# Optimal Brain Connection: Towards Efficient Structural Pruning

arXiv: https://arxiv.org/abs/2508.05521 · HTML: https://mlsanity.com/paper/2508.05521/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 49 references that are in the map.
- First posted on arXiv 7 Aug 2025.

## Builds on (most cited first, 30 of 33)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [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)
- [AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration](https://mlsanity.com/paper/2306.00978/) (2023)
- [Pruning Filters for Efficient ConvNets](https://mlsanity.com/paper/1608.08710/) (2016)
- [Learning Efficient Convolutional Networks through Network Slimming](https://mlsanity.com/paper/1708.06519/) (2017)
- [Importance Estimation for Neural Network Pruning](https://mlsanity.com/paper/1906.10771/) (2019)
- [Picking Winning Tickets Before Training by Preserving Gradient Flow](https://mlsanity.com/paper/2002.07376/) (2020)
- [Filter Pruning via Geometric Median for Deep Convolutional Neural Networks Acceleration](https://mlsanity.com/paper/1811.00250/) (2018)
- [Optimal Brain Compression: A Framework for Accurate Post-Training Quantization and Pruning](https://mlsanity.com/paper/2208.11580/) (2022)
- [HRank: Filter Pruning using High-Rank Feature Map](https://mlsanity.com/paper/2002.10179/) (2020)
- [NISP: Pruning Networks using Neuron Importance Score Propagation](https://mlsanity.com/paper/1711.05908/) (2017)
- [MetaPruning: Meta Learning for Automatic Neural Network Channel Pruning](https://mlsanity.com/paper/1903.10258/) (2019)
- [Towards Optimal Structured CNN Pruning via Generative Adversarial Learning](https://mlsanity.com/paper/1903.09291/) (2019)
- [Group Fisher Pruning for Practical Network Compression](https://mlsanity.com/paper/2108.00708/) (2021)
- [Gate Decorator: Global Filter Pruning Method for Accelerating Deep Convolutional Neural Networks](https://mlsanity.com/paper/1909.08174/) (2019)
- [Neural Pruning via Growing Regularization](https://mlsanity.com/paper/2012.09243/) (2020)
- [Faster gaze prediction with dense networks and Fisher pruning](https://mlsanity.com/paper/1801.05787/) (2018)
- [ResRep: Lossless CNN Pruning via Decoupling Remembering and Forgetting](https://mlsanity.com/paper/2007.03260/) (2020)
- [CP-ViT: Cascade Vision Transformer Pruning via Progressive Sparsity Prediction](https://mlsanity.com/paper/2203.04570/) (2022)
- [SOSP: Efficiently Capturing Global Correlations by Second-Order Structured Pruning](https://mlsanity.com/paper/2110.11395/) (2021)
- [Asymptotic Soft Filter Pruning for Deep Convolutional Neural Networks](https://mlsanity.com/paper/1808.07471/) (2018)
- [Leveraging Filter Correlations for Deep Model Compression](https://mlsanity.com/paper/1811.10559/) (2018)
- [Pruning Large Language Models with Semi-Structural Adaptive Sparse Training](https://mlsanity.com/paper/2407.20584/) (2024)
- [TSP3D: Text-guided Sparse Voxel Pruning for Efficient 3D Visual Grounding](https://mlsanity.com/paper/2502.10392/) (2025)
- [Neural Network Weights Do Not Converge to Stationary Points: An Invariant Measure Perspective](https://mlsanity.com/paper/2110.06256/) (2021)
- [Masks, Signs, And Learning Rate Rewinding](https://mlsanity.com/paper/2402.19262/) (2024)
- [Auto-Prox: Training-Free Vision Transformer Architecture Search via Automatic Proxy Discovery](https://mlsanity.com/paper/2312.09059/) (2023)
- [MULTIFLOW: Shifting Towards Task-Agnostic Vision-Language Pruning](https://mlsanity.com/paper/2404.05621/) (2024)
- [Influence Function Based Second-Order Channel Pruning-Evaluating True Loss Changes For Pruning Is Possible Without Retraining](https://mlsanity.com/paper/2308.06755/) (2023)

## Built on by (most cited first, 3 of 3)

- [TinyDrop: Tiny Model Guided Token Dropping for Vision Transformers](https://mlsanity.com/paper/2509.03379/) (2025)
- [TPV: Parameter Perturbations Through the Lens of Test Prediction Variance](https://mlsanity.com/paper/2512.11089/) (2025)
- [STARFISH: faST Accuracy Recovery in pruned networks From Internal State Healing](https://mlsanity.com/paper/2606.01126/) (2026)

## Abstract (arXiv)

Structural pruning has been widely studied for its effectiveness in compressing neural networks. However, existing methods often neglect the interconnections among parameters. To address this limitation, this paper proposes a structural pruning framework termed Optimal Brain Connection. First, we introduce the Jacobian Criterion, a first-order metric for evaluating the saliency of structural parameters. Unlike existing first-order methods that assess parameters in isolation, our criterion explicitly captures both intra-component interactions and inter-layer dependencies. Second, we propose the Equivalent Pruning mechanism, which utilizes autoencoders to retain the contributions of all original connection--including pruned ones--during fine-tuning. Experimental results demonstrate that the Jacobian Criterion outperforms several popular metrics in preserving model performance, while the Equivalent Pruning mechanism effectively mitigates performance degradation after fine-tuning. Code: https://github.com/ShaowuChen/Optimal_Brain_Connection