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metadata 
license: mit
pretty_name: whest-p2-bakev2 — cumulant sketches of 16x1024 ReLU MLPs (round 1)
tags:
  - whestbench
  - mlp
  - cumulants
  - sketches
  - monte-carlo

whest-p2-bakev2 — cumulant sketches of 16×1024 ReLU MLPs (round 1, 2026-09-13)

Monte-Carlo cumulants of the pre-/post-activations of 1024-wide, 16-layer ReLU MLPs under standard-normal inputs, stored as Ω-sketches (every net) plus a few dense n×n blocks (validation nets). Companion code: ap_p2_bakev2_schema.py (seeds, Ω generator, conversions, loader), ap_p2_bakev2.py (bake), ap_p2_bakev2_check.py (validation). Schema version bakev2-r1-2026-09-13.

bake family / nets tier N stores HF repo
A d8b 0..2047 (He-init random; extension to 14 048 later) sketch 1e8 marginals + sketches whest-p2-bakev2-d8b-sketch-g00
B-full (primary validation) bench 0..99 (aicrowd config full, rows 0–99) supp 1e8 marginals + sketches (+ --extra-singles) + dense post_K21, post_K22, gate_GX, gate_GG whest-p2-bakev2-bench-supp
B-mini (continuity with the Phase-2 write-up tables) mini 0..99 (aicrowd split mini) supp 1e8 same as B-full whest-p2-bakev2-mini-supp
C nets 0..7 of A, B-full, B-mini, under rep1/… same 1e8 independent sample seed, same Ω → per-quantity noise floors same repos, rep1/ prefix

mini and full are disjoint splits. 99 of the 100 mini names do not occur in full; the one shared name (ashley-williams, mini row 85 / full row 115) is a coincidence whose weights were not verified identical — never do cross-split lookups by name or index. Dense PRE-activation raw blocks (pre_M11/M21/M31/M22, post M11) for these nets are deliberately not re-baked here; they live in keenanpepper/arc-whestbench-p2-full1000-N1e9 (all 1000 full nets, N = 1e9 — the remaining 900 dense-pair nets are ready when validation wants to scale) and, for mini, in the local p2moments_mini bake (100 nets, N = 1e8) plus p2moments_mini_N1e9 (nets 0–1, N = 1e9). The κ₂₂/κ₂₁ sketches of Bake B are cross-checked against those independent bakes (ap_p2_bakev2_check.py --ref-npz): at 1e9-vs-1e8 the expected difference is one 1e8 bake's noise; at 1e8-vs-1e8 it is √2 of that.

Model / layer convention

z_l = a_{l-1} @ W_l, a_l = relu(z_l), a_{-1} = x ~ N(0, I_1024), l = 0..15 (0-based weight index), W_l is (n_in, n_out); ReLU after every layer including the last (= grader's local_engine forward). Forward in fp32 with TF32 disabled (torch.backends.cuda.matmul.allow_tf32 = False, set_float32_matmul_precision("highest")); every accumulator fp64 on GPU.

d8b weights: W = torch.randn(16,1024,1024, generator=torch.Generator("cpu").manual_seed(770000+idx)) * sqrt(2/1024) (fp32). Weights are not stored; marg.npz carries w_sha256 (sha256 of the fp32 bytes in (l, in, out) order) and torch_version so a regeneration can be verified.

Sampling / seeds

One Philox stream per net (torch.Generator("cuda")), consumed in chunks of CHUNK = 131072 samples (torch.randn(chunk, 1024)); the chunk size is part of the reproducibility contract and is recorded in marg.npz["chunk"]. Seeds are splitmix64 of a packed integer:

packed = idx | family<<20 | tier<<24 | rep<<28 | kind<<32 | layer<<40
seed   = splitmix64(packed) & (2**63-1)
family: bench=0, d8b=1   tier: full=0, sketch=1   rep: 0 main, 1 re-bake
kind:   0 sample stream, 1 pilot stream (shift estimation), 2 Omega (tier=rep=0 forced)

Pilot: n_pilot = 262144 samples from the kind-1 stream give per-neuron means used as shifts c (fp32, stored); all accumulators run on u = z − c, v = a − c. End-of-bake conversions (fp64) are exact, so the residual shift E[u] (~1e-3 σ) has no effect on stored central/cumulant quantities.

