# Solving Oscillation Problem in Post-Training Quantization Through a Theoretical Perspective

arXiv: https://arxiv.org/abs/2303.11906 · HTML: https://mlsanity.com/paper/2303.11906/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 47 references that are in the map.
- First posted on arXiv 21 Mar 2023.

## Builds on (most cited first, 30 of 37)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [DARTS: Differentiable Architecture Search](https://mlsanity.com/paper/1806.09055/) (2018)
- [Inception-v4, Inception-ResNet and the Impact of Residual Connections on Learning](https://mlsanity.com/paper/1602.07261/) (2016)
- [Designing Network Design Spaces](https://mlsanity.com/paper/2003.13678/) (2020)
- [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)
- [Quantizing deep convolutional networks for efficient inference: A whitepaper](https://mlsanity.com/paper/1806.08342/) (2018)
- [Progressive Neural Architecture Search](https://mlsanity.com/paper/1712.00559/) (2017)
- [BRECQ: Pushing the Limit of Post-Training Quantization by Block Reconstruction](https://mlsanity.com/paper/2102.05426/) (2021)
- [PACT: Parameterized Clipping Activation for Quantized Neural Networks](https://mlsanity.com/paper/1805.06085/) (2018)
- [HAQ: Hardware-Aware Automated Quantization with Mixed Precision](https://mlsanity.com/paper/1811.08886/) (2018)
- [ZeroQ: A Novel Zero Shot Quantization Framework](https://mlsanity.com/paper/2001.00281/) (2020)
- [Differentiable Soft Quantization: Bridging Full-Precision and Low-Bit Neural Networks](https://mlsanity.com/paper/1908.05033/) (2019)
- [Bi-Real Net: Enhancing the Performance of 1-bit CNNs With Improved Representational Capability and Advanced Training Algorithm](https://mlsanity.com/paper/1808.00278/) (2018)
- [QDrop: Randomly Dropping Quantization for Extremely Low-bit Post-Training Quantization](https://mlsanity.com/paper/2203.05740/) (2022)
- [Loss Aware Post-training Quantization](https://mlsanity.com/paper/1911.07190/) (2019)
- [Improving Post Training Neural Quantization: Layer-wise Calibration and Integer Programming](https://mlsanity.com/paper/2006.10518/) (2020)
- [Towards Unified INT8 Training for Convolutional Neural Network](https://mlsanity.com/paper/1912.12607/) (2019)
- [Towards Effective Low-bitwidth Convolutional Neural Networks](https://mlsanity.com/paper/1711.00205/) (2017)
- [Revisiting Random Channel Pruning for Neural Network Compression](https://mlsanity.com/paper/2205.05676/) (2022)
- [OMPQ: Orthogonal Mixed Precision Quantization](https://mlsanity.com/paper/2109.07865/) (2021)
- [When to Prune? A Policy towards Early Structural Pruning](https://mlsanity.com/paper/2110.12007/) (2021)
- [Fire Together Wire Together: A Dynamic Pruning Approach with Self-Supervised Mask Prediction](https://mlsanity.com/paper/2110.08232/) (2021)
- [Multinomial Distribution Learning for Effective Neural Architecture Search](https://mlsanity.com/paper/1905.07529/) (2019)
- [An Information Theory-inspired Strategy for Automatic Network Pruning](https://mlsanity.com/paper/2108.08532/) (2021)

## Built on by (most cited first, 17 of 17)

- [AffineQuant: Affine Transformation Quantization for Large Language Models](https://mlsanity.com/paper/2403.12544/) (2024)
- [PTQ4SAM: Post-Training Quantization for Segment Anything](https://mlsanity.com/paper/2405.03144/) (2024)
- [Low-bit Model Quantization for Deep Neural Networks: A Survey](https://mlsanity.com/paper/2505.05530/) (2025)
- [EPTQ: Enhanced Post-Training Quantization via Hessian-guided Network-wise Optimization](https://mlsanity.com/paper/2309.11531/) (2023)
- [Motion-Aware Caching for Efficient Autoregressive Video Generation](https://mlsanity.com/paper/2605.01725/) (2026)
- [MetaAug: Meta-Data Augmentation for Post-Training Quantization](https://mlsanity.com/paper/2407.14726/) (2024)
- [Pack-PTQ: Advancing Post-training Quantization of Neural Networks by Pack-wise Reconstruction](https://mlsanity.com/paper/2505.00259/) (2025)
- [Efficiently Training A Flat Neural Network Before It has been Quantizated](https://mlsanity.com/paper/2511.01462/) (2025)
- [CAR-SAM: Cross-Attention Reconstruction for Post-Training Quantization of the Segment Anything Model](https://mlsanity.com/paper/2605.16901/) (2026)
- [ALGOGEN: Tool-Generated Verifiable Traces for Reliable Algorithm Visualization](https://mlsanity.com/paper/2605.12159/) (2026)
- [A2RBench: An Automatic Paradigm for Formally Verifiable Abstract Reasoning Benchmark Generation](https://mlsanity.com/paper/2605.17278/) (2026)
- [InTrain: Intrinsic Trainability for Zero-Cost Neural Architecture Search](https://mlsanity.com/paper/2606.18676/) (2026)
- [FUSE: Frequency-domain Unification and Spectral Energy Alignment for Multi-modal Object Re-Identification](https://mlsanity.com/paper/2606.20044/) (2026)
- [Efficient Tuning Before Low-Bit Post-Training Quantization for Stochastic Gradient Descent-optimized Models](https://mlsanity.com/paper/2607.11359/) (2026)
- [CommitKV: Lifecycle-Aware KV Cache Compression via Commit Transitions for Multi-Turn Agents](https://mlsanity.com/paper/2608.07855/) (2026)
- [UC-VLM: Consistency-Driven Learning for AI-Generated Image Detection with Vision-Language Large Models](https://mlsanity.com/paper/2608.15238/) (2026)
- [STEPQuant: When and Where Errors Matter in Delta-Rule Recurrent State Quantization](https://mlsanity.com/paper/2609.38169/) (2026)

## Abstract (arXiv)

Post-training quantization (PTQ) is widely regarded as one of the most efficient compression methods practically, benefitting from its data privacy and low computation costs. We argue that an overlooked problem of oscillation is in the PTQ methods. In this paper, we take the initiative to explore and present a theoretical proof to explain why such a problem is essential in PTQ. And then, we try to solve this problem by introducing a principled and generalized framework theoretically. In particular, we first formulate the oscillation in PTQ and prove the problem is caused by the difference in module capacity. To this end, we define the module capacity (ModCap) under data-dependent and data-free scenarios, where the differentials between adjacent modules are used to measure the degree of oscillation. The problem is then solved by selecting top-k differentials, in which the corresponding modules are jointly optimized and quantized. Extensive experiments demonstrate that our method successfully reduces the performance drop and is generalized to different neural networks and PTQ methods. For example, with 2/4 bit ResNet-50 quantization, our method surpasses the previous state-of-the-art method by 1.9%. It becomes more significant on small model quantization, e.g. surpasses BRECQ method by 6.61% on MobileNetV2*0.5.