causal-automata

A blazing-fast, JAX-accelerated Cellular Automaton engine for causal discovery.

Installation

pip install causal-automata

With CPU JAX:

pip install "causal-automata[jax]"

With NVIDIA CUDA JAX (and the Colab-style stack):

pip install "causal-automata[cuda]"

Or using uv:

uv add "causal-automata[jax]"

Benchmark — N=100 on Tesla T4

Final figures (Colab Tesla T4, GOLEM num_iter=20000):

Bayesian CA is ~778× faster than GOLEM and ~1636× faster than PC, while beating GOLEM on both skeleton (0.812 vs 0.577) and directed (0.483 vs 0.403) F1.

Documentation

Full docs (theory, physics, API, CLI): https://causal-automata.readthedocs.io/en/latest/

How it works — CA physics + V-well

State is a binary DAG adjacency A, node elevations E ∈ [0,1], and a fixed empirical covariance Cov from continuous observations. Each tick is a local cellular update:

1. Gravity — keep only downhill edges (E[parent] > E[child]), then drift elevations toward the midpoint of parent/child means.
2. V-structure gravity well — absent undirected pairs that share neighbors and are marginally independent (|ρ| below the death threshold with empty conditioning set) mark shared neighbors as colliders. Those elevations are sunk (E -= 2·lr), so later birth prefers arrows into the collider — the classic V-structure i → k ← j.
3. Death / birth — kill weak edges and birth strong ones using partial correlations conditioned on the top-k union neighbors ranked by |Cov|. Birth orients by elevation after the |ρ| gate.

The NumPy prototype (bayesian.step) and the pure functional JAX port (jax_core.step, @jax.jit) share this physics.

Run

# Synthetic DAG harness (NumPy default; use --backend jax for JIT)
python -m causal_automata.bayesian_synth --n 10
python -m causal_automata.bayesian_synth --n 50 --backend jax
python -m causal_automata.bayesian_synth --n 100

# Benchmark vs gCastle PC / GOLEM (default N=100)
python -m causal_automata.benchmark
python -m causal_automata.benchmark --n 100 --seed 0 --ticks 100
python -m causal_automata.benchmark --smoke   # device checks + GOLEM init only

Smoke the JAX compile:

python -c "from causal_automata import warmup; print(warmup())"

Package layout

causal-automata/
├── causal_automata/
│   ├── __init__.py
│   ├── bayesian.py          # NumPy Bayesian CA step
│   ├── bayesian_synth.py    # Synthetic linear-DAG harness
│   ├── jax_core.py          # JAX @jit port of step
│   └── benchmark.py         # vs gCastle PC / GOLEM
├── docs/                    # Sphinx / Read the Docs
├── .readthedocs.yaml
├── pyproject.toml
├── README.md
└── NOTICE

License / notice

See NOTICE. Copyright 2026 Masakazu Yamagiwa.