Ω (sketch matrices)

Per (net, layer): G ~ N(0,1) of shape (1024, 128) from a CPU generator seeded with omega_seed(family, idx, layer); layer 16 is the input-space Ω (used only by gate_GX_O at l=0).

Omega_l  = G / sqrt(128)               (n, K1=128)  single sketches  X @ Omega
Psi_l    = G[:, :32] / sqrt(32) = 2*Omega_l[:, :32]   (n, K2=32)  double sketches
Omega'_l = W_{l+1} @ Omega_{l+1}      (transport basis; Psi'_l = 2*Omega'_l[:, :32])

E[ΩΩᵀ] = I, so ‖AΩ‖²_F estimates ‖A‖²_F and Ω rotates across nets (no fixed subspace a model could overfit). Only Omega is stored (fp32, every layer file); Ω′, Ψ, Ψ′ are derived by the rules above.

Files 

<run>/sNN/net_NNNNN/marg.npz          run = d8b_sketch | bench_supp | mini_supp  [ rep1/… for Bake C ]
<run>/sNN/net_NNNNN/layer_LL.npz      NN = idx // 1000, LL = 00..15

marg.npz (np.savez_compressed) — all layers

key shape dtype meaning
pre_shift, post_shift (16,1024) f32 pilot shifts c for z / a
pre_s, post_s (6,16,1024) f64 s[p-1] = E[(z−c)^p], p = 1..6 (a likewise)
gate_p (16,1024) f64 P(z > 0)
pre_mean, pre_var, post_mean, post_var (16,1024) f64 convenience (derived from the above)
gt_mean (16,1024) f32 aicrowd all_layer_means (bench and mini)
metadata scalars family, tier, rep, idx, name, n_samples, chunk, n_pilot, sample_seed, pilot_seed, omega_seeds(17), k1, k2, w_sha256, torch_version, cuda_version, gpu_name, allow_tf32, schema_version, bake_seconds, acc_seconds

ap_p2_bakev2_schema.marg_summary(marg, "pre") → (mean, var, kappa[1..6]) per layer/neuron via central_from_shifted (exact binomial) and cumulants_from_central.

layer_LL.npz (np.savez, uncompressed)

All pair objects are central / cumulant, not raw. Index convention: first index carries the higher power (K21[i,j] = κ(z_i, z_i, z_j)); T suffix = transpose before sketching.

Dense, supp tier only, (1024,1024) f32:

key definition
post_K21 κ(a_i,a_i,a_j) = E[ã_i² ã_j]
post_K22 κ(a_i,a_i,a_j,a_j) = E[ã_i² ã_j²] − σ²_i σ²_j − 2 C^a_ij²
gate_GG P(z_i>0, z_j>0) (Gaussian closed form: ¼ + asin(ρ_ij)/2π at μ = 0; bivariate-normal CDF in general)
gate_GX E[1[z_{l,i}>0] (a_{l−1,j} − μ^a_{l−1,j})] (cross-layer; a_{−1} = x)

Single sketches, every tier, (1024,128) f32:

key =
pre_K21_O, pre_K21T_O K21 @ Ω_l, K21ᵀ @ Ω_l (contract the linear / the squared index)
pre_K31_O, pre_K31T_O K31 @ Ω_l, K31ᵀ @ Ω_l
pre_K22_O K22 @ Ω_l
gate_GX_O GX @ Ω_{l−1} (input-space Ω at l = 0)
pre_K11_O, post_K21_O, post_K21T_O only with --extra-singles (Bake B)

