aicrowd/arc-whestbench-convergence-2026

WhestBench convergence study — v1-warmup-100mlps

Per-neuron cumulative mean activations of the first 100 MLPs of aicrowd/arc-whestbench-public-2026 captured at 860 log-spaced sample budgets from N=1 to N=1,000,000,000.

This is a research sidecar to v1-warmup. It demonstrates how Monte Carlo mean estimates of the activations converge as the sample budget grows.

Quick start

from datasets import load_dataset
import numpy as np

ds = load_dataset(
    "aicrowd/arc-whestbench-convergence-2026",
    revision="v1-warmup-100mlps",
    split="public",
)

# Mean absolute error vs each run's own final, averaged across all MLPs/layers/neurons:
all_means = np.stack([np.asarray(r["running_means"]) for r in ds])     # (n_mlps, S, depth, width)
finals = all_means[:, -1:, :, :]
fleet_mae = np.abs(all_means - finals).mean(axis=(0, 2, 3))            # (S,)
snapshot_n = np.asarray(ds[0]["snapshot_n"])                           # (S,)
# Plot snapshot_n (log x) vs fleet_mae (log y).

Schema (whestbench-convergence-1.0)

Column	Type	Shape	Meaning
mlp_id	int64	scalar	Same as source MLP id.
mlp_name	string	scalar	Human label.
mlp_seed	int64	scalar	int63 input seed (seed_protocol 3.0).
snapshot_n	list	(S,)	Actual sample count at each snapshot; strictly ascending. Identical across rows.
running_means	list<list<list>>	(S, depth, width) ≈ (860, 8, 256)	Per-neuron running mean. float64.
v1_warmup_all_layer_means	list<list>	(depth, width) = (8, 256)	Published value from the source dataset. float32.

Snapshot schedule

n_min = 1
n_max = 1,000,000,000
n_snapshots_requested = 1000
n_snapshots_actual    = 860

Log-spaced over [n_min, n_max], rounded to int64, deduplicated. The actual count is below the requested count because low-decade integers collapse on rounding.

Reproducibility note

running_means[-1] (at N=1,000,000,000) is NOT bit-identical to v1_warmup_all_layer_means. The convergence study uses variable chunk decomposition (to land precisely on log-spaced snapshot boundaries), while v1-warmup used uniform chunk_size=524288. Float64 addition is non-associative; the two final values agree to ~1 float64 ULP per element.

Use running_means[-1] (this run's own final) as the reference for in-study convergence-error analysis. Compare to v1_warmup_all_layer_means only with statistical tolerances.

Provenance

Configuration 1 — 100 MLPs

• GPU: NVIDIA A100-SXM4-80GB (compute capability 8.0)
• PyTorch: 2.4.1+cu124
• whestbench: 0.5.0
• Determinism: torch.use_deterministic_algorithms=True, cudnn.deterministic=True, CUBLAS_WORKSPACE_CONFIG=:4096:8
• CUDA drivers observed: 550.127.05, 565.57.01, 570.133.20, 570.172.08, 570.195.03, 580.126.16, 580.126.20

Source

• Source dataset: aicrowd/arc-whestbench-public-2026@v1-warmup
• MLP range: [0, 100)
• Source split: public