In this paper, we tackle the challenge of predicting stock movements in financial markets by introducing Higher Order Transformers, a novel architecture designed for processing multivariate time-series data. We extend the self-attention mechanism and the transformer architecture to a higher order, effectively capturing complex market dynamics across time and variables. To manage computational complexity, we propose a low-rank approximation of the potentially large attention tensor using tensor decomposition and employ kernel attention, reducing complexity to linear with respect to the data size. Additionally, we present an encoder-decoder model that integrates technical and fundamental analysis, utilizing multimodal signals from historical prices and related tweets. Our experiments on the Stocknet dataset demonstrate the effectiveness of our method, highlighting its potential for enhancing stock movement prediction in financial markets.

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.