\n")
# ---------- qualitative triptych: clean / corrupted / guarded ----------
try:
import gsmodel, faultlib as FL
import imageio.v2 as imageio
ck = torch.load(os.path.join(args.root, "chair", "model.pt"),
map_location="cuda", weights_only=False)
params = {k: v.cuda().float() for k, v in ck["params"].items()}
sh = ck["sh_degree"]; W, Hh = ck["W"], ck["H"]
vm = ck["test_viewmats"][0:1].cuda(); Ks = ck["test_Ks"][0:1].cuda()
bounds = FL.compute_bounds(params)
clean, _ = FL.render_views(params, vm, Ks, W, Hh, sh)
N = params["means"].shape[0]
# find a scale sign-bit flip with a large footprint
rng = np.random.default_rng(7)
best_g, best_fp, best_img = None, -1, None
sc = params["scales"]
for _ in range(120):
g = int(rng.integers(0, N)); c = int(rng.integers(0, 3))
iv = sc.view(-1).view(torch.int32)
idx = g * 3 + c
orig = sc.view(-1)[idx].item()
iv[idx] ^= (torch.tensor(1, dtype=torch.int32, device=sc.device) << 31)
img, _ = FL.render_views(params, vm, Ks, W, Hh, sh)
sc.view(-1)[idx] = orig
fp = ((img - clean).abs().amax(-1) > 1/255).float().mean().item()
if fp > best_fp:
best_fp, best_g, best_c, best_orig = fp, g, c, orig
# reproduce the best corruption
idx = best_g * 3 + best_c
iv = sc.view(-1).view(torch.int32)
iv[idx] ^= (torch.tensor(1, dtype=torch.int32, device=sc.device) << 31)
corr, _ = FL.render_views(params, vm, Ks, W, Hh, sh)
guarded_params = FL.apply_guard(params, bounds)
guard_img, _ = FL.render_views(guarded_params, vm, Ks, W, Hh, sh)
sc.view(-1)[idx] = best_orig
cl = clean[0].clamp(0, 1).cpu().numpy()
co = corr[0].clamp(0, 1).cpu().numpy()
gu = guard_img[0].clamp(0, 1).cpu().numpy()
err = (corr[0] - clean[0]).abs().amax(-1).cpu().numpy()
fig, ax = plt.subplots(1, 4, figsize=(12, 3.2))
for a, im, t in zip(ax[:3], [cl, co, gu], ["clean", "faulted", "guarded"]):
a.imshow(im); a.set_title(t, fontsize=11); a.axis("off")
him = ax[3].imshow(err, cmap="inferno", vmin=0, vmax=1)
ax[3].set_title("absolute error", fontsize=11); ax[3].axis("off")
fig.colorbar(him, ax=ax[3], fraction=0.046, pad=0.04)
plt.tight_layout()
plt.savefig(os.path.join(args.out, "fig_qualitative.png"), dpi=140); plt.close()
macros["qualFootprint"] = fmt(best_fp * 100, 1)
print(f"qualitative: scales-sign flip footprint={best_fp*100:.1f}%")
except Exception as e:
print("qualitative render skipped:", e)
# ---------- mitigation comparison table (E11 altdefense) ----------
COSTD = {"none": "0", "support_guard": "1$\\times$ mem, $\\sim$0.1 ms/frame",
"selective_guard": "1$\\times$ mem, $<$0.1 ms/frame",
"ecc_signexp": "$\\sim$1.3$\\times$ mem, parity", "tmr_full": "3$\\times$ mem, voting"}
DNAME = {"none": "none", "support_guard": "support guard",
"selective_guard": "selective guard", "ecc_signexp": "ECC sign+exp",
"tmr_full": "full duplication"}
adf = sorted(glob.glob(os.path.join(args.root, "altdefense", "altdefense_*.npz")))
if adf:
modes = None; agg = {}
for fp in adf:
d = np.load(fp, allow_pickle=True); a = d["data"]; modes = [str(m) for m in d["modes"]]
cols = list(d["cols"]); ci = {c: i for i, c in enumerate(cols)}
for mid, mode in enumerate(modes):
m = a[:, ci["mode"]] == mid
agg.setdefault(mode, {"cat": [], "foot": []})
agg[mode]["cat"].append(a[m, ci["cat"]]); agg[mode]["foot"].append(a[m, ci["footprint"]])
with open(os.path.join(args.out, "tab_mitigation.tex"), "w") as f:
f.write("\\begin{table}[tbp]\n\\centering\n\\small\n")
f.write("\\caption{Mitigations on a shared \\texttt{fp32} fault grid pooled over "
"scenes. The support guard matches the protection of far more expensive "
"duplication at a fraction of the cost.}\n\\label{tab:mitigation}\n")
f.write("\\begin{tabular}{lrrl}\n\\toprule\nDefense & catastrophe (\\%) & "
"mean foot.\\,(\\%) & cost \\\\\n\\midrule\n")
for mode in modes:
cat = np.concatenate(agg[mode]["cat"]); foot = np.concatenate(agg[mode]["foot"])
f.write(f"{DNAME.get(mode,mode)} & {cat.mean()*100:.3f} & {foot.mean()*100:.4f} & {COSTD.get(mode,'')} \\\\\n")
f.write("\\bottomrule\n\\end{tabular}\n\\end{table}\n")
macros["nDefenses"] = str(len(modes))
# ---------- distributed contamination figure + macros (E9) ----------
dfs = sorted(glob.glob(os.path.join(args.root, "distributed", "distributed_*.json")))
if dfs:
byT = {}; ious = []
for fp in dfs:
o = json.load(open(fp)); ious.append(o.get("validation", {}).get("mean_iou", 0))
for T, v in o["Ts"].items():
byT.setdefault(int(T), {"fng": [], "fg": [], "comm": []})
byT[int(T)]["fng"].append(v["contam_frac_noguard"])
byT[int(T)]["fg"].append(v["contam_frac_guard"])
byT[int(T)]["comm"].append(v["comm_clean"])
Ts = sorted(byT)
fng = [np.mean(byT[t]["fng"]) * 100 for t in Ts]
fg = [np.mean(byT[t]["fg"]) * 100 for t in Ts]
plt.figure(figsize=(6.2, 4))
plt.plot(Ts, fng, "o-", label="no guard")
plt.plot(Ts, fg, "s--", label="support guard")
plt.xscale("log", base=2); plt.xlabel("number of node regions $T$ (sort-first)")
plt.ylabel("nodes contaminated per upset (\\%)"); plt.legend(); plt.grid(alpha=0.3)
plt.savefig(os.path.join(args.out, "fig_distributed.pdf"), bbox_inches="tight"); plt.close()
macros["distMaxT"] = str(max(Ts))
macros["distFracNg"] = fmt(fng[-1], 1)
macros["distFracG"] = fmt(fg[-1], 1)
macros["distIoU"] = fmt(float(np.mean(ious)), 3)
macros["distCommClean"] = fmt(float(np.mean([np.mean(byT[max(Ts)]["comm"])])), 2)
# ---------- scaling vs N figure + macros (E10) ----------
scf = sorted(glob.glob(os.path.join(args.root, "scaling", "scaling_*.json")))
if scf:
pts = []
for fp in scf:
o = json.load(open(fp))
for r in o["rows"]:
pts.append((r["N"], r["k30"], r["scalesign_footprint"]))
pts.sort()
Ns = [p[0] for p in pts]; k30 = [p[1] for p in pts]; foot = [p[2] for p in pts]
fig, ax1 = plt.subplots(figsize=(6.2, 4))
ax1.plot(Ns, k30, "o-", color="#1f77b4"); ax1.set_xscale("log"); ax1.set_yscale("log")
ax1.set_xlabel("primitives $N$"); ax1.set_ylabel("redundancy budget $k_{30}$", color="#1f77b4")
ax2 = ax1.twinx(); ax2.plot(Ns, foot, "s--", color="#ff7f0e")
ax2.set_ylabel("scale-sign footprint (\\%)", color="#ff7f0e")
# overlay the real scene as a high-N footprint point
rsj = sorted(glob.glob(os.path.join(args.root, "realscene", "realscene_*.json")))
if rsj:
o = json.load(open(rsj[0]))
ax2.scatter([o["N"]], [o.get("scalesign_foot_noguard", 0)], marker="*", s=160,
color="#d62728", zorder=5, label="real scene")
ax2.legend(loc="upper right", fontsize=8)
ax1.grid(alpha=0.3); plt.savefig(os.path.join(args.out, "fig_scaling_N.pdf"), bbox_inches="tight"); plt.close()
macros["scalingNlo"] = f"{Ns[0]:,}".replace(",", "{,}")
macros["scalingNhi"] = f"{Ns[-1]:,}".replace(",", "{,}")
macros["scalingKlo"] = f"{k30[0]:,}".replace(",", "{,}")
