Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality

While Transformers have been the main architecture behind deep learning’s success in language modeling, state-space models (SSMs) such as Mamba have recently been shown to match or outperform Transformers at small to medium scale. We show that these families of models are actually quite closely related, and develop a rich framework of theoretical connections between SSMs and variants of attention, connected through various decompositions of a well-studied class of structured semiseparable matrices. Our state space duality (SSD) framework allows us to design a new architecture (Mamba-2) whose core layer is an a refinement of Mamba’s selective SSM that is 2-8× faster, while continuing to be competitive with Transformers on language modeling.

Our main goal is to develop a rich body of theoretical connections between structured SSMs and variants of attention. This will allow us to transfer algorithmic and systems optimizations originally developed for Transformers to SSMs, towards the goal of building foundation models that perform better than Transformers while scaling more efficiently in sequence length. A milestone contribution in this direction was the Linear Attention (LA) framework (Katharopoulos et al. 2020), which derived a connection between autoregressive attention and linear RNNs by showing the equivalence between “dual forms” of quadratic kernelized attention and a particular linear recurrence. This duality allows new capabilities such as the ability to have both efficient parallelizable training and efficient autoregressive inference. In the same spirit, this paper provides multiple viewpoints connecting linear-complexity SSMs with quadratic-complexity forms to combine the strengths of SSMs and attention.1