SPECTER (v1.0.0)

SPECTER is an implementation of the Spectral EMD (SEMD) and Spectral Shape Observables as outlined in "SPECTER: fficient Evaluation of the Spectral EMD" (arxiv:2410.2410.05379). This package can be used for evaluating an extremely large class of IRC-safe observables, with modules in place to define custom observables and jet algorithms using an intuitive geometric language. Compared to ordinary EMD methods, this package is extremely fast, precise, and accurate. The SEMD is first defined in (arxiv:2305.03751)[https://arxiv.org/abs/2305.03751].

Example Usage

Several end-to-end examples of how to use SPECTER can be found in the examples subfolder of this repository. This examples include computing pairwise SEMDs, computing spectral shape observables, and some basic image manipulation.

The code used to perform all of the studies in "SPECTER: fficient Evaluation of the Spectral EMD" (arxiv:2410.2410.05379) can be found in the studies subfolder.

Installation

From PyPI

In your Python environment run

python -m pip install specterpy

From this repository locally

In your Python environment from the top level of this repository run:

pip install -.

Dependencies

The primary dependencies are jax and jaxlib.

To install jax and jaxlib, run the following commands:

pip install --upgrade pip
pip install --upgrade jax jaxlib==0.1.69+cuda111 -f https://storage.googleapis.com/jax-releases/jax_releases.html

Many of the examples and studies depend on the ParticleLoader package for downloading particle physics datasets. However, this package is not necessary for general usage of SPECTER

Changelog

• v1.2.0: 8 July 2026. Rewrote the spectral EMD evaluation as a direct sum over the monotone coupling: float32 precision improved by several orders of magnitude (self-distances now exactly zero), roughly 4x faster on GPU. Previous implementation kept as ds2_old. Added optional float64 mode via SPECTER(dtype=jax.numpy.float64). Fixed compatibility with jax >= 0.6.
• v1.1.0: 13 May 2025. Added support for cylindrical metrics. Added support for unbalanced OT. Resolved bugs relating to zero-padding.
• v1.0.0: 8 October 2024. Official public release.

Based on the work in "SPECTER: fficient Evaluation of the Spectral EMD" (arxiv:2410.XXXXX)

Bugs, Fixes, Ideas, or Questions? Contact me at rikab@mit.edu