Double sketches, every tier, (1024,32,32) f32, centered all-distinct third cumulants:

key =
pre_K3ad_PP Σ_{j≠k, j≠i, k≠i} κ(z_i,z_j,z_k) Ψ_ja Ψ_kb, Ψ = 2 Ω_l[:, :32] — the CP/learned-memory target; slices (K21, marginal κ₃) are stored separately
post_K3ad_PPp Σ_{j≠k, j≠i, k≠i} κ(a_i,a_j,a_k) Ψ'_ja Ψ'_kb, Ψ' = 2 (W_{l+1} Ω_{l+1})[:, :32] (absent l = 15)

Removed coincidence terms (recoverable where the dense blocks exist): j=k: Σ_j K21[j,i] Ψ_ja Ψ_jb; j=i: Ψ_ia (K21 Ψ)_ib; k=i: Ψ_ib (K21 Ψ)_ia; plus 2 κ₃(x_i) Ψ_ia Ψ_ib. The full (coincidences included) sketch obeys the exact transport identity Σ_i W_{l+1}[i,c] · post_full[l][i,a,b] = pre_full[l+1][c,a,b]; with all-distinct storage this identity needs post_K21 dense (Bake B) to reconstruct post_full.

Omega (n,128) f32 is stored per layer; Ω' is not (derive as W_{l+1} @ Omega_{l+1}).

Parity / validation (round-1 smoke, N = 1e6, out_bakev2_smoke3/4/6.log)

  • Layer 0 is exactly Gaussian; residuals in units of the 1/√N MC noise match estimator theory: mean 1.02 (1), var 1.42 (√2), κ₃ 2.52 (√6), κ₄ 4.91 (√24), κ₅ 11.6 (√120), κ₆ 25.5 (√720), P(z>0)−½ 0.51 (½), GG−orthant 0.44 (√(p(1−p))), K21·Ω 5.65 (√(2·trC/128)/σ²), K3ad 32.6 (trC/32/σ²). No bias anywhere, both families.
  • Same-stream two-pass (exactly-centered recomputation) vs stored conversions: ~1e-9 relative on every dense block, single sketch and marginal cumulant (= fp32 storage roundoff).
  • Brute-force 1024³ κ₃ with coincidences masked vs pre_K3ad_PP: 1.7e-8; vs post_K3ad_PPp (Ψ′ basis): 3e-9. All-distinct part = 95% of the full pre sketch RMS at l=3.
  • Independent-bake cross-check (--ref-npz): pre_K21_O / pre_K22_O of the smoke bake vs the same cumulants formed offline from the raw fp32 blocks of independent bakes and contracted with the same Ω — full1000 (N=1e9, bench net 0), p2moments_mini_N1e9 and p2moments_mini (N=1e9 / 1e8, mini net 0), layers 3 and 9: |difference| / (empirical estimator noise from the 7-chunk k-statistic spread, ref noise added in quadrature) = 1.00–1.01 in all 12 comparisons. Two bakes with different seeds, different code paths (raw-about-zero vs shifted-central) and different N agree to exactly the MC noise.
  • gt parity: rms(post_mean − aicrowd gt_mean) = 4.4e-4 (bench net 0) / 4.8e-4 (mini net 0) at N=1e6, per layer 8e-4 → 2.6e-4 = σ_a/√N.

MC noise floors (Bake C: 8 independent-seed re-bakes per run, same Ω; N = 1e8)

Noise std of every stored quantity = rms(rep0 − rep1)/√2 over the 8 paired nets (ap_p2_bakev2_noise.py; full arrays in noise_<run>.npz: per-(layer, neuron) for marginals and cumulants κ₂..κ₆, per-layer RMS for every block). Layer 0 of the pre-activation blocks reads relative noise 1.0 because the true value is exactly zero there (Gaussian layer). Worst channel is pre_K31_O (κ₃₁ is small relative to its estimator variance in the near-Gaussian early layers), not κ₂₂. The three runs agree closely; d8b_sketch shown in full, the two supp runs below.

