# Colinearity Decay: Training Quantization-Friendly ViTs with Outlier Decay

arXiv: https://arxiv.org/abs/2605.01330 · HTML: https://mlsanity.com/paper/2605.01330/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 50 references that are in the map.
- First posted on arXiv 2 May 2026.

## Builds on (most cited first, 30 of 42)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [Qwen3-VL Technical Report](https://mlsanity.com/paper/2511.21631/) (2025)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [Fine-Grained Visual Classification of Aircraft](https://mlsanity.com/paper/1306.5151/) (2013)
- [EuroSAT: A Novel Dataset and Deep Learning Benchmark for Land Use and Land Cover Classification](https://mlsanity.com/paper/1709.00029/) (2017)
- [DINOv3](https://mlsanity.com/paper/2508.10104/) (2025)
- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [gpt-oss-120b & gpt-oss-20b Model Card](https://mlsanity.com/paper/2508.10925/) (2025)
- [MMDetection: Open MMLab Detection Toolbox and Benchmark](https://mlsanity.com/paper/1906.07155/) (2019)
- [Mixed Precision Training](https://mlsanity.com/paper/1710.03740/) (2017)
- [Vision Transformers Need Registers](https://mlsanity.com/paper/2309.16588/) (2023)
- [Learned Step Size Quantization](https://mlsanity.com/paper/1902.08153/) (2019)
- [Massive Activations in Large Language Models](https://mlsanity.com/paper/2402.17762/) (2024)
- [Outlier Suppression: Pushing the Limit of Low-bit Transformer Language Models](https://mlsanity.com/paper/2209.13325/) (2022)
- [PTQ4ViT: Post-training quantization for vision transformers with twin uniform quantization](https://mlsanity.com/paper/2111.12293/) (2021)
- [FQ-ViT: Post-Training Quantization for Fully Quantized Vision Transformer](https://mlsanity.com/paper/2111.13824/) (2021)
- [RepQ-ViT: Scale Reparameterization for Post-Training Quantization of Vision Transformers](https://mlsanity.com/paper/2212.08254/) (2022)
- [Q-ViT: Accurate and Fully Quantized Low-bit Vision Transformer](https://mlsanity.com/paper/2210.06707/) (2022)
- [Oscillation-free Quantization for Low-bit Vision Transformers](https://mlsanity.com/paper/2302.02210/) (2023)
- [NICE: Noise Injection and Clamping Estimation for Neural Network Quantization](https://mlsanity.com/paper/1810.00162/) (2018)

## Built on by (most cited first, 1 of 1)

- [Ovis-Embedding: Pushing the Frontiers of Universal Omni-Modal Embeddings](https://mlsanity.com/paper/2609.25165/) (2026)

## Abstract (arXiv)

Low-bit quantization is a practical route for efficiently deploying vision Transformers, yet activation outliers complicate fully quantized deployment. Existing methods either handle quantization post-training or suppress large activations during training; however, aggressively restricting outliers in vision models can lead to a poorer trade-off between full-precision and quantized accuracy. We argue that rather than simply suppressing outliers, the training objective should control the structural amplification that makes them harmful. To this end, we introduce Colinearity-Decay (CD), a structural regularizer for ordered matrix pairs within Transformer blocks. CD penalizes detrimental cross-matrix alignment and mitigates extreme activations without altering the architecture or task loss. Applied as a decoupled update, CD is non-invasive and introduces minimal training overhead. Across ImageNet-1K pre-training, COCO detection, and downstream fine-tuning, CD consistently boosts quantized accuracy across multiple pipelines while preserving, or even improving, full-precision performance. Ultimately, our results demonstrate that structural regularization effectively prepares vision Transformers for low-bit deployment with zero inference-time overhead.