MemMamba: Rethinking Memory Patterns in State Space Model
Authors: name: Youjin Wang, name: Yangjingyi Chen, name: Jiahao Yan, name: Jiaxuan Lu, name: Xiao Sun

With the explosive growth of data, long-sequence modeling has become
increasingly important in tasks such as natural language processing and
bioinformatics. However, existing methods face inherent trade-offs between
efficiency and memory. Recurrent neural networks suffer from gradient vanishing
and explosion, making them hard to scale. Transformers can model global
dependencies but are constrained by quadratic complexity. Recently, selective
state-space models such as Mamba have demonstrated high efficiency with O(n)
time and O(1) recurrent inference, yet their long-range memory decays
exponentially. In this work, we conduct mathematical derivations and
information-theoretic analysis to systematically uncover the memory decay
mechanism of Mamba, answering a fundamental question: what is the nature of
Mamba's long-range memory and how does it retain information? To quantify key
information loss, we further introduce horizontal-vertical memory fidelity
metrics that capture degradation both within and across layers. Inspired by how
humans distill and retain salient information when reading long documents, we
propose MemMamba, a novel architectural framework that integrates state
summarization mechanism together with cross-layer and cross-token attention,
which alleviates long-range forgetting while preserving linear complexity.
MemMamba achieves significant improvements over existing Mamba variants and
Transformers on long-sequence benchmarks such as PG19 and Passkey Retrieval,
while delivering a 48% speedup in inference efficiency. Both theoretical
analysis and empirical results demonstrate that MemMamba achieves a
breakthrough in the complexity-memory trade-off, offering a new paradigm for
ultra-long sequence modeling.