d8b_sketch

quantity noise RMS (per layer 0..15)
pre_mean 1.4e-04 1.2e-04 9.7e-05 8.5e-05 7.6e-05 6.9e-05 6.3e-05 5.8e-05 5.4e-05 5.1e-05 4.8e-05 4.4e-05 4.2e-05 4.0e-05 3.8e-05 3.7e-05
pre_var 2.8e-04 1.9e-04 1.4e-04 1.1e-04 9.1e-05 7.6e-05 6.4e-05 5.5e-05 4.8e-05 4.2e-05 3.8e-05 3.4e-05 3.1e-05 2.8e-05 2.6e-05 2.3e-05
post_mean 8.3e-05 6.9e-05 6.1e-05 5.4e-05 4.9e-05 4.5e-05 4.1e-05 3.8e-05 3.6e-05 3.4e-05 3.1e-05 3.0e-05 2.8e-05 2.7e-05 2.6e-05 2.5e-05
post_var 1.4e-04 9.8e-05 7.6e-05 6.0e-05 5.0e-05 4.4e-05 3.7e-05 3.2e-05 2.9e-05 2.5e-05 2.3e-05 2.1e-05 2.0e-05 1.8e-05 1.6e-05 1.5e-05
gate_p 4.9e-05 4.4e-05 4.0e-05 3.8e-05 3.6e-05 3.4e-05 3.3e-05 3.1e-05 3.0e-05 2.9e-05 2.8e-05 2.7e-05 2.6e-05 2.6e-05 2.6e-05 2.4e-05
pre_kappa2 2.8e-04 1.9e-04 1.4e-04 1.1e-04 9.1e-05 7.6e-05 6.4e-05 5.5e-05 4.8e-05 4.2e-05 3.8e-05 3.4e-05 3.1e-05 2.8e-05 2.6e-05 2.3e-05
pre_kappa3 7.1e-04 3.9e-04 2.5e-04 1.7e-04 1.3e-04 9.4e-05 7.5e-05 6.0e-05 4.9e-05 4.2e-05 3.6e-05 3.0e-05 2.7e-05 2.3e-05 2.0e-05 1.8e-05
pre_kappa4 1.9e-03 9.3e-04 5.2e-04 3.1e-04 2.0e-04 1.4e-04 1.0e-04 7.8e-05 6.0e-05 4.8e-05 4.0e-05 3.2e-05 2.7e-05 2.3e-05 1.9e-05 1.6e-05
pre_kappa5 6.2e-03 2.5e-03 1.2e-03 6.4e-04 3.8e-04 2.5e-04 1.7e-04 1.2e-04 8.7e-05 6.6e-05 5.1e-05 4.0e-05 3.3e-05 2.8e-05 2.2e-05 1.9e-05
pre_kappa6 2.2e-02 7.3e-03 3.1e-03 1.5e-03 7.9e-04 4.6e-04 3.0e-04 2.0e-04 1.3e-04 1.0e-04 7.9e-05 5.7e-05 4.7e-05 4.0e-05 3.0e-05 2.5e-05
post_kappa2 1.4e-04 9.8e-05 7.6e-05 6.0e-05 5.0e-05 4.4e-05 3.7e-05 3.2e-05 2.9e-05 2.5e-05 2.3e-05 2.1e-05 2.0e-05 1.8e-05 1.6e-05 1.5e-05
post_kappa3 3.6e-04 2.0e-04 1.3e-04 9.3e-05 7.1e-05 5.3e-05 4.4e-05 3.5e-05 2.9e-05 2.5e-05 2.2e-05 1.9e-05 1.7e-05 1.5e-05 1.3e-05 1.1e-05
post_kappa4 1.1e-03 5.0e-04 2.9e-04 1.7e-04 1.2e-04 8.1e-05 6.1e-05 4.6e-05 3.6e-05 3.0e-05 2.4e-05 2.0e-05 1.8e-05 1.5e-05 1.3e-05 1.1e-05
post_kappa5 3.6e-03 1.4e-03 6.9e-04 3.7e-04 2.2e-04 1.4e-04 1.0e-04 7.2e-05 5.3e-05 4.1e-05 3.3e-05 2.7e-05 2.2e-05 1.8e-05 1.5e-05 1.3e-05
post_kappa6 1.3e-02 4.4e-03 1.8e-03 9.0e-04 4.8e-04 2.9e-04 1.9e-04 1.2e-04 8.7e-05 6.6e-05 5.2e-05 3.9e-05 3.2e-05 2.7e-05 2.1e-05 1.8e-05
block relative noise per layer (noise RMS / quantity RMS)
pre_K21_O 0.999 0.033 0.023 0.016 0.013 0.010 0.009 0.007 0.006 0.006 0.005 0.005 0.004 0.004 0.004 0.004
pre_K21T_O 1.000 0.033 0.023 0.016 0.012 0.010 0.009 0.007 0.006 0.006 0.005 0.005 0.004 0.004 0.004 0.003
pre_K31_O 0.999 0.361 0.213 0.151 0.115 0.092 0.077 0.065 0.055 0.048 0.042 0.037 0.034 0.029 0.027 0.025
pre_K31T_O 0.999 0.361 0.213 0.151 0.116 0.092 0.076 0.065 0.056 0.048 0.042 0.037 0.033 0.029 0.027 0.025
pre_K22_O 1.000 0.063 0.039 0.027 0.023 0.020 0.018 0.016 0.015 0.014 0.013 0.012 0.012 0.011 0.011 0.010
gate_GX_O 0.006 0.003 0.003 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.001 0.001 0.001 0.001 0.001
pre_K3ad_PP 1.000 0.040 0.032 0.027 0.022 0.019 0.017 0.015 0.013 0.012 0.011 0.010 0.009 0.009 0.008 0.008
post_K3ad_PPp 0.117 0.046 0.034 0.027 0.022 0.019 0.016 0.014 0.013 0.012 0.010 0.010 0.009 0.008 0.008 nan