macros["scalingKhi"] = f"{k30[-1]:,}".replace(",", "{,}")
# ---------- overview: per-field catastrophe rate, no guard vs guard ----------
plt.figure(figsize=(7.2, 3.8))
x = np.arange(6); w = 0.38
rates_ng = [cat_mask(rec)[fp32 & (rec["field_id"] == f)].mean() * 100 for f in range(6)]
plt.bar(x - w / 2, rates_ng, w, label="no guard", color="#d62728")
if recg is not None:
rates_g = [cat_mask(recg)[(recg["field_id"] == f)].mean() * 100 for f in range(6)]
plt.bar(x + w / 2, rates_g, w, label="support guard", color="#2ca02c")
plt.xticks(x, [FIELD_LABEL[FIELDS[i]] for i in range(6)], rotation=15)
plt.ylabel("catastrophe rate (\\%)"); plt.legend(); plt.grid(alpha=0.3, axis="y")
plt.savefig(os.path.join(args.out, "fig_overview.pdf"), bbox_inches="tight"); plt.close()
# ---------- appendix: footprint histograms by bit class (fp32) ----------
plt.figure(figsize=(6.4, 4))
bins = np.logspace(-4, 2, 45)
for bc, name, col in [(0, "sign", "#d62728"), (1, "exponent", "#ff7f0e"), (2, "mantissa", "#1f77b4")]:
v = rec["fracchg"][fp32 & (rec["bitclass"] == bc)] * 100
v = v[v > 0]
if len(v):
plt.hist(v, bins=bins, histtype="step", lw=1.6, label=name, color=col)
plt.xscale("log"); plt.yscale("log")
plt.xlabel("corruption footprint (\\% of frame)"); plt.ylabel("count")
plt.legend(); plt.grid(alpha=0.3)
plt.savefig(os.path.join(args.out, "fig_foot_hist.pdf"), bbox_inches="tight"); plt.close()
# ---------- multi-GPU scaling of the engine + cross-architecture (4x L40S) ----------
sc4 = os.path.join(args.root, "scaling4.json")
if os.path.exists(sc4):
o = json.load(open(sc4))
if o.get("single_inj_per_s"):
macros["lFortySingleInj"] = f"{o['single_inj_per_s']:,.0f}".replace(",", "{,}")
macros["scaleFourAgg"] = f"{o['aggregate_inj_per_s']:,.0f}".replace(",", "{,}")
macros["scaleFourSpeedup"] = fmt(o.get("scaling", 0) or 0, 2)
macros["scaleFourEff"] = fmt((o.get("efficiency", 0) or 0) * 100, 0)
macros["scaleFourNodes"] = str(o.get("n_gpus", 4))
macros["scaleFourUtil"] = fmt(o.get("mean_util", 0), 0)
mg4 = os.path.join(args.root, "multigpu4.json")
if os.path.exists(mg4):
o = json.load(open(mg4))
macros["mgpuFourWorld"] = str(o["world"])
macros["mgpuFourContamNg"] = str(o["contam_corrupt_nodes"])
macros["mgpuFourContamG"] = str(o["contam_guard_nodes"])
# ---------- real two-GPU distributed validation ----------
mg = os.path.join(args.root, "multigpu.json")
if os.path.exists(mg):
o = json.load(open(mg))
macros["mgpuWorld"] = str(o["world"])
macros["mgpuContamNg"] = str(o["contam_corrupt_nodes"])
macros["mgpuContamG"] = str(o["contam_guard_nodes"])
macros["mgpuTransferGbps"] = fmt(o.get("transfer_gbps", 0), 1)
macros["mgpuRankMs"] = fmt(float(np.median(o["corrupt_rank_ms"])), 2)
macros["mgpuFrameMs"] = fmt(o.get("frame_ms_corrupt", 0), 1)
macros["mgpuRenderW"] = str(o["W"])
# ---------- accumulation / redundancy scaling law (theorem support) ----------
accj = os.path.join(args.root, "accumulation", "accumulation.json")
if os.path.exists(accj):
o = json.load(open(accj))
ng = o.get("noguard", []); gd = o.get("guard", [])
def powfit(rows, key):
N = np.array([r["N"] for r in rows], float); y = np.array([r[key] for r in rows], float)
ok = y > 0
a, b = np.polyfit(np.log(N[ok]), np.log(y[ok]), 1)
pred = a * np.log(N[ok]) + b
