Machine learning models are increasingly being scaled in both sequence length and model dimension to reach longer contexts and better performance.

Machine learning models are increasingly being scaled in both sequence length and model dimension to reach longer contexts and better performance. We ask: are there performant architectures that can scale sub-quadratically along sequence length and model dimension? We introduce Monarch Mixer (M2), a new architecture that uses the same sub-quadratic primitive along both sequence length and model dimension: Monarch matrices, a simple class of expressive structured matrices that captures many linear transforms, achieves high hardware efficiency on GPUs, and scales sub-quadratically. As a proof of concept, we explore the performance of M2 in three domains: non-causal BERT-style language modeling, ViT-style image classification, and causal GPT-style language modeling. For non-causal BERT-style modeling, M2 matches BERT-base and BERT-large in downstream GLUE quality with up to 27% fewer parameters, and achieves up to 9.1 \times higher throughput at sequence length 4K.

We present the Linear Complexity Sequence Model (LCSM), a comprehensive solution that unites various sequence modeling techniques with linear complexity, including linear attention, state space model, long convolution, and linear RNN, within a single framework. The goal is to enhance comprehension of these models by analyzing the impact of each component from a cohesive and streamlined viewpoint. Specifically, we segment the modeling processes of these models into three distinct stages: Expand, Oscillation, and Shrink (EOS), with each model having its own specific settings. The Expand stage involves projecting the input signal onto a high-dimensional memory state. This is followed by recursive operations performed on the memory state in the Oscillation stage. Finally, the memory state is projected back to a low-dimensional space in the Shrink stage. We perform comprehensive experiments to analyze the impact of different stage settings on language modeling and retrieval tasks. Our results show that data-driven methods are crucial for the effectiveness of the three stages in language modeling, whereas hand-crafted methods yield better performance in retrieval tasks.