bench_supp (rows 0–99 of full)

quantity noise RMS (per layer 0..15)
pre_mean 1.4e-04 1.1e-04 9.9e-05 8.8e-05 7.8e-05 7.1e-05 6.5e-05 6.1e-05 5.6e-05 5.3e-05 5.0e-05 4.7e-05 4.4e-05 4.2e-05 4.1e-05 4.0e-05
pre_var 2.8e-04 1.9e-04 1.4e-04 1.1e-04 9.0e-05 7.5e-05 6.3e-05 5.6e-05 4.8e-05 4.3e-05 3.8e-05 3.4e-05 3.1e-05 2.9e-05 2.6e-05 2.4e-05
post_mean 8.1e-05 7.0e-05 6.2e-05 5.6e-05 5.0e-05 4.6e-05 4.3e-05 4.0e-05 3.8e-05 3.5e-05 3.3e-05 3.1e-05 3.0e-05 2.9e-05 2.8e-05 2.7e-05
post_var 1.4e-04 9.9e-05 7.5e-05 6.1e-05 5.1e-05 4.3e-05 3.7e-05 3.3e-05 2.9e-05 2.6e-05 2.4e-05 2.1e-05 2.0e-05 1.8e-05 1.7e-05 1.5e-05
gate_p 5.0e-05 4.4e-05 4.1e-05 3.8e-05 3.6e-05 3.5e-05 3.2e-05 3.2e-05 3.0e-05 2.9e-05 2.8e-05 2.7e-05 2.7e-05 2.6e-05 2.5e-05 2.5e-05
pre_kappa2 2.8e-04 1.9e-04 1.4e-04 1.1e-04 9.0e-05 7.5e-05 6.3e-05 5.6e-05 4.8e-05 4.3e-05 3.8e-05 3.4e-05 3.1e-05 2.9e-05 2.6e-05 2.4e-05
pre_kappa3 6.9e-04 4.0e-04 2.5e-04 1.8e-04 1.3e-04 9.7e-05 7.5e-05 6.1e-05 5.0e-05 4.2e-05 3.5e-05 3.0e-05 2.6e-05 2.3e-05 2.0e-05 1.8e-05
pre_kappa4 2.0e-03 9.4e-04 5.2e-04 3.2e-04 2.1e-04 1.5e-04 1.0e-04 8.0e-05 6.0e-05 4.8e-05 3.9e-05 3.2e-05 2.7e-05 2.3e-05 1.9e-05 1.7e-05
pre_kappa5 6.2e-03 2.4e-03 1.2e-03 6.6e-04 3.9e-04 2.5e-04 1.7e-04 1.2e-04 8.4e-05 6.5e-05 5.1e-05 3.9e-05 3.2e-05 2.8e-05 2.3e-05 1.9e-05
pre_kappa6 2.2e-02 7.2e-03 3.0e-03 1.5e-03 8.0e-04 4.7e-04 2.9e-04 2.0e-04 1.4e-04 1.0e-04 7.5e-05 5.8e-05 4.5e-05 3.9e-05 3.1e-05 2.6e-05
post_kappa2 1.4e-04 9.9e-05 7.5e-05 6.1e-05 5.1e-05 4.3e-05 3.7e-05 3.3e-05 2.9e-05 2.6e-05 2.4e-05 2.1e-05 2.0e-05 1.8e-05 1.7e-05 1.5e-05
post_kappa3 3.5e-04 2.1e-04 1.3e-04 9.6e-05 7.0e-05 5.4e-05 4.4e-05 3.7e-05 3.1e-05 2.5e-05 2.1e-05 1.9e-05 1.6e-05 1.4e-05 1.3e-05 1.2e-05
post_kappa4 1.0e-03 5.0e-04 2.8e-04 1.8e-04 1.2e-04 8.4e-05 6.1e-05 4.7e-05 3.7e-05 3.0e-05 2.4e-05 2.0e-05 1.8e-05 1.5e-05 1.3e-05 1.1e-05
