Hyperiax

Hyperiax is a pure-JAX library for message passing on rooted trees. It provides immutable tree data structures, typed per-node arrays, and decorator-based sweeps that compose with jax.jit, jax.vmap, and jax.lax.scan.

Hyperiax is designed for phylogenetic and tree-structured scientific computing, including Gaussian graphical models, phylogenetic means, and guided inference for diffusion processes on trees.

Installation

Hyperiax requires Python 3.11 or newer.

pip install hyperiax

The core package depends only on JAX, jaxlib, and NumPy. For accelerator-backed JAX installations, follow the official JAX installation instructions for your platform before or after installing Hyperiax.

Quick Start

import jax.numpy as jnp
import hyperiax as hx

topology = hx.symmetric_topology(depth=2, degree=2)
tree = hx.Tree.empty(topology, {"value": (2,)})

leaf_count = int(topology.is_leaf.sum())
tree = tree.at[topology.is_leaf].set(value=jnp.ones((leaf_count, 2)))


@hx.up(reads_children=("value",), writes=("value",))
def average_children(node, children, params):
    return {"value": children.value.mean(0)}


result = average_children(tree)
root_value = result.value[0]

Sweeps are ordinary Tree -> Tree functions. The @hx.up and @hx.down decorators declare which fields are read and written, so dispatch remains explicit and JAX-friendly.

Architecture

hyperiax/
├── core/      # Topology, Tree, Schema, views, sweep dispatch, builders
├── utils/     # Pure-JAX ODE and SDE solvers
└── prebuilt/  # Ready-to-use sweeps for BFFG and phylogenetic means

Core

hyperiax.core contains the public primitives:

• Topology for rooted tree structure.
• Tree for immutable per-node JAX arrays.
• Schema for field shape and dtype validation.
• @hx.up and @hx.down for message-passing sweeps.
• Newick helpers for importing and exporting rooted trees.

Utilities

hyperiax.utils contains pure-JAX numerical helpers, including ODE and SDE solvers used by the prebuilt guided-inference routines.

Prebuilt Sweeps

hyperiax.prebuilt contains focused implementations for common tree workflows:

• phylo_mean for weighted phylogenetic means.
• bffg for Backward Filtering Forward Guiding on discrete Gaussian and continuous SDE edges.

Documentation

Tutorials and API reference are available in the project documentation:

• Quickstart and sweep-writing tutorials under docs/source/notebooks/.
• Public API reference under docs/source/api/.

Reference

The BFFG implementation follows:

van der Meulen, F. H. & Sommer, S. (2025). Backward Filtering Forward Guiding. JMLR 26(281), 1-51. https://arxiv.org/abs/2505.18239

Contact

Hyperiax is maintained by CCEM, University of Copenhagen. For technical questions, please open a GitHub issue or contact Stefan Sommer.