New spherical codes by tuning an annealing solver
Abstract
The spherical code problem asks how to place N points on a unit sphere in D dimensions to maximize the smallest distance between two points. It is a non-smooth and non-convex max-min problem, where few problem sizes have known optimal solutions, some have constructions, but most still only have numerically obtained solutions. We use a simple solver, with seven parameters, that anneals a LogSumExp surrogate, minimizes with L-BFGS, applies a random perturbation between anneals, and repeats with no acceptance test until a fixed limit is reached. We search the solver parameters for every instance with N ≤ 1024, 3 ≤ D ≤ 32, and N > 2D, a total of 29,670 instances, using 32 parameter trials. We then run the solver for 60 seconds with the best parameters for each instance, without utilizing any symmetries or existing solutions. After enforcing monotonicity of the results and numerically polishing the solutions, we improve the best known code in 4,577 instances. When a single set of solver parameters is used for all instances, with one 60-second episode, the number of improvements is still 3,649. From our records, we find 24 codes with an exact algebraic cosine. Among our ablations, we find that 1) the repeated anneal contributes most to improvements, 2) at our 32 × 60-second budget only fitting one parameter per-instance is better than fitting all seven, and 3) good parameters can be predicted from the instance size. We provide the solver code, the fitted parameters, and the codes.
Related
- Computational compressive imaging reconstruction with a simulated-annealing-based Ising solver
- Simulated Annealing for Model‐Robust Partial Profile Choice Designs in Healthcare Preference Studies
- Flow Annealing Posterior Sampling for Function-Space Regression and Inverse Problems
- Ising-machine-like Driving Condition Restrictions in SSBM and Additional Pseudo-annealing- Driving Method for SSBM that Achieves Best Cut Value Search -
- Transport along Local Annealing Paths: Wasserstein Geometry and Multimodal Sampling
BibTeX
@misc{vahteristo2026spherical,
title = {{New spherical codes by tuning an annealing solver}},
author = {Ilmari Vahteristo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.19988},
eprint = {2610.19988},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.19988},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - New spherical codes by tuning an annealing solver
AU - Ilmari Vahteristo
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.19988
UR - https://arxiv.org/abs/2610.19988
AB - The spherical code problem asks how to place N points on a unit sphere in D dimensions to maximize the smallest distance between two points. It is a non-smooth and non-convex max-min problem, where few problem sizes have known optimal solutions, some have constructions, but most still only have numerically obtained solutions. We use a simple solver, with seven parameters, that anneals a LogSumExp surrogate, minimizes with L-BFGS, applies a random perturbation between anneals, and repeats with no acceptance test until a fixed limit is reached. We search the solver parameters for every instance with N ≤ 1024, 3 ≤ D ≤ 32, and N > 2D, a total of 29,670 instances, using 32 parameter trials. We then run the solver for 60 seconds with the best parameters for each instance, without utilizing any symmetries or existing solutions. After enforcing monotonicity of the results and numerically polishing the solutions, we improve the best known code in 4,577 instances. When a single set of solver parameters is used for all instances, with one 60-second episode, the number of improvements is still 3,649. From our records, we find 24 codes with an exact algebraic cosine. Among our ablations, we find that 1) the repeated anneal contributes most to improvements, 2) at our 32 × 60-second budget only fitting one parameter per-instance is better than fitting all seven, and 3) good parameters can be predicted from the instance size. We provide the solver code, the fitted parameters, and the codes.
ER -