post_kappa5 3.5e-03 1.4e-03 6.8e-04 3.8e-04 2.3e-04 1.5e-04 1.0e-04 7.3e-05 5.3e-05 4.2e-05 3.2e-05 2.5e-05 2.2e-05 1.7e-05 1.6e-05 1.2e-05
post_kappa6 1.3e-02 4.4e-03 1.8e-03 9.2e-04 4.9e-04 2.9e-04 1.9e-04 1.3e-04 8.6e-05 6.7e-05 5.0e-05 3.9e-05 3.1e-05 2.5e-05 2.2e-05 1.7e-05
block relative noise per layer (noise RMS / quantity RMS)
post_K21 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003
post_K22 0.005 0.007 0.008 0.008 0.008 0.009 0.009 0.009 0.010 0.009 0.009 0.009 0.009 0.009 0.009 0.009
gate_GX 0.006 0.003 0.003 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.001 0.001 0.001 0.001 0.001
gate_GG 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
pre_K21_O 0.999 0.033 0.022 0.016 0.013 0.010 0.008 0.007 0.006 0.006 0.005 0.005 0.004 0.004 0.004 0.003
pre_K21T_O 1.000 0.033 0.022 0.016 0.012 0.010 0.008 0.007 0.006 0.006 0.005 0.005 0.004 0.004 0.004 0.003
pre_K31_O 0.999 0.364 0.212 0.151 0.116 0.093 0.076 0.064 0.054 0.048 0.041 0.036 0.032 0.028 0.026 0.023
pre_K31T_O 1.001 0.364 0.211 0.151 0.116 0.093 0.076 0.064 0.054 0.048 0.041 0.037 0.032 0.028 0.027 0.023
pre_K22_O 1.000 0.061 0.038 0.028 0.023 0.020 0.018 0.016 0.015 0.014 0.013 0.013 0.012 0.011 0.011 0.010
gate_GX_O 0.006 0.003 0.003 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.001 0.001 0.001 0.001 0.001
pre_K11_O 0.002 0.002 0.002 0.002 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001
post_K21_O 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003
post_K21T_O 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003
pre_K3ad_PP 1.000 0.041 0.032 0.027 0.023 0.019 0.017 0.015 0.013 0.012 0.011 0.010 0.009 0.008 0.008 0.007
post_K3ad_PPp 0.118 0.046 0.034 0.027 0.022 0.018 0.016 0.014 0.013 0.011 0.010 0.010 0.009 0.008 0.008 nan

