# EcoFormer: Energy-Saving Attention with Linear Complexity

arXiv: https://arxiv.org/abs/2209.09004 · HTML: https://mlsanity.com/paper/2209.09004/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 52 of its 84 references that are in the map.
- First posted on arXiv 19 Sep 2022.

## Builds on (most cited first, 30 of 52)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [Longformer: The Long-Document Transformer](https://mlsanity.com/paper/2004.05150/) (2020)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [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)
- [Perceiver: General Perception with Iterative Attention](https://mlsanity.com/paper/2103.03206/) (2021)
- [XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networks](https://mlsanity.com/paper/1603.05279/) (2016)
- [PVT v2: Improved Baselines with Pyramid Vision Transformer](https://mlsanity.com/paper/2106.13797/) (2021)
- [Long Range Arena: A Benchmark for Efficient Transformers](https://mlsanity.com/paper/2011.04006/) (2020)
- [Universal Transformers](https://mlsanity.com/paper/1807.03819/) (2018)
- [Learned Step Size Quantization](https://mlsanity.com/paper/1902.08153/) (2019)
- [BinaryConnect: Training Deep Neural Networks with binary weights during propagations](https://mlsanity.com/paper/1511.00363/) (2015)
- [DoReFa-Net: Training Low Bitwidth Convolutional Neural Networks with Low Bitwidth Gradients](https://mlsanity.com/paper/1606.06160/) (2016)
- [Twins: Revisiting the Design of Spatial Attention in Vision Transformers](https://mlsanity.com/paper/2104.13840/) (2021)
- [Nystr"omformer: A Nystr"om-Based Algorithm for Approximating Self-Attention](https://mlsanity.com/paper/2102.03902/) (2021)
- [Quantized Neural Networks: Training Neural Networks with Low Precision Weights and Activations](https://mlsanity.com/paper/1609.07061/) (2016)
- [Q-BERT: Hessian Based Ultra Low Precision Quantization of BERT](https://mlsanity.com/paper/1909.05840/) (2019)
- [Random Feature Attention](https://mlsanity.com/paper/2103.02143/) (2021)
- [Q8BERT: Quantized 8Bit BERT](https://mlsanity.com/paper/1910.06188/) (2019)
- [EIE: Efficient Inference Engine on Compressed Deep Neural Network](https://mlsanity.com/paper/1602.01528/) (2016)
- [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)
- [cosFormer: Rethinking Softmax in Attention](https://mlsanity.com/paper/2202.08791/) (2022)
- [BinaryBERT: Pushing the Limit of BERT Quantization](https://mlsanity.com/paper/2012.15701/) (2020)
- [Learning to Quantize Deep Networks by Optimizing Quantization Intervals with Task Loss](https://mlsanity.com/paper/1808.05779/) (2018)

## Built on by (most cited first, 21 of 21)

- [Outlier Suppression+: Accurate quantization of large language models by equivalent and optimal shifting and scaling](https://mlsanity.com/paper/2304.09145/) (2023)
- [A survey on efficient vision transformers: algorithms, techniques, and performance benchmarking](https://mlsanity.com/paper/2309.02031/) (2023)
- [Graph Transformers: A Survey](https://mlsanity.com/paper/2407.09777/) (2024)
- [BiViT: Extremely Compressed Binary Vision Transformer](https://mlsanity.com/paper/2211.07091/) (2022)
- [Castling-ViT: Compressing Self-Attention via Switching Towards Linear-Angular Attention at Vision Transformer Inference](https://mlsanity.com/paper/2211.10526/) (2022)
- [On Efficient Training of Large-Scale Deep Learning Models: A Literature Review](https://mlsanity.com/paper/2304.03589/) (2023)
- [Spiking Vision Transformer with Saccadic Attention](https://mlsanity.com/paper/2502.12677/) (2025)
- [ShiftAddViT: Mixture of Multiplication Primitives Towards Efficient Vision Transformer](https://mlsanity.com/paper/2306.06446/) (2023)
- [RIFormer: Keep Your Vision Backbone Effective While Removing Token Mixer](https://mlsanity.com/paper/2304.05659/) (2023)
- [Fcaformer: Forward Cross Attention in Hybrid Vision Transformer](https://mlsanity.com/paper/2211.07198/) (2022)
- [SlowFormer: Universal Adversarial Patch for Attack on Compute and Energy Efficiency of Inference Efficient Vision Transformers](https://mlsanity.com/paper/2310.02544/) (2023)
- [Trimming Down Large Spiking Vision Transformers via Heterogeneous Quantization Search](https://mlsanity.com/paper/2412.05505/) (2024)
- [MSVIT: Improving Spiking Vision Transformer Using Multi-scale Attention Fusion](https://mlsanity.com/paper/2505.14719/) (2025)
- [Neural Dynamics Self-Attention for Spiking Transformers](https://mlsanity.com/paper/2603.19290/) (2026)
- [SenDaL: An Effective and Efficient Calibration Framework of Low-Cost Sensors for Daily Life](https://mlsanity.com/paper/2502.10460/) (2025)
- [Deeply Dual Supervised learning for melanoma recognition](https://mlsanity.com/paper/2508.01994/) (2025)
- [Edge Detection for Organ Boundaries via Top Down Refinement and SubPixel Upsampling](https://mlsanity.com/paper/2508.06805/) (2025)
- [DualResolution Residual Architecture with Artifact Suppression for Melanocytic Lesion Segmentation](https://mlsanity.com/paper/2508.06816/) (2025)
- [VesselRW: Weakly Supervised Subcutaneous Vessel Segmentation via Learned Random Walk Propagation](https://mlsanity.com/paper/2508.06819/) (2025)
- [Sensor Calibration Model Balancing Accuracy, Real-time, and Efficiency](https://mlsanity.com/paper/2511.06715/) (2025)
- [PatchDenoiser: Parameter-efficient multi-scale patch learning and fusion denoiser for Low-dose CT imaging](https://mlsanity.com/paper/2602.21987/) (2026)

## Abstract (arXiv)

Transformer is a transformative framework that models sequential data and has achieved remarkable performance on a wide range of tasks, but with high computational and energy cost. To improve its efficiency, a popular choice is to compress the models via binarization which constrains the floating-point values into binary ones to save resource consumption owing to cheap bitwise operations significantly. However, existing binarization methods only aim at minimizing the information loss for the input distribution statistically, while ignoring the pairwise similarity modeling at the core of the attention. To this end, we propose a new binarization paradigm customized to high-dimensional softmax attention via kernelized hashing, called EcoFormer, to map the original queries and keys into low-dimensional binary codes in Hamming space. The kernelized hash functions are learned to match the ground-truth similarity relations extracted from the attention map in a self-supervised way. Based on the equivalence between the inner product of binary codes and the Hamming distance as well as the associative property of matrix multiplication, we can approximate the attention in linear complexity by expressing it as a dot-product of binary codes. Moreover, the compact binary representations of queries and keys enable us to replace most of the expensive multiply-accumulate operations in attention with simple accumulations to save considerable on-chip energy footprint on edge devices. Extensive experiments on both vision and language tasks show that EcoFormer consistently achieves comparable performance with standard attentions while consuming much fewer resources. For example, based on PVTv2-B0 and ImageNet-1K, Ecoformer achieves a 73% on-chip energy footprint reduction with only a 0.33% performance drop compared to the standard attention. Code is available at https://github.com/ziplab/EcoFormer.