This document explores the Mamba architecture, a novel approach to sequence modeling that offers an efficient alternative to Transformers. It primarily investigates the role of "input selectivity" within Mamba's core component, the S6 layer, and its impact on the model's capabilities. The research proves Mamba's superiority over its predecessor, S4D, in approximating discontinuous functions and demonstrates how input selectivity helps counteract memory decay for long sequences. Furthermore, the paper analyzes how the complete Mamba architecture, including convolution and gating, efficiently solves complex associative recall tasks like Multiple-Query Associative Recall (MQAR) and Induction Heads, with theoretical bounds on model size confirmed by empirical results. The findings offer a mechanistic understanding of Mamba's performance and suggest pathways for future enhancements, such as optimizing input dependence within its state matrix.

Source: https://arxiv.org/pdf/2506.11891