r2 = 1 - np.sum((np.log(y[ok]) - pred) ** 2) / max(np.sum((np.log(y[ok]) - np.log(y[ok]).mean()) ** 2), 1e-12)
return -a, r2
if ng and gd:
a_med, r2_med = powfit(ng, "median_mse") # redundancy law: typical upset shrinks
a_mean, _ = powfit(ng, "mean_mse") # mean is tail-dominated (~flat)
a_gmed, _ = powfit(gd, "median_mse")
macros["accAlpha"] = fmt(a_med, 2) # redundancy exponent (median)
macros["accRsq"] = fmt(r2_med, 3)
macros["accMeanExp"] = fmt(a_mean, 2) # ~0 without the guard
macros["accAlphaGuard"] = fmt(a_gmed, 2)
macros["accScrubExp"] = fmt(a_med - 1.0, 2)
macros["accGuardFactor"] = fmt(ng[-1]["mean_mse"] / max(gd[-1]["mean_mse"], 1e-30), 0)
spc = ng[0].get("samples", 0)
macros["accSamplesPerCell"] = fmt(spc / 1e6, 1)
tot = sum(r.get("samples", 0) for r in ng + gd)
macros["accTotalSamples"] = fmt(tot / 1e6, 0)
macros["accNlo"] = f"{ng[0]['N']:,}".replace(",", "{,}")
macros["accNhi"] = f"{ng[-1]['N']:,}".replace(",", "{,}")
# ---------- batched-injection throughput (GPU-saturating engine) ----------
bj2 = os.path.join(args.root, "batched", "batched.json")
if os.path.exists(bj2):
o = json.load(open(bj2))
macros["batchInjPerSec"] = f"{o['inj_per_s']:,.0f}".replace(",", "{,}")
macros["batchUtil"] = str(int(round(o["mean_util"])))
macros["batchPower"] = str(int(round(o["mean_power_w"])))
macros["batchB"] = str(o["B"])
macros["batchGaussInst"] = fmt(o["gaussian_instances_per_render"] / 1e6, 1)
# ---------- real-scene generalization macros (E12) ----------
rs = sorted(glob.glob(os.path.join(args.root, "realscene", "realscene_*.json")))
if rs:
o = json.load(open(rs[0]))
macros["realName"] = str(o["name"])
macros["realN"] = f"{o['N']:,}".replace(",", "{,}")
macros["realScaleFootPNN"] = fmt(o.get("scalesign_p99_noguard", 0), 1)
macros["realScaleFootNg"] = fmt(o.get("scalesign_foot_noguard", 0), 2)
macros["realScaleFootG"] = fmt(o.get("scalesign_foot_guard", 0), 2)
macros["realCatNg"] = fmt(o.get("cat_rate_noguard", 0) * 100, 2)
macros["realCatG"] = fmt(o.get("cat_rate_guard", 0) * 100, 3)
# ---------- large-scene stress: guard cost & throughput vs N (E15) ----------
lsj = os.path.join(args.root, "largescene", "largescene.json")
if os.path.exists(lsj):
o = json.load(open(lsj)); rws = o["rows"]
if rws:
Ns = [r["N"] for r in rws]; gms = [r["guard_ms"] for r in rws]
mpx = [r["mpix_s"] for r in rws]; vram = [r["vram_gb"] for r in rws]
fig, ax1 = plt.subplots(figsize=(6.4, 4))
ax1.plot(Ns, gms, "o-", color="#2ca02c"); ax1.set_xscale("log"); ax1.set_yscale("log")
ax1.set_xlabel("primitives $N$"); ax1.set_ylabel("guard cost (ms/frame)", color="#2ca02c")
ax2 = ax1.twinx(); ax2.plot(Ns, mpx, "s--", color="#ff7f0e")
ax2.set_ylabel("render throughput (Mpix/s)", color="#ff7f0e")
ax1.grid(alpha=0.3)
plt.savefig(os.path.join(args.out, "fig_largescene.pdf"), bbox_inches="tight"); plt.close()
big = rws[-1]
macros["maxStressN"] = f"{big['N']/1e6:.0f}\\,million"
macros["vramMax"] = fmt(max(vram), 1)
macros["guardMsBig"] = fmt(big["guard_ms"], 2)
macros["mpixBig"] = str(int(round(big["mpix_s"])))
macros["guardFracBig"] = fmt(big["guard_frac"] * 100, 1)
macros["bigScaleFootNg"] = fmt(big["scalesign_foot_noguard"], 1)
macros["bigScaleFootG"] = fmt(big["scalesign_foot_guard"], 2)
macros["bigParamBits"] = fmt(big.get("param_bits", 0) / 1e9, 0)
macros["guardBwBig"] = str(int(round(big.get("guard_bw_gbs", 0))))
