| --- |
| configs: |
| - config_name: 1d_w81 |
| data_files: "data/1d_w81/*.parquet" |
| - config_name: 1d_w400 |
| data_files: "data/1d_w400/*.parquet" |
| - config_name: 1d_w900 |
| data_files: "data/1d_w900/*.parquet" |
| - config_name: 2d_9x9 |
| data_files: "data/2d_9x9/*.parquet" |
| - config_name: 2d_20x20 |
| data_files: "data/2d_20x20/*.parquet" |
| - config_name: 2d_30x30 |
| data_files: "data/2d_30x30/*.parquet" |
| license: mit |
| task_categories: |
| - reasoning |
| tags: |
| - cellular-automata |
| - recursive-reasoning |
| - rule110 |
| - game-of-life |
| - parquet |
| size_categories: |
| - 100K<n<1M |
| --- |
| |
| # CAInvert: Cellular Automata Inversion Reasoning Benchmark |
|
|
| Official Dataset Repository for [CAInvert (GitHub)](https://github.com/randomNumber101/cainvert). |
|
|
| 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: |
| $$\mathbf{X} = [S_D] \circ [\mathtt{[SEP]=3}] \circ [H_0 \text{ (with MASK=2)}]$$ |
| Total input length: $2N + 1$ tokens. Target: $S_0 \in \{0, 1\}^N$. |
|
|
| ## Loading Data |
|
|
| ### 1. PyTorch (`cainvert`) |
| ```python |
| 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 |
| ```python |
| from datasets import load_dataset |
| |
| ds = load_dataset("randomnumber101/cainvert-benchmark", "1d_w81") |
| ``` |
|
|
| ### 3. Zero-Download DuckDB Queries |
| ```python |
| 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) |
| ``` |
|
|
