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Initial public release: array-form Taylor-mode AD in JAX
Provides jet() with leading-axis array storage for Taylor-series coefficients, enabling jit/vmap/scan over the order axis and an effective_order parameter for dynamic truncation depth at static shapes. Derived from jax.experimental.jet (Apache-2.0, Copyright 2020 The JAX Authors); copyright headers preserved per Apache-2.0 §4. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
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‎README.md‎

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# jet-array
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Array-form Taylor-mode automatic differentiation in JAX.
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`jet_array` propagates truncated Taylor polynomials through arbitrary JAX
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computations, returning all coefficients up to a specified order in a single
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forward pass. This is the higher-order analogue of `jax.jvp`: where `jvp`
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takes a primal and one tangent and returns one derivative, `jet` takes a
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primal and a series of tangents and returns the full Taylor expansion.
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This package is a derivative of JAX's experimental `jax.experimental.jet`
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([Bettencourt, Johnson, Duvenaud 2019][taylor-mode]) with the series stored as
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a single leading-axis array rather than a Python tuple. The array layout
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enables `jit`/`vmap`/`scan` over the order axis, and adds an
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`effective_order` parameter for dynamic computation depth at static shapes —
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useful when the truncation order varies across a batch.
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## Install
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```bash
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pip install jet-array
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```
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`jet_array` uses `jax._src` internals and is currently pinned to
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`jax>=0.8,<0.9`. Compatibility across JAX versions will be tightened as the
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package matures.
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## Quickstart
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```python
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import jax.numpy as jnp
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from jet_array import jet
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def f(x):
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return jnp.exp(jnp.sin(x))
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# 5th-order Taylor series of f at x=0.5, with input series [1, 0, 0, 0, 0]
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# (i.e. expand around x = 0.5 + t).
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x0 = 0.5
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series_in = jnp.zeros(5).at[0].set(1.0)
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primal_out, series_out = jet(f, (x0,), (series_in,))
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# primal_out = f(0.5)
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# series_out = [f'(0.5), f''(0.5)/2!, f'''(0.5)/3!, f^(4)(0.5)/4!, f^(5)(0.5)/5!]
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```
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## Why arrays instead of tuples
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`jax.experimental.jet` stores the series as a Python tuple, which prevents
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`jit`/`vmap` from treating the order axis as a regular array dimension. This
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matters when:
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- The series order is large (hundreds of coefficients) — Python-level
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iteration becomes a tracing-time cost.
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- The order is data-dependent — tuples force re-tracing every time the
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length changes.
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- You want to `vmap` or `scan` over a batch where each element has its own
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effective order.
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`jet_array` stores all coefficients along axis 0 of a single array,
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addressing all three.
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## Citation
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If you use `jet-array` in academic work, please cite:
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```bibtex
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@misc{yang2026copulaad,
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title={Archimedean Copula Inference via Taylor-Mode AD},
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author={Yang, Cambridge and Li, Dongdong},
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year={2026},
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note={arXiv preprint},
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}
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```
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The underlying Taylor-mode algorithm is from:
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```bibtex
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@inproceedings{bettencourt2019taylor,
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title={Taylor-mode automatic differentiation for higher-order derivatives in JAX},
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author={Bettencourt, Jesse and Johnson, Matthew J. and Duvenaud, David},
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booktitle={NeurIPS Program Transformations Workshop},
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year={2019},
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}
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```
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## License
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Apache-2.0. Portions derived from JAX (Apache-2.0, Copyright 2020 The JAX
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Authors); copyright headers preserved per Apache-2.0 §4.
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[taylor-mode]: https://github.com/jax-ml/jax/files/6717197/jet.pdf

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