# EcoTransformer: Attention without Multiplication

arXiv: https://arxiv.org/abs/2507.20096 · HTML: https://mlsanity.com/paper/2507.20096/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 19 references that are in the map.
- First posted on arXiv 27 Jul 2025.

## Builds on (most cited first, 16 of 16)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Longformer: The Long-Document Transformer](https://mlsanity.com/paper/2004.05150/) (2020)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [Big Bird: Transformers for Longer Sequences](https://mlsanity.com/paper/2007.14062/) (2020)
- [Rethinking Attention with Performers](https://mlsanity.com/paper/2009.14794/) (2020)
- [Generating Long Sequences with Sparse Transformers](https://mlsanity.com/paper/1904.10509/) (2019)
- [Linformer: Self-Attention with Linear Complexity](https://mlsanity.com/paper/2006.04768/) (2020)
- [Effective Approaches to Attention-based Neural Machine Translation](https://mlsanity.com/paper/1508.04025/) (2015)
- [Nystr"omformer: A Nystr"om-Based Algorithm for Approximating Self-Attention](https://mlsanity.com/paper/2102.03902/) (2021)
- [Hyena Hierarchy: Towards Larger Convolutional Language Models](https://mlsanity.com/paper/2302.10866/) (2023)
- [Synthesizer: Rethinking Self-Attention in Transformer Models](https://mlsanity.com/paper/2005.00743/) (2020)
- [IrEne: Interpretable Energy Prediction for Transformers](https://mlsanity.com/paper/2106.01199/) (2021)
- [Addition is All You Need for Energy-efficient Language Models](https://mlsanity.com/paper/2410.00907/) (2024)

## Abstract (arXiv)

The Transformer, with its scaled dot-product attention mechanism, has become a foundational architecture in modern AI. However, this mechanism is computationally intensive and incurs substantial energy costs. We propose a new Transformer architecture EcoTransformer, in which the output context vector is constructed as the convolution of the values using a Laplacian kernel, where the distances are measured by the L1 metric between the queries and keys. Compared to dot-product based attention, the new attention score calculation is free of matrix multiplication. It performs on par with, or even surpasses, scaled dot-product attention in NLP, bioinformatics, and vision tasks, while consuming significantly less energy. (This version (v2) supersedes v1 and reflects the intended release and licensing.)