# Advancing Model Pruning via Bi-level Optimization

arXiv: https://arxiv.org/abs/2210.04092 · HTML: https://mlsanity.com/paper/2210.04092/

## Key facts

- Cited by 56 papers in the map (data through 14 Oct 2026).
- Builds on 74 of its 109 references that are in the map.
- First posted on arXiv 8 Oct 2022.

## Builds on (most cited first, 30 of 74)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (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)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [DARTS: Differentiable Architecture Search](https://mlsanity.com/paper/1806.09055/) (2018)
- [Pruning Filters for Efficient ConvNets](https://mlsanity.com/paper/1608.08710/) (2016)
- [SNIP: Single-shot Network Pruning based on Connection Sensitivity](https://mlsanity.com/paper/1810.02340/) (2018)
- [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)
- [Linear Mode Connectivity and the Lottery Ticket Hypothesis](https://mlsanity.com/paper/1912.05671/) (2019)
- [To prune, or not to prune: exploring the efficacy of pruning for model compression](https://mlsanity.com/paper/1710.01878/) (2017)
- [Learning Sparse Neural Networks through L0 Regularization](https://mlsanity.com/paper/1712.01312/) (2017)
- [What is the State of Neural Network Pruning?](https://mlsanity.com/paper/2003.03033/) (2020)
- [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)
- [Sparsity in Deep Learning: Pruning and growth for efficient inference and training in neural networks](https://mlsanity.com/paper/2102.00554/) (2021)
- [Meta-Learning with Implicit Gradients](https://mlsanity.com/paper/1909.04630/) (2019)
- [Rigging the Lottery: Making All Tickets Winners](https://mlsanity.com/paper/1911.11134/) (2019)
- [Pruning neural networks without any data by iteratively conserving synaptic flow](https://mlsanity.com/paper/2006.05467/) (2020)
- [The State of Sparsity in Deep Neural Networks](https://mlsanity.com/paper/1902.09574/) (2019)
- [Picking Winning Tickets Before Training by Preserving Gradient Flow](https://mlsanity.com/paper/2002.07376/) (2020)
- [AMC: AutoML for Model Compression and Acceleration on Mobile Devices](https://mlsanity.com/paper/1802.03494/) (2018)
- [PyHessian: Neural Networks Through the Lens of the Hessian](https://mlsanity.com/paper/1912.07145/) (2019)
- [The Lottery Ticket Hypothesis for Pre-trained BERT Networks](https://mlsanity.com/paper/2007.12223/) (2020)
- [Comparing Rewinding and Fine-tuning in Neural Network Pruning](https://mlsanity.com/paper/2003.02389/) (2020)
- [Deep learning: a statistical viewpoint](https://mlsanity.com/paper/2103.09177/) (2021)
- [What's Hidden in a Randomly Weighted Neural Network?](https://mlsanity.com/paper/1911.13299/) (2019)

