# Higher-Order Transformers With Kronecker-Structured Attention

arXiv: https://arxiv.org/abs/2412.02919 · HTML: https://mlsanity.com/paper/2412.02919/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 47 references that are in the map.
- First posted on arXiv 4 Dec 2024.

## Builds on (most cited first, 30 of 32)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Longformer: The Long-Document Transformer](https://mlsanity.com/paper/2004.05150/) (2020)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [Is Space-Time Attention All You Need for Video Understanding?](https://mlsanity.com/paper/2102.05095/) (2021)
- [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)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Multiscale Vision Transformers](https://mlsanity.com/paper/2104.11227/) (2021)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [MedMNIST v2 -- A large-scale lightweight benchmark for 2D and 3D biomedical image classification](https://mlsanity.com/paper/2110.14795/) (2021)
- [Axial Attention in Multidimensional Transformers](https://mlsanity.com/paper/1912.12180/) (2019)
- [Stabilizing Transformers for Reinforcement Learning](https://mlsanity.com/paper/1910.06764/) (2019)
- [Tensorizing Neural Networks](https://mlsanity.com/paper/1509.06569/) (2015)
- [Speeding-up Convolutional Neural Networks Using Fine-tuned CP-Decomposition](https://mlsanity.com/paper/1412.6553/) (2014)
- [An End-to-End Spatio-Temporal Attention Model for Human Action Recognition from Skeleton Data](https://mlsanity.com/paper/1611.06067/) (2016)
- [A Tensorized Transformer for Language Modeling](https://mlsanity.com/paper/1906.09777/) (2019)
- [SegFormer3D: an Efficient Transformer for 3D Medical Image Segmentation](https://mlsanity.com/paper/2404.10156/) (2024)
- [Tensor Methods and Recommender Systems](https://mlsanity.com/paper/1603.06038/) (2016)
- [Covariance Estimation in High Dimensions via Kronecker Product Expansions](https://mlsanity.com/paper/1302.2686/) (2013)
- [Kronecker Attention Networks](https://mlsanity.com/paper/2007.08442/) (2020)
- [Robust Kronecker Product PCA for Spatio-Temporal Covariance Estimation](https://mlsanity.com/paper/1411.1352/) (2014)

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

- [Tucker Bottleneck Attention for Multi-Dimensional Sequence Modeling](https://mlsanity.com/paper/2610.09090/) (2026)

## Abstract (arXiv)

Modern datasets are increasingly high-dimensional and multiway, often represented as tensor-valued data with multi-indexed variables. While Transformers excel in sequence modeling and high-dimensional tasks, their direct application to multiway data is computationally prohibitive due to the quadratic cost of dot-product attention and the need to flatten inputs, which disrupts tensor structure and cross-dimensional dependencies. We propose the Higher-Order Transformer (HOT), a novel factorized attention framework that represents multiway attention as sums of Kronecker products or sums of mode-wise attention matrices. HOT efficiently captures dense and sparse relationships across dimensions while preserving tensor structure. Theoretically, HOT retains the expressiveness of full high-order attention and allows complexity control via factorization rank. Experiments on 2D and 3D datasets show that HOT achieves competitive performance in multivariate time series forecasting and image classification, with significantly reduced computational and memory costs. Visualizations of mode-wise attention matrices further reveal interpretable high-order dependencies learned by HOT, demonstrating its versatility for complex multiway data across diverse domains. The implementation of our proposed method is publicly available at https://github.com/s-omranpour/HOT.