# Neural Network Pruning via QUBO Optimization

arXiv: https://arxiv.org/abs/2604.05856 · HTML: https://mlsanity.com/paper/2604.05856/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 38 references that are in the map.
- First posted on arXiv 7 Apr 2026.

## Builds on (most cited first, 26 of 26)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Restormer: Efficient Transformer for High-Resolution Image Restoration](https://mlsanity.com/paper/2111.09881/) (2021)
- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (2017)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Pruning Filters for Efficient ConvNets](https://mlsanity.com/paper/1608.08710/) (2016)
- [Channel Pruning for Accelerating Very Deep Neural Networks](https://mlsanity.com/paper/1707.06168/) (2017)
- [Learning Efficient Convolutional Networks through Network Slimming](https://mlsanity.com/paper/1708.06519/) (2017)
- [Learned Step Size Quantization](https://mlsanity.com/paper/1902.08153/) (2019)
- [Learning Structured Sparsity in Deep Neural Networks](https://mlsanity.com/paper/1608.03665/) (2016)
- [Importance Estimation for Neural Network Pruning](https://mlsanity.com/paper/1906.10771/) (2019)
- [AMC: AutoML for Model Compression and Acceleration on Mobile Devices](https://mlsanity.com/paper/1802.03494/) (2018)
- [Filter Pruning via Geometric Median for Deep Convolutional Neural Networks Acceleration](https://mlsanity.com/paper/1811.00250/) (2018)
- [Proving the Lottery Ticket Hypothesis: Pruning is All You Need](https://mlsanity.com/paper/2002.00585/) (2020)
- [NetAdapt: Platform-Aware Neural Network Adaptation for Mobile Applications](https://mlsanity.com/paper/1804.03230/) (2018)
- [Group Fisher Pruning for Practical Network Compression](https://mlsanity.com/paper/2108.00708/) (2021)
- [On-Device Language Models: A Comprehensive Review](https://mlsanity.com/paper/2409.00088/) (2024)
- [Faster gaze prediction with dense networks and Fisher pruning](https://mlsanity.com/paper/1801.05787/) (2018)
- [Convolutional Neural Network Pruning with Structural Redundancy Reduction](https://mlsanity.com/paper/2104.03438/) (2021)
- [Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives](https://mlsanity.com/paper/1708.09165/) (2017)
- [Fast as CHITA: Neural Network Pruning with Combinatorial Optimization](https://mlsanity.com/paper/2302.14623/) (2023)
- [Leveraging Filter Correlations for Deep Model Compression](https://mlsanity.com/paper/1811.10559/) (2018)
- [Is Quantum Optimization Ready? An Effort Towards Neural Network Compression using Adiabatic Quantum Computing](https://mlsanity.com/paper/2505.16332/) (2025)
- [What Scalable Second-Order Information Knows for Pruning at Initialization](https://mlsanity.com/paper/2502.11450/) (2025)

## Abstract (arXiv)

Neural network pruning can be formulated as a combinatorial optimization problem, yet most existing approaches rely on greedy heuristics that ignore complex interactions between filters. Formal optimization methods such as Quadratic Unconstrained Binary Optimization (QUBO) provide a principled alternative but have so far underperformed due to oversimplified objective formulations based on metrics like the L1-norm. In this work, we propose a unified Hybrid QUBO framework that bridges heuristic importance estimation with global combinatorial optimization. Our formulation integrates gradient-aware sensitivity metrics - specifically first-order Taylor and second-order Fisher information - into the linear term, while utilizing data-driven activation similarity in the quadratic term. This allows the QUBO objective to jointly capture individual filter relevance and inter-filter functional redundancy. We further introduce a dynamic capacity-driven search to strictly enforce target sparsity without distorting the optimization landscape. Finally, we employ a two-stage pipeline featuring a Tensor-Train (TT) Refinement stage - a gradient-free optimizer that fine-tunes the QUBO-derived solution directly against the true evaluation metric. Experiments on the SIDD image denoising dataset demonstrate that the proposed Hybrid QUBO significantly outperforms both greedy Taylor pruning and traditional L1-based QUBO, with TT Refinement providing further consistent gains at appropriate combinatorial scales. This highlights the potential of hybrid combinatorial formulations for robust, scalable, and interpretable neural network compression.