# Optimization of the quantization of dense neural networks from an exact QUBO formulation

arXiv: https://arxiv.org/abs/2510.16075 · HTML: https://mlsanity.com/paper/2510.16075/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 27 references that are in the map.
- First posted on arXiv 17 Oct 2025.

## Builds on (most cited first, 11 of 11)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Energy and Policy Considerations for Deep Learning in NLP](https://mlsanity.com/paper/1906.02243/) (2019)
- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [Learned Step Size Quantization](https://mlsanity.com/paper/1902.08153/) (2019)
- [Up or Down? Adaptive Rounding for Post-Training Quantization](https://mlsanity.com/paper/2004.10568/) (2020)
- [A White Paper on Neural Network Quantization](https://mlsanity.com/paper/2106.08295/) (2021)
- [Quantized Neural Networks: Training Neural Networks with Low Precision Weights and Activations](https://mlsanity.com/paper/1609.07061/) (2016)
- [EMNIST: an extension of MNIST to handwritten letters](https://mlsanity.com/paper/1702.05373/) (2017)
- [Ising formulations of many NP problems](https://mlsanity.com/paper/1302.5843/) (2013)
- [Learning to Quantize Deep Networks by Optimizing Quantization Intervals with Task Loss](https://mlsanity.com/paper/1808.05779/) (2018)
- [Improving Neural Network Quantization without Retraining using Outlier Channel Splitting](https://mlsanity.com/paper/1901.09504/) (2019)

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

- [Layer-wise QUBO-Based Training of CNN Classifiers for Quantum Annealing](https://mlsanity.com/paper/2603.02958/) (2026)
- [Task-Aware QUBO Allocation for Mixed-Precision Quantization](https://mlsanity.com/paper/2609.22238/) (2026)

## Abstract (arXiv)

This work introduces a post-training quantization (PTQ) method for dense neural networks via a novel ADAROUND-based QUBO formulation. Using the Frobenius distance between the theoretical output and the dequantized output (before the activation function) as the objective, an explicit QUBO whose binary variables represent the rounding choice for each weight and bias is obtained. Additionally, by exploiting the structure of the coefficient QUBO matrix, the global problem can be exactly decomposed into n independent subproblems of size f+1, which can be efficiently solved using some heuristics such as simulated annealing. The approach is evaluated on MNIST, Fashion-MNIST, EMNIST, and CIFAR-10 across integer precisions from int8 to int1 and compared with a round-to-nearest traditional quantization methodology.