Higher Order Transformers: Efficient Attention Mechanism for Tensor Structured Data

ICLR 2025 Conference Submission12743 Authors

Keywords: transformers, multihead attention, high order tensor, kronecker decomposition, multivariate timeseries forecasting, 3D medical image classification

TL;DR: We introduce HOT, a transformer architecture that efficiently applies attention on multi-dimensional tensor data using tensor factorization.

Abstract:

Transformers are now ubiquitous for sequence modeling tasks, but their extension to multi-dimensional data remains a challenge due to the quadratic cost of the attention mechanism. In this paper, we propose Higher-Order Transformers (HOT), a novel architecture designed to efficiently process data with more than two axes, i.e. higher-order tensors.
To address the computational challenges associated with high-order tensor attention, we introduce a novel Kronecker factorized attention mechanism that reduces the attention cost to quadratic in each axis' dimension, rather than quadratic in the total size of the input tensor. To further enhance efficiency, HOT leverages kernelized attention, reducing the complexity to linear. This strategy maintains the model's expressiveness while enabling scalable attention computation.
We validate the effectiveness of HOT on two high-dimensional tasks, including multivariate time series forecasting, and 3D medical image classification. Experimental results demonstrate that HOT achieves competitive performance while significantly improving computational efficiency, showcasing its potential for tackling a wide range of complex, multi-dimensional data.

Primary Area: foundation or frontier models, including LLMs

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Submission Number: 12743