mini_supp

quantity noise RMS (per layer 0..15)
pre_mean 1.4e-04 1.2e-04 1.0e-04 8.7e-05 7.9e-05 7.3e-05 6.6e-05 6.1e-05 5.8e-05 5.5e-05 5.1e-05 5.0e-05 4.7e-05 4.5e-05 4.3e-05 4.1e-05
pre_var 2.8e-04 1.9e-04 1.4e-04 1.1e-04 9.0e-05 7.6e-05 6.6e-05 5.6e-05 4.9e-05 4.4e-05 3.9e-05 3.5e-05 3.2e-05 3.0e-05 2.7e-05 2.5e-05
post_mean 8.2e-05 7.1e-05 6.2e-05 5.5e-05 5.1e-05 4.7e-05 4.3e-05 4.1e-05 3.9e-05 3.7e-05 3.5e-05 3.4e-05 3.2e-05 3.0e-05 2.9e-05 2.8e-05
post_var 1.4e-04 9.9e-05 7.7e-05 5.9e-05 5.0e-05 4.4e-05 3.8e-05 3.4e-05 3.0e-05 2.7e-05 2.4e-05 2.2e-05 2.1e-05 1.9e-05 1.7e-05 1.6e-05
gate_p 5.0e-05 4.4e-05 4.1e-05 3.9e-05 3.6e-05 3.4e-05 3.2e-05 3.2e-05 3.0e-05 3.0e-05 2.9e-05 2.7e-05 2.7e-05 2.6e-05 2.6e-05 2.4e-05
pre_kappa2 2.8e-04 1.9e-04 1.4e-04 1.1e-04 9.0e-05 7.6e-05 6.6e-05 5.6e-05 4.9e-05 4.4e-05 3.9e-05 3.5e-05 3.2e-05 3.0e-05 2.7e-05 2.5e-05
pre_kappa3 6.9e-04 4.0e-04 2.5e-04 1.8e-04 1.3e-04 1.0e-04 7.8e-05 6.5e-05 5.2e-05 4.4e-05 3.8e-05 3.2e-05 2.8e-05 2.5e-05 2.2e-05 2.0e-05
pre_kappa4 2.0e-03 9.4e-04 5.3e-04 3.2e-04 2.1e-04 1.5e-04 1.1e-04 8.8e-05 6.5e-05 5.3e-05 4.1e-05 3.5e-05 2.9e-05 2.6e-05 2.2e-05 2.0e-05
pre_kappa5 6.3e-03 2.5e-03 1.2e-03 6.6e-04 4.0e-04 2.6e-04 1.8e-04 1.3e-04 9.4e-05 7.5e-05 5.5e-05 4.4e-05 3.7e-05 3.2e-05 2.7e-05 2.4e-05
pre_kappa6 2.2e-02 7.2e-03 3.0e-03 1.5e-03 8.2e-04 5.2e-04 3.3e-04 2.3e-04 1.6e-04 1.2e-04 8.5e-05 6.5e-05 5.4e-05 4.7e-05 3.7e-05 3.3e-05
post_kappa2 1.4e-04 9.9e-05 7.7e-05 5.9e-05 5.0e-05 4.4e-05 3.8e-05 3.4e-05 3.0e-05 2.7e-05 2.4e-05 2.2e-05 2.1e-05 1.9e-05 1.7e-05 1.6e-05
post_kappa3 3.5e-04 2.0e-04 1.3e-04 9.4e-05 7.1e-05 5.6e-05 4.6e-05 3.9e-05 3.1e-05 2.6e-05 2.3e-05 2.0e-05 1.8e-05 1.6e-05 1.4e-05 1.3e-05
post_kappa4 1.1e-03 5.1e-04 2.9e-04 1.8e-04 1.2e-04 9.0e-05 6.7e-05 5.3e-05 4.0e-05 3.2e-05 2.6e-05 2.2e-05 1.9e-05 1.7e-05 1.4e-05 1.3e-05
post_kappa5 3.6e-03 1.4e-03 6.9e-04 3.8e-04 2.3e-04 1.6e-04 1.1e-04 8.3e-05 6.0e-05 4.7e-05 3.6e-05 2.8e-05 2.5e-05 2.2e-05 1.8e-05 1.6e-05
post_kappa6 1.3e-02 4.4e-03 1.9e-03 9.0e-04 5.2e-04 3.3e-04 2.1e-04 1.5e-04 1.1e-04 7.8e-05 5.5e-05 4.3e-05 3.8e-05 3.2e-05 2.4e-05 2.2e-05
