# ShiftAddViT: Mixture of Multiplication Primitives Towards Efficient Vision Transformer

arXiv: https://arxiv.org/abs/2306.06446 · HTML: https://mlsanity.com/paper/2306.06446/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Placed in Vision mixture-of-experts, one of 12 directions in Mixture-of-experts.
- Builds on 63 of its 77 references that are in the map.
- First posted on arXiv 10 Jun 2023.

## Placed in

- Mixture-of-experts / [Vision mixture-of-experts](https://mlsanity.com/moe/vision-mixture-of-experts/)

## Builds on (most cited first, 30 of 63)

- [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)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [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)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [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)
- [Rethinking Attention with Performers](https://mlsanity.com/paper/2009.14794/) (2020)
- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (2017)
- [Linformer: Self-Attention with Linear Complexity](https://mlsanity.com/paper/2006.04768/) (2020)
- [Tokens-to-Token ViT: Training Vision Transformers from Scratch on ImageNet](https://mlsanity.com/paper/2101.11986/) (2021)
- [Token Merging: Your ViT But Faster](https://mlsanity.com/paper/2210.09461/) (2022)
- [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)
- [PVT v2: Improved Baselines with Pyramid Vision Transformer](https://mlsanity.com/paper/2106.13797/) (2021)
- [Scaling Vision with Sparse Mixture of Experts](https://mlsanity.com/paper/2106.05974/) (2021)
- [Long Range Arena: A Benchmark for Efficient Transformers](https://mlsanity.com/paper/2011.04006/) (2020)
- [Local Light Field Fusion: Practical View Synthesis with Prescriptive Sampling Guidelines](https://mlsanity.com/paper/1905.00889/) (2019)
- [MobileViT: Light-weight, General-purpose, and Mobile-friendly Vision Transformer](https://mlsanity.com/paper/2110.02178/) (2021)
- [MViTv2: Improved Multiscale Vision Transformers for Classification and Detection](https://mlsanity.com/paper/2112.01526/) (2021)
- [MaxViT: Multi-Axis Vision Transformer](https://mlsanity.com/paper/2204.01697/) (2022)
- [LeViT: a Vision Transformer in ConvNet's Clothing for Faster Inference](https://mlsanity.com/paper/2104.01136/) (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)

## Built on by (most cited first, 15 of 15)

- [ShiftAddLLM: Accelerating Pretrained LLMs via Post-Training Multiplication-Less Reparameterization](https://mlsanity.com/paper/2406.05981/) (2024)
- [HAMoBE: Hierarchical and Adaptive Mixture of Biometric Experts for Video-based Person ReID](https://mlsanity.com/paper/2508.05038/) (2025)
- [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)
- [BETA: Binarized Energy-Efficient Transformer Accelerator at the Edge](https://mlsanity.com/paper/2401.11851/) (2024)
- [PADRe: A Unifying Polynomial Attention Drop-in Replacement for Efficient Vision Transformer](https://mlsanity.com/paper/2407.11306/) (2024)
- [PikeLPN: Mitigating Overlooked Inefficiencies of Low-Precision Neural Networks](https://mlsanity.com/paper/2404.00103/) (2024)
- [Mixture-of-Experts for Open Set Domain Adaptation: A Dual-Space Detection Approach](https://mlsanity.com/paper/2311.00285/) (2023)
- [EViT: An Eagle Vision Transformer with Bi-Fovea Self-Attention](https://mlsanity.com/paper/2310.06629/) (2023)
- [ShiftAddAug: Augment Multiplication-Free Tiny Neural Network with Hybrid Computation](https://mlsanity.com/paper/2407.02881/) (2024)
- [NASH: Neural Architecture and Accelerator Search for Multiplication-Reduced Hybrid Models](https://mlsanity.com/paper/2409.04829/) (2024)
- [Compound and Parallel Modes of Tropical Convolutional Neural Networks](https://mlsanity.com/paper/2504.06881/) (2025)
- [Focus Your Attention: Towards Data-Intuitive Lightweight Vision Transformers](https://mlsanity.com/paper/2506.18791/) (2025)
- [DeVIT: Low-Power Vision Transformer Acceleration Using Delta Computation](https://mlsanity.com/paper/2608.01343/) (2026)
- [QTEA: Ternary LLMs with Sparse Residual Salient Weight and By-Column Optimization](https://mlsanity.com/paper/2609.00224/) (2026)

## Abstract (arXiv)

Vision Transformers (ViTs) have shown impressive performance and have become a unified backbone for multiple vision tasks. However, both the attention mechanism and multi-layer perceptrons (MLPs) in ViTs are not sufficiently efficient due to dense multiplications, leading to costly training and inference. To this end, we propose to reparameterize pre-trained ViTs with a mixture of multiplication primitives, e.g., bitwise shifts and additions, towards a new type of multiplication-reduced model, dubbed ShiftAddViT, which aims to achieve end-to-end inference speedups on GPUs without requiring training from scratch. Specifically, all textttMatMuls among queries, keys, and values are reparameterized using additive kernels, after mapping queries and keys to binary codes in Hamming space. The remaining MLPs or linear layers are then reparameterized with shift kernels. We utilize TVM to implement and optimize those customized kernels for practical hardware deployment on GPUs. We find that such a reparameterization on attention maintains model accuracy, while inevitably leading to accuracy drops when being applied to MLPs. To marry the best of both worlds, we further propose a new mixture of experts (MoE) framework to reparameterize MLPs by taking multiplication or its primitives as experts, e.g., multiplication and shift, and designing a new latency-aware load-balancing loss. Such a loss helps to train a generic router for assigning a dynamic amount of input tokens to different experts according to their latency. Extensive experiments on various 2D/3D Transformer-based vision tasks consistently validate the effectiveness of our proposed ShiftAddViT, achieving up to 5.18× latency reductions on GPUs and 42.9% energy savings, while maintaining a comparable accuracy as original or efficient ViTs.