# Efficient and Mathematically Robust Operations for Certified Neural Networks Inference

arXiv: https://arxiv.org/abs/2401.08225 · HTML: https://mlsanity.com/paper/2401.08225/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 39 references that are in the map.
- First posted on arXiv 16 Jan 2024.

## Builds on (most cited first, 7 of 7)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (2017)
- [HAWQ: Hessian AWare Quantization of Neural Networks with Mixed-Precision](https://mlsanity.com/paper/1905.03696/) (2019)
- [A Study of BFLOAT16 for Deep Learning Training](https://mlsanity.com/paper/1905.12322/) (2019)
- [Flexpoint: An Adaptive Numerical Format for Efficient Training of Deep Neural Networks](https://mlsanity.com/paper/1711.02213/) (2017)
- [Deep Positron: A Deep Neural Network Using the Posit Number System](https://mlsanity.com/paper/1812.01762/) (2018)
- [Fixed-Point Code Synthesis For Neural Networks](https://mlsanity.com/paper/2202.02095/) (2022)

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

- [Implementation of airborne ML models with semantics preservation](https://mlsanity.com/paper/2509.18681/) (2025)
- [Certified ML Object Detection for Surveillance Missions](https://mlsanity.com/paper/2406.12362/) (2024)

## Abstract (arXiv)

In recent years, machine learning (ML) and neural networks (NNs) have gained widespread use and attention across various domains, particularly in transportation for achieving autonomy, including the emergence of flying taxis for urban air mobility (UAM). However, concerns about certification have come up, compelling the development of standardized processes encompassing the entire ML and NN pipeline. This paper delves into the inference stage and the requisite hardware, highlighting the challenges associated with IEEE 754 floating-point arithmetic and proposing alternative number representations. By evaluating diverse summation and dot product algorithms, we aim to mitigate issues related to non-associativity. Additionally, our exploration of fixed-point arithmetic reveals its advantages over floating-point methods, demonstrating significant hardware efficiencies. Employing an empirical approach, we ascertain the optimal bit-width necessary to attain an acceptable level of accuracy, considering the inherent complexity of bit-width optimization.