block relative noise per layer (noise RMS / quantity RMS)
post_K21 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003
post_K22 0.005 0.007 0.007 0.008 0.009 0.009 0.009 0.009 0.009 0.010 0.009 0.009 0.009 0.009 0.009 0.009
gate_GX 0.006 0.003 0.003 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.001 0.001 0.001 0.001 0.001
gate_GG 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
pre_K21_O 0.999 0.033 0.022 0.016 0.013 0.010 0.008 0.007 0.006 0.006 0.005 0.004 0.004 0.004 0.003 0.003
pre_K21T_O 1.001 0.033 0.022 0.016 0.012 0.010 0.008 0.007 0.006 0.006 0.005 0.004 0.004 0.004 0.004 0.003
pre_K31_O 1.000 0.363 0.213 0.151 0.116 0.093 0.076 0.065 0.055 0.048 0.042 0.036 0.032 0.028 0.025 0.024
pre_K31T_O 1.001 0.364 0.214 0.152 0.116 0.093 0.076 0.065 0.055 0.048 0.042 0.036 0.032 0.028 0.025 0.024
pre_K22_O 1.001 0.061 0.037 0.028 0.023 0.020 0.018 0.016 0.015 0.014 0.013 0.012 0.011 0.011 0.011 0.011
gate_GX_O 0.006 0.003 0.003 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.001 0.001 0.001 0.001 0.001 0.001
pre_K11_O 0.002 0.002 0.002 0.002 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001
post_K21_O 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003
post_K21T_O 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003
pre_K3ad_PP 1.000 0.040 0.032 0.027 0.023 0.019 0.017 0.015 0.013 0.012 0.011 0.010 0.009 0.008 0.008 0.007
post_K3ad_PPp 0.117 0.046 0.034 0.027 0.022 0.019 0.016 0.014 0.013 0.011 0.010 0.009 0.009 0.008 0.008 nan

Cost / size (measured, one H200, chunk 131072, round-1 block spec)

µs / sample per net @ N = 1e8 size / net run total
A d8b_sketch (7 dense fp64 accumulators + 2 double sketches per chunk-layer) 8.0 ≈ 13.5 min 183 MiB 2048 nets: ≈ 460 GPU-h, 375 GB
B bench_supp / mini_supp (+ post22, gg accumulators, 4 dense blocks stored) 9.1 ≈ 15 min 463 MiB 100 nets each: ≈ 25 GPU-h, 46 GB
C reps (8 + 8 + 8 nets) ≈ 6 GPU-h

Round-1 total ≈ 520 GPU-h, ≈ 470 GB (streamed to HF by ap_p2_bakev2_janitor.py, local disk bounded to what is in flight). fp32 storage everywhere (fp16 would eat the 1e-4 relative MC floor at N = 1e8); compression only on marg.npz.