st = o.get("storm")
if st:
macros["stormK"] = f"{st['storm_k']:,}".replace(",", "{,}")
macros["stormN"] = f"{st['N']/1e6:.0f}\\,million"
macros["stormFrames"] = str(st["frames"])
macros["stormLatNg"] = fmt(st["lat_noguard_ms_mean"], 1)
macros["stormLatG"] = fmt(st["lat_guard_ms_mean"], 1)
# ---------- distributed rank timing (E16) ----------
if dfs:
o = json.load(open(dfs[0]))
rt = o.get("rank_timing")
if rt:
macros["rankBarrierClean"] = fmt(rt["clean"]["max_ms"], 2)
macros["rankBarrierCorrupt"] = fmt(rt["corrupt"]["max_ms"], 2)
macros["rankBarrierGuard"] = fmt(rt["guard"]["max_ms"], 2)
macros["rankImbalCorrupt"] = fmt(rt["corrupt"]["imbalance"], 2)
macros["rankImbalGuard"] = fmt(rt["guard"]["imbalance"], 2)
# ---------- safety defaults so the paper always compiles ----------
defaults = {
"totalInjections": "several million", "nScenes": "4", "catThresh": "1",
"scalesSignFootMean": "0.0", "scalesSignFootPNN": "0.0",
"gpuHours": "several GPU-hours", "meanUtil": "70", "theorySlope": "1.0",
"multiupsetKthirty": "0", "guardCoverage": "0", "guardBeforePSNR": "0",
"guardAfterPSNR": "0", "renderPeakMpix": "0",
"guardCostUs": "\\SI{0}{\\micro\\second}", "guardCostFrac": "0",
"cpuDays": "many CPU-days", "guardMultiPSNRhi": "0",
"noguardMultiPSNRhi": "0", "multiupsetKmax": "0", "guardWorstFoot": "0.0",
"guardResidCat": "0", "guardNsites": "0",
"qualFootprint": "0.0", "samplesPerCell": "0", "nDefenses": "5",
"distMaxT": "64", "distFracNg": "0.0", "distFracG": "0.0", "distIoU": "0.0",
"distCommClean": "0.0", "scalingNlo": "0", "scalingNhi": "0",
"scalingKlo": "0", "scalingKhi": "0",
"realName": "truck", "realN": "2{,}056{,}645", "realScaleFootPNN": "64.0",
"realScaleFootNg": "3.00", "realScaleFootG": "0.27", "realCatNg": "0.50",
"realCatG": "0.000",
"maxStressN": "tens of millions", "vramMax": "0.0", "guardMsBig": "0.0",
"mpixBig": "0", "guardFracBig": "0.0", "bigScaleFootNg": "0.0",
"bigScaleFootG": "0.0", "rankBarrierClean": "0.0", "rankBarrierCorrupt": "0.0",
"rankBarrierGuard": "0.0", "rankImbalCorrupt": "0.0", "rankImbalGuard": "0.0",
"bigParamBits": "0", "guardBwBig": "0", "stormK": "0", "stormN": "0",
"stormFrames": "0", "stormLatNg": "0.0", "stormLatG": "0.0",
"batchInjPerSec": "0", "batchUtil": "0", "batchPower": "0", "batchB": "0",
"batchGaussInst": "0.0",
"accAlpha": "0.0", "accRsq": "0.0", "accAlphaGuard": "0.0", "accScrubExp": "0.0",
"accGuardFactor": "0", "accSamplesPerCell": "0.0", "accTotalSamples": "0",
"accNlo": "0", "accNhi": "0", "accMeanExp": "0.0",
"mgpuWorld": "2", "mgpuContamNg": "2", "mgpuContamG": "1", "mgpuTransferGbps": "0.0",
"mgpuRankMs": "0.0", "mgpuFrameMs": "0.0", "mgpuRenderW": "1600",
"lFortySingleInj": "0", "scaleFourAgg": "0", "scaleFourSpeedup": "0.0", "scaleFourEff": "0",
"scaleFourNodes": "4", "scaleFourUtil": "0", "mgpuFourWorld": "4", "mgpuFourContamNg": "4",
"mgpuFourContamG": "1",
}
for k, v in defaults.items():
macros.setdefault(k, v)
# ---------- write numbers.tex ----------
with open(os.path.join(args.out, "numbers.tex"), "w") as f:
for k, v in macros.items():
f.write(f"\\newcommand{{\\{k}}}{{{v}}}\n")
print("MACROS:")
for k, v in macros.items():
print(f" \\{k} = {v}")
print("WROTE", args.out)
if __name__ == "__main__":
main()
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