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.

Introduction. Transformers, in particular decoder-only models (e.g. GPT (Brown et al. 2020), Llama (Touvron, Lavril, et al. 2023)) which process input sequences in a causal fashion, are one of the main drivers of modern deep learning’s success. Numerous approaches attempt to approximate the core attention layer to address its efficiency issues (Tay et al. 2022), such as scaling quadratically in sequence length during training and requiring a cache of size linear in sequence length during autoregressive generation. In parallel, a class of alternative sequence models, structured state-space models (SSMs), have emerged with linear scaling in sequence length during training and constant state size during generation. They show strong performance on long-range tasks (e.g. S4 (Gu, Goel, and Ré 2022)) and recently matched or beat Transformers on language modeling (e.g. Mamba (Gu and Dao 2023)) at small to moderate scale.

Discussion / Conclusion. We proposed a theoretical framework based on well-studied classes of structured matrices that bridges the conceptual gap between SSMs and attention variants. This framework yields insights on how recent SSMs (e.g. Mamba) perform as well as Transformers on language modeling. Moreover, our theoretical tools provide new ideas to improve SSMs (and potentially Transformers) by connecting the algorithmic and systems advances on both sides. As a demonstration, the framework guides our design of a new architecture (Mamba-2) at the intersection of SSMs and structured attention.