# Non-asymptotic quantisation of spherically symmetric distributions

arXiv: https://arxiv.org/abs/2605.12568 · HTML: https://mlsanity.com/paper/2605.12568/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 13 references that are in the map.
- First posted on arXiv 12 May 2026.

## Builds on (most cited first, 1 of 1)

- [Incremental space-filling design based on coverings and spacings: improving upon low discrepancy sequences](https://mlsanity.com/paper/2106.05833/) (2021)

## Abstract (arXiv)

Zador's celebrated theorem is a cornerstone of optimal quantisation, establishing both the weak limit of the empirical distribution of an n-point optimal quantiser in Rd and the decay rate of the associated Ls-mean quantisation error. However, for large dimensions d, observing this asymptotic behaviour demands an astronomically large sample size n, which grows super-exponentially with d. Through a detailed analysis of the quantisation problem for spherically symmetric distributions, we demonstrate that for moderate n random quantisers uniformly distributed on a sphere of suitable radius r achieve exceptional performance. The expected distortion, expressed as a triple integral, can be computed with arbitrary precision, and the optimal radius r can be efficiently determined numerically. Leveraging results from extreme-value theory, we derive approximations for r, particularly in scenarios where n scales with d. Depending on the growth rate of n, r may either converge to zero or approach a limiting value that is independent of s.