# On Quasi-Isometry of Threshold-Based Sampling

arXiv: https://arxiv.org/abs/1811.01436 · HTML: https://mlsanity.com/paper/1811.01436/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Nov 2018.

## Built on by (most cited first, 2 of 2)

- [Quantization in Spiking Neural Networks](https://mlsanity.com/paper/2305.08012/) (2023)
- [On Leaky-Integrate-and Fire as Spike-Train-Quantization Operator on Dirac-Superimposed Continuous-Time Signals](https://mlsanity.com/paper/2402.07954/) (2024)

## Abstract (arXiv)

The problem of isometry for threshold-based sampling such as integrate-and-fire (IF) or send-on-delta (SOD) is addressed. While for uniform sampling the Parseval theorem provides isometry and makes the Euclidean metric canonical, there is no analogy for threshold-based sampling. The relaxation of the isometric postulate to quasi-isometry, however, allows the discovery of the underlying metric structure of threshold-based sampling. This paper characterizes this metric structure making Hermann Weyl's discrepancy measure canonical for threshold-based sampling.