NeurIPS 2024 Papers

Structured state-space models (SSMs) are gaining popularity as effective foundational architectures for sequential data, demonstrating outstanding performance across a diverse set of domains alongside desirable scalability properties. Recent developments show that if the linear recurrence powering SSMs allows for a selectivity mechanism leveraging multiplicative interactions between inputs and hidden states (e.g. Mamba, GLA, Hawk/Griffin, HGRN2), then the resulting architecture can surpass attention-powered foundation models trained on text in both accuracy and efficiency, at scales of billion parameters. In this paper, we give theoretical grounding to the selectivity mechanism, often linked to in-context learning, using tools from Rough Path Theory. We provide a framework for the theoretical analysis of generalized selective SSMs, fully characterizing their expressive power and identifying the gating mechanism as the crucial architectural choice. Our analysis provides a closed-form description of the expressive powers of modern SSMs, such as Mamba, quantifying theoretically the drastic improvement in performance from the previous generation of models, such as S4. Our theory not only motivates the success of modern selective state-space models, but also provides a solid framework to understand the expressive power of future SSM variants. In particular, it suggests cross-channel interactions could play a vital role in future improvements.

Recent sequence modeling approaches using selective state space sequence models, referred to as Mamba models, have seen a surge of interest. These models allow efficient processing of long sequences in linear time and are rapidly being adopted in a wide range of applications such as language modeling, demonstrating promising performance. To foster their reliable use in real-world scenarios, it is crucial to augment their transparency. Our work bridges this critical gap by bringing explainability, particularly Layer-wise Relevance Propagation (LRP), to the Mamba architecture. Guided by the axiom of relevance conservation, we identify specific components in the Mamba architecture, which cause unfaithful explanations. To remedy this issue, we propose MambaLRP, a novel algorithm within the LRP framework, which ensures a more stable and reliable relevance propagation through these components. Our proposed method is theoretically sound and excels in achieving state-of-the-art explanation performance across a diverse range of models and datasets. Moreover, MambaLRP facilitates a deeper inspection of Mamba architectures, uncovering various biases and evaluating their significance. It also enables the analysis of previous speculations regarding the long-range capabilities of Mamba models.