Torx

Probabilistic circuits in JAX.

Torx is a JAX-based library for building and sampling probabilistic programs, with all the benefits of JAX (native GPU/TPU acceleration, differentiability, vectorization). Its two core objects are the parametrised stochastic circuit (PSC), a circuit of probabilistic gates whose wiring mirrors the sampling hardware it targets, and the directed factor graph (DFG), the layer beneath the circuits: a directed acyclic graph of conditional samplers, arranged so that each variable appears after the variables it depends on.

Whitepaper: A Framework for Stochastic Differentiable Programming (arXiv:2608.01612) introduces the framework, works through examples, and reports experimental results on Extropic's XTR-0 hardware.

Installation

Requires Python 3.11+.

pip install extro-torx

or

git clone https://github.com/extropic-ai/torx.git
cd torx
pip install -e ".[testing,examples]"

Documentation

Available at docs.torx.ai.

Quick example

Build and simulate a simple probabilistic circuit:

import jax
import jax.numpy as jnp
from torx import psc

gates = [
    psc.PNOT(0),
    psc.PCNOT([0, 1]),
]

circuit = psc.DiscretePCircuit(gates)
thetas = circuit.init_params(jax.random.key(0))
sim = psc.StateVectorSimulator()
compiled = sim.build_circuit(circuit, thetas)

state = jnp.array([1.0, 0.0, 0.0, 0.0])

density = sim.density(compiled, state)
print(f"Final distribution: {density}")

Citation

If you found this library useful in academic research, please cite:

@misc{verdon2026frameworkstochasticdifferentiableprogramming,
  title         = {A Framework for Stochastic Differentiable Programming},
  author        = {Guillaume Verdon and Leo Tyrpak and Owen Lockwood and Seth Morton and Alexander Neagoe and Anton Sugolov and Ian MacCormack and Mirko Amico},
  year          = {2026},
  eprint        = {2608.01612},
  archivePrefix = {arXiv},
  primaryClass  = {cs.ET},
  url           = {https://arxiv.org/abs/2608.01612},
}

See also: other libraries in the JAX ecosystem

thrml: probabilistic graphical models and block Gibbs sampling in JAX.

Awesome JAX: a longer list of other JAX projects.