# Sliceformer: Make Multi-head Attention as Simple as Sorting in Discriminative Tasks

arXiv: https://arxiv.org/abs/2310.17683 · HTML: https://mlsanity.com/paper/2310.17683/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 43 references that are in the map.
- First posted on arXiv 26 Oct 2023.

## Builds on (most cited first, 30 of 33)

- [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)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [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)
- [Longformer: The Long-Document Transformer](https://mlsanity.com/paper/2004.05150/) (2020)
- [XLNet: Generalized Autoregressive Pretraining for Language Understanding](https://mlsanity.com/paper/1906.08237/) (2019)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [Transformer-XL: Attentive Language Models Beyond a Fixed-Length Context](https://mlsanity.com/paper/1901.02860/) (2019)
- [ViViT: A Video Vision Transformer](https://mlsanity.com/paper/2103.15691/) (2021)
- [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)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [MLP-Mixer: An all-MLP Architecture for Vision](https://mlsanity.com/paper/2105.01601/) (2021)
- [Simplified State Space Layers for Sequence Modeling](https://mlsanity.com/paper/2208.04933/) (2022)
- [Long Range Arena: A Benchmark for Efficient Transformers](https://mlsanity.com/paper/2011.04006/) (2020)
- [Attention is Not All You Need: Pure Attention Loses Rank Doubly Exponentially with Depth](https://mlsanity.com/paper/2103.03404/) (2021)
- [OGB-LSC: A Large-Scale Challenge for Machine Learning on Graphs](https://mlsanity.com/paper/2103.09430/) (2021)
- [Do Transformers Really Perform Bad for Graph Representation?](https://mlsanity.com/paper/2106.05234/) (2021)
- [Mesh Graphormer](https://mlsanity.com/paper/2104.00272/) (2021)
- [Sparse Sinkhorn Attention](https://mlsanity.com/paper/2002.11296/) (2020)
- [Transformer Hawkes Process](https://mlsanity.com/paper/2002.09291/) (2020)
- [Transformer Dissection: A Unified Understanding of Transformer's Attention via the Lens of Kernel](https://mlsanity.com/paper/1908.11775/) (2019)
- [cosFormer: Rethinking Softmax in Attention](https://mlsanity.com/paper/2202.08791/) (2022)
- [Synthesizer: Rethinking Self-Attention in Transformer Models](https://mlsanity.com/paper/2005.00743/) (2020)
- [Mega: Moving Average Equipped Gated Attention](https://mlsanity.com/paper/2209.10655/) (2022)
- [Sinkformers: Transformers with Doubly Stochastic Attention](https://mlsanity.com/paper/2110.11773/) (2021)

## Built on by (most cited first, 1 of 1)

- [Sliced ReLU attention: Quasi-linear contextual expressivity via sorting](https://mlsanity.com/paper/2512.11411/) (2025)

## Abstract (arXiv)

As one of the most popular neural network modules, Transformer plays a central role in many fundamental deep learning models, e.g., the ViT in computer vision and the BERT and GPT in natural language processing. The effectiveness of the Transformer is often attributed to its multi-head attention (MHA) mechanism. In this study, we discuss the limitations of MHA, including the high computational complexity due to its ``query-key-value'' architecture and the numerical issue caused by its softmax operation. Considering the above problems and the recent development tendency of the attention layer, we propose an effective and efficient surrogate of the Transformer, called Sliceformer. Our Sliceformer replaces the classic MHA mechanism with an extremely simple ``slicing-sorting'' operation, i.e., projecting inputs linearly to a latent space and sorting them along different feature dimensions (or equivalently, called channels). For each feature dimension, the sorting operation implicitly generates an implicit attention map with sparse, full-rank, and doubly-stochastic structures. We consider different implementations of the slicing-sorting operation and analyze their impacts on the Sliceformer. We test the Sliceformer in the Long-Range Arena benchmark, image classification, text classification, and molecular property prediction, demonstrating its advantage in computational complexity and universal effectiveness in discriminative tasks. Our Sliceformer achieves comparable or better performance with lower memory cost and faster speed than the Transformer and its variants. Moreover, the experimental results reveal that applying our Sliceformer can empirically suppress the risk of mode collapse when representing data. The code is available at urlhttps://github.com/SDS-Lab/sliceformer.