Sparse Mamba: Reinforcing Controllability In Structural State Space Models

In this article, we introduce the concept of controllability and observability to the M amba architecture in our Sparse-Mamba (S-Mamba) for natural language processing (NLP) applications. The structured state space model (SSM) development in recent studies, such as Mamba and Mamba2, outperformed and solved the computational inefficiency of transformers and large language models (LLMs) on longer sequences in small to medium NLP tasks. The Mamba SSMs architecture drops the need for attention layer or MLB blocks in transformers. However, the current Mamba models do not reinforce the controllability on state space equations in the calculation of A, B, C, and D matrices at each time step, which increase the complexity and the computational cost needed. In this article we show that the number of parameters can be significantly decreased by reinforcing controllability in the state space equations in the proposed Sparse-Mamba (S-Mamba), while maintaining the performance. The controllable n x n state matrix A is sparse and it has only n free parameters. Our novel approach will ensure a controllable system and could be the gate key for Mamba 3.