README.md

---
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`.