# Algorithms and data structures for automatic precision estimation of neural networks

arXiv: https://arxiv.org/abs/2509.24607 · HTML: https://mlsanity.com/paper/2509.24607/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 44 references that are in the map.
- First posted on arXiv 29 Sep 2025.

## Builds on (most cited first, 22 of 22)

- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [Universal Approximation with Deep Narrow Networks](https://mlsanity.com/paper/1905.08539/) (2019)
- [Kolmogorov-Arnold Networks (KANs) for Time Series Analysis](https://mlsanity.com/paper/2405.08790/) (2024)
- [Convolutional Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.13155/) (2024)
- [A Survey on Kolmogorov-Arnold Network](https://mlsanity.com/paper/2411.06078/) (2024)
- [KAN-ODEs: Kolmogorov-Arnold Network Ordinary Differential Equations for Learning Dynamical Systems and Hidden Physics](https://mlsanity.com/paper/2407.04192/) (2024)
- [GKAN: Graph Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.06470/) (2024)
- [KAGNNs: Kolmogorov-Arnold Networks meet Graph Learning](https://mlsanity.com/paper/2406.18380/) (2024)
- [Universal Approximation Theorems for Differentiable Geometric Deep Learning](https://mlsanity.com/paper/2101.05390/) (2021)
- [Demonstrating the Efficacy of Kolmogorov-Arnold Networks in Vision Tasks](https://mlsanity.com/paper/2406.14916/) (2024)
- [rKAN: Rational Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.14495/) (2024)
- [The universal approximation theorem for complex-valued neural networks](https://mlsanity.com/paper/2012.03351/) (2020)
- [A Universal Approximation Theorem for Mixture of Experts Models](https://mlsanity.com/paper/1602.03683/) (2016)
- [On the Complexity of Learning Neural Networks](https://mlsanity.com/paper/1707.04615/) (2017)
- [Reduced Effectiveness of Kolmogorov-Arnold Networks on Functions with Noise](https://mlsanity.com/paper/2407.14882/) (2024)
- [Universal Approximation Theorem and error bounds for quantum neural networks and quantum reservoirs](https://mlsanity.com/paper/2307.12904/) (2023)
- [Arbitrary-Depth Universal Approximation Theorems for Operator Neural Networks](https://mlsanity.com/paper/2109.11354/) (2021)
- [Universal Approximation Theorem of Deep Q-Networks](https://mlsanity.com/paper/2505.02288/) (2025)
- [Neural Networks in Adversarial Setting and Ill-Conditioned Weight Space](https://mlsanity.com/paper/1801.00905/) (2018)
- [Universal approximation with complex-valued deep narrow neural networks](https://mlsanity.com/paper/2305.16910/) (2023)
- [Algorithms and data structures for numerical computations with automatic precision estimation](https://mlsanity.com/paper/2403.16660/) (2024)
- [Geometrical structures of digital fluctuations in parameter space of neural networks trained with adaptive momentum optimization](https://mlsanity.com/paper/2408.12273/) (2024)

## Abstract (arXiv)

We describe algorithms and data structures to extend a neural network library with automatic precision estimation for floating point computations. We also discuss conditions to make estimations exact and preserve high computation performance of neural networks training and inference. Numerical experiments show the consequences of significant precision loss for particular values such as inference, gradients and deviations from mathematically predicted behavior. It turns out that almost any neural network accumulates computational inaccuracies. As a result, its behavior does not coincide with predicted by the mathematical model of neural network. This shows that tracking of computational inaccuracies is important for reliability of inference, training and interpretability of results.