# CEG4N: Counter-Example Guided Neural Network Quantization Refinement

arXiv: https://arxiv.org/abs/2207.04231 · HTML: https://mlsanity.com/paper/2207.04231/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 32 references that are in the map.
- First posted on arXiv 9 Jul 2022.

## Builds on (most cited first, 17 of 17)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (2017)
- [End to End Learning for Self-Driving Cars](https://mlsanity.com/paper/1604.07316/) (2016)
- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [Quantizing deep convolutional networks for efficient inference: A whitepaper](https://mlsanity.com/paper/1806.08342/) (2018)
- [Quantized Neural Networks: Training Neural Networks with Low Precision Weights and Activations](https://mlsanity.com/paper/1609.07061/) (2016)
- [A Survey of Model Compression and Acceleration for Deep Neural Networks](https://mlsanity.com/paper/1710.09282/) (2017)
- [Algorithms for Verifying Deep Neural Networks](https://mlsanity.com/paper/1903.06758/) (2019)
- [Verifying Properties of Binarized Deep Neural Networks](https://mlsanity.com/paper/1709.06662/) (2017)
- [The Second International Verification of Neural Networks Competition (VNN-COMP 2021): Summary and Results](https://mlsanity.com/paper/2109.00498/) (2021)
- [Introduction to Neural Network Verification](https://mlsanity.com/paper/2109.10317/) (2021)
- [Post-training Quantization for Neural Networks with Provable Guarantees](https://mlsanity.com/paper/2201.11113/) (2022)
- [On Neural Network Equivalence Checking using SMT Solvers](https://mlsanity.com/paper/2203.11629/) (2022)
- [A Survey of Safety and Trustworthiness of Deep Neural Networks: Verification, Testing, Adversarial Attack and Defence, and Interpretability](https://mlsanity.com/paper/1812.08342/) (2018)
- [Geometric Path Enumeration for Equivalence Verification of Neural Networks](https://mlsanity.com/paper/2112.06582/) (2021)
- [Sound and Automated Synthesis of Digital Stabilizing Controllers for Continuous Plants](https://mlsanity.com/paper/1610.04761/) (2016)

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

- [NeuroCodeBench: a plain C neural network benchmark for software verification](https://mlsanity.com/paper/2309.03617/) (2023)
- [Floating-Point Neural Network Verification at the Software Level](https://mlsanity.com/paper/2510.23389/) (2025)

## Abstract (arXiv)

Neural networks are essential components of learning-based software systems. However, their high compute, memory, and power requirements make using them in low resources domains challenging. For this reason, neural networks are often quantized before deployment. Existing quantization techniques tend to degrade the network accuracy. We propose Counter-Example Guided Neural Network Quantization Refinement (CEG4N). This technique combines search-based quantization and equivalence verification: the former minimizes the computational requirements, while the latter guarantees that the network's output does not change after quantization. We evaluate CEG4N~on a diverse set of benchmarks, including large and small networks. Our technique successfully quantizes the networks in our evaluation while producing models with up to 72% better accuracy than state-of-the-art techniques.