# Algorithms and data structures for numerical computations with automatic precision estimation

arXiv: https://arxiv.org/abs/2403.16660 · HTML: https://mlsanity.com/paper/2403.16660/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Mar 2024.

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

- [Geometrical structures of digital fluctuations in parameter space of neural networks trained with adaptive momentum optimization](https://mlsanity.com/paper/2408.12273/) (2024)
- [Algorithms and data structures for automatic precision estimation of neural networks](https://mlsanity.com/paper/2509.24607/) (2025)

## Abstract (arXiv)

We introduce data structures and algorithms to count numerical inaccuracies arising from usage of floating numbers described in IEEE 754. Here we describe how to estimate precision for some collection of functions most commonly used for array manipulations and training of neural networks. For highly optimized functions like matrix multiplication, we provide a fast estimation of precision and some hint how the estimation can be strengthened.