# Castling-ViT: Compressing Self-Attention via Switching Towards Linear-Angular Attention at Vision Transformer Inference

arXiv: https://arxiv.org/abs/2211.10526 · HTML: https://mlsanity.com/paper/2211.10526/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- Builds on 64 of its 79 references that are in the map.
- First posted on arXiv 18 Nov 2022.

## Builds on (most cited first, 30 of 64)

- [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)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [End-to-End Object Detection with Transformers](https://mlsanity.com/paper/2005.12872/) (2020)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [Deformable DETR: Deformable Transformers for End-to-End Object Detection](https://mlsanity.com/paper/2010.04159/) (2020)
- [Longformer: The Long-Document Transformer](https://mlsanity.com/paper/2004.05150/) (2020)
- [Masked-attention Mask Transformer for Universal Image Segmentation](https://mlsanity.com/paper/2112.01527/) (2021)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [Searching for MobileNetV3](https://mlsanity.com/paper/1905.02244/) (2019)
- [Pyramid Vision Transformer: A Versatile Backbone for Dense Prediction without Convolutions](https://mlsanity.com/paper/2102.12122/) (2021)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [Rethinking Attention with Performers](https://mlsanity.com/paper/2009.14794/) (2020)
- [Linformer: Self-Attention with Linear Complexity](https://mlsanity.com/paper/2006.04768/) (2020)
- [Per-Pixel Classification is Not All You Need for Semantic Segmentation](https://mlsanity.com/paper/2107.06278/) (2021)
- [Tokens-to-Token ViT: Training Vision Transformers from Scratch on ImageNet](https://mlsanity.com/paper/2101.11986/) (2021)
- [YOLOX: Exceeding YOLO Series in 2021](https://mlsanity.com/paper/2107.08430/) (2021)
- [Token Merging: Your ViT But Faster](https://mlsanity.com/paper/2210.09461/) (2022)
- [EfficientDet: Scalable and Efficient Object Detection](https://mlsanity.com/paper/1911.09070/) (2019)
- [Designing Network Design Spaces](https://mlsanity.com/paper/2003.13678/) (2020)
- [CvT: Introducing Convolutions to Vision Transformers](https://mlsanity.com/paper/2103.15808/) (2021)
- [Revisiting Unreasonable Effectiveness of Data in Deep Learning Era](https://mlsanity.com/paper/1707.02968/) (2017)
- [Multiscale Vision Transformers](https://mlsanity.com/paper/2104.11227/) (2021)
- [DynamicViT: Efficient Vision Transformers with Dynamic Token Sparsification](https://mlsanity.com/paper/2106.02034/) (2021)
- [CrossViT: Cross-Attention Multi-Scale Vision Transformer for Image Classification](https://mlsanity.com/paper/2103.14899/) (2021)
- [Going deeper with Image Transformers](https://mlsanity.com/paper/2103.17239/) (2021)

