# Influence Function Based Second-Order Channel Pruning-Evaluating True Loss Changes For Pruning Is Possible Without Retraining

arXiv: https://arxiv.org/abs/2308.06755 · HTML: https://mlsanity.com/paper/2308.06755/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 60 of its 83 references that are in the map.
- First posted on arXiv 13 Aug 2023.

## Builds on (most cited first, 30 of 60)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [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)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [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)
- [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)
- [Picking Winning Tickets Before Training by Preserving Gradient Flow](https://mlsanity.com/paper/2002.07376/) (2020)
- [ThiNet: A Filter Level Pruning Method for Deep Neural Network Compression](https://mlsanity.com/paper/1707.06342/) (2017)
- [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)
- [Soft Filter Pruning for Accelerating Deep Convolutional Neural Networks](https://mlsanity.com/paper/1808.06866/) (2018)
- [Optimizing Millions of Hyperparameters by Implicit Differentiation](https://mlsanity.com/paper/1911.02590/) (2019)
- [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)
- [Learning to Prune Deep Neural Networks via Layer-wise Optimal Brain Surgeon](https://mlsanity.com/paper/1705.07565/) (2017)
- [Data-Driven Sparse Structure Selection for Deep Neural Networks](https://mlsanity.com/paper/1707.01213/) (2017)
- [Discrimination-aware Channel Pruning for Deep Neural Networks](https://mlsanity.com/paper/1810.11809/) (2018)
- [Channel-wise Knowledge Distillation for Dense Prediction](https://mlsanity.com/paper/2011.13256/) (2020)
- [Drawing Early-Bird Tickets: Towards More Efficient Training of Deep Networks](https://mlsanity.com/paper/1909.11957/) (2019)
- [Towards Optimal Structured CNN Pruning via Generative Adversarial Learning](https://mlsanity.com/paper/1903.09291/) (2019)
- [Natural Language Descriptions of Deep Visual Features](https://mlsanity.com/paper/2201.11114/) (2022)

## Built on by (most cited first, 4 of 4)

- [Benchmarking Post-Training Quantization in LLMs: Comprehensive Taxonomy, Unified Evaluation, and Comparative Analysis](https://mlsanity.com/paper/2502.13178/) (2025)
- [Optimal Brain Connection: Towards Efficient Structural Pruning](https://mlsanity.com/paper/2508.05521/) (2025)
- [MGAA: Multi-Granular Adaptive Allocation fof Low-Rank Compression of LLMs](https://mlsanity.com/paper/2507.03294/) (2025)
- [InterPruner: Interactive Structured Pruning via Taylor-Implicit Criterion and Language-Prior Modulator for Multimodal Object Detection](https://mlsanity.com/paper/2608.10724/) (2026)

## Abstract (arXiv)

A challenge of channel pruning is designing efficient and effective criteria to select channels to prune. A widely used criterion is minimal performance degeneration. To accurately evaluate the truth performance degeneration requires retraining the survived weights to convergence, which is prohibitively slow. Hence existing pruning methods use previous weights (without retraining) to evaluate the performance degeneration. However, we observe the loss changes differ significantly with and without retraining. It motivates us to develop a technique to evaluate true loss changes without retraining, with which channels to prune can be selected more reliably and confidently. We first derive a closed-form estimator of the true loss change per pruning mask change, using influence functions without retraining. Influence function which is from robust statistics reveals the impacts of a training sample on the model's prediction and is repurposed by us to assess impacts on true loss changes. We then show how to assess the importance of all channels simultaneously and develop a novel global channel pruning algorithm accordingly. We conduct extensive experiments to verify the effectiveness of the proposed algorithm. To the best of our knowledge, we are the first that shows evaluating true loss changes for pruning without retraining is possible. This finding will open up opportunities for a series of new paradigms to emerge that differ from existing pruning methods. The code is available at https://github.com/hrcheng1066/IFSO.