randomnumber101/cainvert-benchmark

CAInvert: Cellular Automata Inversion Reasoning Benchmark

Official Dataset Repository for CAInvert (GitHub).

CAInvert evaluates recursive and latent neural reasoning models on computationally irreducible cellular automata dynamics. Given an evolved future state $S_D$ at depth $D$ alongside sparse disambiguating hints, the model's task is to invert the physical trajectory and reconstruct the ancestral ground-truth initial state $S_0$.

Dataset Portfolio

Total verified preimage trees: 510,364 across 1D and 2D lattices:

Config	Dimension	Rule	Lattice Shape	Sequence Length	Total Trees	Shards	Depths ($d$)
1d_w81	1D	Rule 110	(81,)	$N = 81$	249,920	100 shards	1, 2, 3, 4, 6, 8, 10, 12
1d_w400	1D	Rule 110	(400,)	$N = 400$	149,920	60 shards	1, 2, 3, 4, 6, 8, 10, 12
1d_w900	1D	Rule 110	(900,)	$N = 900$	100,000	40 shards	1, 2, 3, 4, 6, 8, 10, 12
2d_9x9	2D	Life B3/S23	(9, 9)	$N = 81$	6,000	192 shards	1, 2, 3, 4, 6, 8, 10, 12
2d_20x20	2D	Life B3/S23	(20, 20)	$N = 400$	2,200	411 shards	1, 2, 3, 4, 6, 8, 10
2d_30x30	2D	Life B3/S23	(30, 30)	$N = 900$	2,324	437 shards	1, 2, 3, 4, 6, 8, 10

Sequence Layout & Prediction Task

Every sample in the Parquet files contains:

• target_state: Byte buffer of length $N$ representing $S_D$.
• ground_truth_s0: Byte buffer of length $N$ representing target $S_0$.
• hints_s0: Int8 array of length $N$ where -1 represents unrevealed/masked bits and values in {0, 1} represent spatial hint tape tokens.
• depth: Integer recursion depth $d$.
• leaf_count: Number of alternative preimages in the branching tree ($\Lambda$).
• effective_branching: Geometric branching rate $b_{\text{eff}} = \Lambda^{1/d}$.

Model Input Format:

$$\mathbf{X}=[S_D]\circ [[\mathtt{S}\mathtt{E}\mathtt{P}]=\mathtt{3}]\circ [H_0\text{ (with MASK=2)}]\backslash mathbf\{X\}\; =\; [S\_D]\; \backslash circ\; [\backslash mathtt\{[SEP]=3\}]\; \backslash circ\; [H\_0\; \backslash text\{\; (with\; MASK=2)\}]$$ Total input length: $2N + 1$ tokens. Target: $S_0 \in {0, 1}^N$.

Loading Data

1. PyTorch (cainvert)

from cainvert.storage.torch_dataset import CAInversionDataset

dataset = CAInversionDataset.from_hub(
    repo_id="randomnumber101/cainvert-benchmark",
    split="1d_w81",
    depth_min=4,
    depth_max=8
)

2. Hugging Face Datasets

from datasets import load_dataset

ds = load_dataset("randomnumber101/cainvert-benchmark", "1d_w81")

3. Zero-Download DuckDB Queries

import duckdb

conn = duckdb.connect()
conn.execute("INSTALL httpfs; LOAD httpfs;")
df = conn.execute("""
    SELECT depth, COUNT(*), AVG(leaf_count)
    FROM read_parquet('https://huggingface.co/datasets/randomnumber101/cainvert-benchmark/resolve/main/data/1d_w81/*.parquet')
    GROUP BY depth
""").df()
print(df)