## Built on by (most cited first, 30 of 56)

- [Model Sparsity Can Simplify Machine Unlearning](https://mlsanity.com/paper/2304.04934/) (2023)
- [A Survey on Deep Neural Network Pruning-Taxonomy, Comparison, Analysis, and Recommendations](https://mlsanity.com/paper/2308.06767/) (2023)
- [Defensive Unlearning with Adversarial Training for Robust Concept Erasure in Diffusion Models](https://mlsanity.com/paper/2405.15234/) (2024)
- [NetLLM: Adapting Large Language Models for Networking](https://mlsanity.com/paper/2402.02338/) (2024)
- [DeepZero: Scaling up Zeroth-Order Optimization for Deep Model Training](https://mlsanity.com/paper/2310.02025/) (2023)
- [The Emergence of Essential Sparsity in Large Pre-trained Models: The Weights that Matter](https://mlsanity.com/paper/2306.03805/) (2023)
- [An Introduction to Bi-level Optimization: Foundations and Applications in Signal Processing and Machine Learning](https://mlsanity.com/paper/2308.00788/) (2023)
- [Robust Mixture-of-Expert Training for Convolutional Neural Networks](https://mlsanity.com/paper/2308.10110/) (2023)
- [Unleashing the Power of Data Tsunami: A Comprehensive Survey on Data Assessment and Selection for Instruction Tuning of Language Models](https://mlsanity.com/paper/2408.02085/) (2024)
- [WAGLE: Strategic Weight Attribution for Effective and Modular Unlearning in Large Language Models](https://mlsanity.com/paper/2410.17509/) (2024)
- [Ten Lessons We Have Learned in the New "Sparseland": A Short Handbook for Sparse Neural Network Researchers](https://mlsanity.com/paper/2302.02596/) (2023)
- [Visual Prompting Upgrades Neural Network Sparsification: A Data-Model Perspective](https://mlsanity.com/paper/2312.01397/) (2023)
- [Pruning Foundation Models for High Accuracy without Retraining](https://mlsanity.com/paper/2410.15567/) (2024)
- [ECoFLaP: Efficient Coarse-to-Fine Layer-Wise Pruning for Vision-Language Models](https://mlsanity.com/paper/2310.02998/) (2023)
- [Text-Visual Prompting for Efficient 2D Temporal Video Grounding](https://mlsanity.com/paper/2303.04995/) (2023)
- [Search for Efficient Large Language Models](https://mlsanity.com/paper/2409.17372/) (2024)
- [Fast and Memory-Efficient Video Diffusion Using Streamlined Inference](https://mlsanity.com/paper/2411.01171/) (2024)
- [Selectivity Drives Productivity: Efficient Dataset Pruning for Enhanced Transfer Learning](https://mlsanity.com/paper/2310.08782/) (2023)
- [Memory-Efficient Gradient Unrolling for Large-Scale Bi-level Optimization](https://mlsanity.com/paper/2406.14095/) (2024)
- [RoRA: Efficient Fine-Tuning of LLM with Reliability Optimization for Rank Adaptation](https://mlsanity.com/paper/2501.04315/) (2025)
- [QuartDepth: Post-Training Quantization for Real-Time Depth Estimation on the Edge](https://mlsanity.com/paper/2503.16709/) (2025)
- [Building Variable-sized Models via Learngene Pool](https://mlsanity.com/paper/2312.05743/) (2023)
- [The Right to be Forgotten in Pruning: Unveil Machine Unlearning on Sparse Models](https://mlsanity.com/paper/2507.18725/) (2025)
- [An Efficient Privacy-aware Split Learning Framework for Satellite Communications](https://mlsanity.com/paper/2409.08538/) (2024)
- [BYOM: Building Your Own Multi-Task Model For Free](https://mlsanity.com/paper/2310.01886/) (2023)
- [Poor Man's Training on MCUs: A Memory-Efficient Quantized Back-Propagation-Free Approach](https://mlsanity.com/paper/2411.05873/) (2024)
- [Open-Source Multimodal Moxin Models with Moxin-VLM and Moxin-VLA](https://mlsanity.com/paper/2512.22208/) (2025)
- [BiSLS/SPS: Auto-tune Step Sizes for Stable Bi-level Optimization](https://mlsanity.com/paper/2305.18666/) (2023)
- [Influence Function Based Second-Order Channel Pruning-Evaluating True Loss Changes For Pruning Is Possible Without Retraining](https://mlsanity.com/paper/2308.06755/) (2023)
- [The Power of Few: Accelerating and Enhancing Data Reweighting with Coreset Selection](https://mlsanity.com/paper/2403.12166/) (2024)

## Abstract (arXiv)

The deployment constraints in practical applications necessitate the pruning of large-scale deep learning models, i.e., promoting their weight sparsity. As illustrated by the Lottery Ticket Hypothesis (LTH), pruning also has the potential of improving their generalization ability. At the core of LTH, iterative magnitude pruning (IMP) is the predominant pruning method to successfully find 'winning tickets'. Yet, the computation cost of IMP grows prohibitively as the targeted pruning ratio increases. To reduce the computation overhead, various efficient 'one-shot' pruning methods have been developed, but these schemes are usually unable to find winning tickets as good as IMP. This raises the question of how to close the gap between pruning accuracy and pruning efficiency? To tackle it, we pursue the algorithmic advancement of model pruning. Specifically, we formulate the pruning problem from a fresh and novel viewpoint, bi-level optimization (BLO). We show that the BLO interpretation provides a technically-grounded optimization base for an efficient implementation of the pruning-retraining learning paradigm used in IMP. We also show that the proposed bi-level optimization-oriented pruning method (termed BiP) is a special class of BLO problems with a bi-linear problem structure. By leveraging such bi-linearity, we theoretically show that BiP can be solved as easily as first-order optimization, thus inheriting the computation efficiency. Through extensive experiments on both structured and unstructured pruning with 5 model architectures and 4 data sets, we demonstrate that BiP can find better winning tickets than IMP in most cases, and is computationally as efficient as the one-shot pruning schemes, demonstrating 2-7 times speedup over IMP for the same level of model accuracy and sparsity.