Hydra: Bidirectional State Space Models Through Generalized Matrix Mixers

TL;DR

Hydra introduces a bidirectional state space model based on matrix mixers that unifies and extends sequence modeling techniques, achieving superior performance on NLP and vision benchmarks by leveraging structured matrix parameterizations.

Contribution

The paper presents Hydra, a novel bidirectional state space model using quasiseparable matrix mixers, unifying various sequence models and demonstrating improved efficiency and accuracy.

Findings

Hydra outperforms BERT by 0.8 points on GLUE.

Hydra achieves 2% higher Top-1 accuracy on ImageNet.

The matrix mixer framework explains the success of Transformers and SSMs.

Abstract

A wide array of sequence models are built on a framework modeled after Transformers, comprising alternating sequence mixer and channel mixer layers. This paper studies a unifying matrix mixer view of sequence mixers that can be conceptualized as a linear map on the input sequence. This framework encompasses a broad range of well-known sequence models, including the self-attention of Transformers as well as recent strong alternatives such as structured state space models (SSMs), and allows understanding downstream characteristics such as efficiency and expressivity through properties of their structured matrix class. We identify a key axis of matrix parameterizations termed sequence alignment, which increases the flexibility and performance of matrix mixers, providing insights into the strong performance of Transformers and recent SSMs such as Mamba. Furthermore, the matrix mixer framework offers a systematic approach to developing sequence mixers with desired properties, allowing us to develop several new sub-quadratic sequence models. In particular, we propose a natural bidirectional extension of the Mamba model (Hydra), parameterized as a quasiseparable matrix mixer, which demonstrates superior performance over other sequence models including Transformers on non-causal tasks. As a drop-in replacement for attention layers, Hydra outperforms BERT by 0.8 points on the GLUE benchmark and ViT by 2% Top-1 accuracy on ImageNet.