# PADRe: A Unifying Polynomial Attention Drop-in Replacement for Efficient Vision Transformer

arXiv: https://arxiv.org/abs/2407.11306 · HTML: https://mlsanity.com/paper/2407.11306/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 37 references that are in the map.
- First posted on arXiv 16 Jul 2024.

## Builds on (most cited first, 30 of 35)

- [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)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [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)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [Visual Instruction Tuning](https://mlsanity.com/paper/2304.08485/) (2023)
- [End-to-End Object Detection with Transformers](https://mlsanity.com/paper/2005.12872/) (2020)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [nuScenes: A multimodal dataset for autonomous driving](https://mlsanity.com/paper/1903.11027/) (2019)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [MLP-Mixer: An all-MLP Architecture for Vision](https://mlsanity.com/paper/2105.01601/) (2021)
- [Vision Mamba: Efficient Visual Representation Learning with Bidirectional State Space Model](https://mlsanity.com/paper/2401.09417/) (2024)
- [The Dawn of LMMs: Preliminary Explorations with GPT-4V(ision)](https://mlsanity.com/paper/2309.17421/) (2023)
- [MetaFormer Is Actually What You Need for Vision](https://mlsanity.com/paper/2111.11418/) (2021)
- [Hyena Hierarchy: Towards Larger Convolutional Language Models](https://mlsanity.com/paper/2302.10866/) (2023)
- [Efficient Attention: Attention with Linear Complexities](https://mlsanity.com/paper/1812.01243/) (2018)
- [ResMLP: Feedforward networks for image classification with data-efficient training](https://mlsanity.com/paper/2105.03404/) (2021)
- [EfficientFormer: Vision Transformers at MobileNet Speed](https://mlsanity.com/paper/2206.01191/) (2022)
- [FLatten Transformer: Vision Transformer using Focused Linear Attention](https://mlsanity.com/paper/2308.00442/) (2023)
- [FastViT: A Fast Hybrid Vision Transformer using Structural Reparameterization](https://mlsanity.com/paper/2303.14189/) (2023)
- [Run, Don't Walk: Chasing Higher FLOPS for Faster Neural Networks](https://mlsanity.com/paper/2303.03667/) (2023)
- [DSVT: Dynamic Sparse Voxel Transformer with Rotated Sets](https://mlsanity.com/paper/2301.06051/) (2023)
- [Conv2Former: A Simple Transformer-Style ConvNet for Visual Recognition](https://mlsanity.com/paper/2211.11943/) (2022)
- [SwiftFormer: Efficient Additive Attention for Transformer-based Real-time Mobile Vision Applications](https://mlsanity.com/paper/2303.15446/) (2023)
- [KVT: k-NN Attention for Boosting Vision Transformers](https://mlsanity.com/paper/2106.00515/) (2021)
- [FasterViT: Fast Vision Transformers with Hierarchical Attention](https://mlsanity.com/paper/2306.06189/) (2023)
- [Hydra Attention: Efficient Attention with Many Heads](https://mlsanity.com/paper/2209.07484/) (2022)

## Built on by (most cited first, 5 of 5)

- [Attention Surgery: An Efficient Recipe to Linearize Your Video Diffusion Transformer](https://mlsanity.com/paper/2509.24899/) (2025)
- [ReHyAt: Recurrent Hybrid Attention for Video Diffusion Transformers](https://mlsanity.com/paper/2601.04342/) (2026)
- [BePo: Dual Representation for 3D Occupancy Prediction](https://mlsanity.com/paper/2506.07002/) (2025)
- [FALO: Fast and Accurate LiDAR 3D Object Detection on Resource-Constrained Devices](https://mlsanity.com/paper/2506.04499/) (2025)
- [MagnifiQ: Patch-aware Text Guided Progressive Upscaling for High-Resolution Image Restoration](https://mlsanity.com/paper/2608.14543/) (2026)

## Abstract (arXiv)

We present Polynomial Attention Drop-in Replacement (PADRe), a novel and unifying framework designed to replace the conventional self-attention mechanism in transformer models. Notably, several recent alternative attention mechanisms, including Hyena, Mamba, SimA, Conv2Former, and Castling-ViT, can be viewed as specific instances of our PADRe framework. PADRe leverages polynomial functions and draws upon established results from approximation theory, enhancing computational efficiency without compromising accuracy. PADRe's key components include multiplicative nonlinearities, which we implement using straightforward, hardware-friendly operations such as Hadamard products, incurring only linear computational and memory costs. PADRe further avoids the need for using complex functions such as Softmax, yet it maintains comparable or superior accuracy compared to traditional self-attention. We assess the effectiveness of PADRe as a drop-in replacement for self-attention across diverse computer vision tasks. These tasks include image classification, image-based 2D object detection, and 3D point cloud object detection. Empirical results demonstrate that PADRe runs significantly faster than the conventional self-attention (11x ~ 43x faster on server GPU and mobile NPU) while maintaining similar accuracy when substituting self-attention in the transformer models.