## Built on by (most cited first, 28 of 28)

- [EfficientSAM: Leveraged Masked Image Pretraining for Efficient Segment Anything](https://mlsanity.com/paper/2312.00863/) (2023)
- [FLatten Transformer: Vision Transformer using Focused Linear Attention](https://mlsanity.com/paper/2308.00442/) (2023)
- [Agent Attention: On the Integration of Softmax and Linear Attention](https://mlsanity.com/paper/2312.08874/) (2023)
- [Bridging the Divide: Reconsidering Softmax and Linear Attention](https://mlsanity.com/paper/2412.06590/) (2024)
- [A Survey on Transformer Compression](https://mlsanity.com/paper/2402.05964/) (2024)
- [A survey on efficient vision transformers: algorithms, techniques, and performance benchmarking](https://mlsanity.com/paper/2309.02031/) (2023)
- [PolaFormer: Polarity-aware Linear Attention for Vision Transformers](https://mlsanity.com/paper/2501.15061/) (2025)
- [Breaking the Low-Rank Dilemma of Linear Attention](https://mlsanity.com/paper/2411.07635/) (2024)
- [Efficient Diffusion Transformer with Step-wise Dynamic Attention Mediators](https://mlsanity.com/paper/2408.05710/) (2024)
- [Efficient Track Anything](https://mlsanity.com/paper/2411.18933/) (2024)
- [Rectifying Magnitude Neglect in Linear Attention](https://mlsanity.com/paper/2507.00698/) (2025)
- [ShiftAddViT: Mixture of Multiplication Primitives Towards Efficient Vision Transformer](https://mlsanity.com/paper/2306.06446/) (2023)
- [Computation-efficient Deep Learning for Computer Vision: A Survey](https://mlsanity.com/paper/2308.13998/) (2023)
- [PaPr: Training-Free One-Step Patch Pruning with Lightweight ConvNets for Faster Inference](https://mlsanity.com/paper/2403.16020/) (2024)
- [When Linear Attention Meets Autoregressive Decoding: Towards More Effective and Efficient Linearized Large Language Models](https://mlsanity.com/paper/2406.07368/) (2024)
- [Not Every Patch is Needed: Towards a More Efficient and Effective Backbone for Video-based Person Re-identification](https://mlsanity.com/paper/2501.16811/) (2025)
- [PADRe: A Unifying Polynomial Attention Drop-in Replacement for Efficient Vision Transformer](https://mlsanity.com/paper/2407.11306/) (2024)
- [Linear Differential Vision Transformer: Learning Visual Contrasts via Pairwise Differentials](https://mlsanity.com/paper/2511.00833/) (2025)
- [Trio-ViT: Post-Training Quantization and Acceleration for Softmax-Free Efficient Vision Transformer](https://mlsanity.com/paper/2405.03882/) (2024)
- [Automatic Channel Pruning for Multi-Head Attention](https://mlsanity.com/paper/2405.20867/) (2024)
- [AnchorFormer: Differentiable Anchor Attention for Efficient Vision Transformer](https://mlsanity.com/paper/2505.16463/) (2025)
- [Norm×Direction: Restoring the Missing Query Norm in Vision Linear Attention](https://mlsanity.com/paper/2506.21137/) (2025)
- [BinaryAttention: One-Bit QK-Attention for Vision and Diffusion Transformers](https://mlsanity.com/paper/2603.09582/) (2026)
- [Long-Term Prediction Accuracy Improvement of Data-Driven Medium-Range Global Weather Forecast](https://mlsanity.com/paper/2407.01598/) (2024)
- [MirrorLA: Reflecting Feature Map for Vision Linear Attention](https://mlsanity.com/paper/2602.04346/) (2026)
- [Attention to details, logits to truth: visual-aware attention and logits enhancement to mitigate hallucinations in LVLMs](https://mlsanity.com/paper/2602.09521/) (2026)
- [RAViT: Resolution-Adaptive Vision Transformer](https://mlsanity.com/paper/2602.24159/) (2026)
- [Do Vision Transformers Need All-to-All Attention? Global Communication Through Elastic Learned Cores](https://mlsanity.com/paper/2605.12491/) (2026)

## Abstract (arXiv)

Vision Transformers (ViTs) have shown impressive performance but still require a high computation cost as compared to convolutional neural networks (CNNs), one reason is that ViTs' attention measures global similarities and thus has a quadratic complexity with the number of input tokens. Existing efficient ViTs adopt local attention (e.g., Swin) or linear attention (e.g., Performer), which sacrifice ViTs' capabilities of capturing either global or local context. In this work, we ask an important research question: Can ViTs learn both global and local context while being more efficient during inference? To this end, we propose a framework called Castling-ViT, which trains ViTs using both linear-angular attention and masked softmax-based quadratic attention, but then switches to having only linear angular attention during ViT inference. Our Castling-ViT leverages angular kernels to measure the similarities between queries and keys via spectral angles. And we further simplify it with two techniques: (1) a novel linear-angular attention mechanism: we decompose the angular kernels into linear terms and high-order residuals, and only keep the linear terms; and (2) we adopt two parameterized modules to approximate high-order residuals: a depthwise convolution and an auxiliary masked softmax attention to help learn both global and local information, where the masks for softmax attention are regularized to gradually become zeros and thus incur no overhead during ViT inference. Extensive experiments and ablation studies on three tasks consistently validate the effectiveness of the proposed Castling-ViT, e.g., achieving up to a 1.8% higher accuracy or 40% MACs reduction on ImageNet classification and 1.2 higher mAP on COCO detection under comparable FLOPs, as compared to ViTs with vanilla softmax-based attentions.