Efficient long-sequence modeling remains a central challenge for large language models, as self-attention scales quadratically with sequence length. Mamba offers a linear-time alternative through selective state space recurrence, but its predominantly diagonal state transitions restrict explicit interactions among state dimensions. We propose Motif-Mamba, a structured state space model that augments Mamba with a motif-constrained low-rank recurrent pathway. Inspired by the dynamics of three-node network motifs, the proposed pathway projects hidden states into a compact dynamical subspace, imposes motif-guided interactions, and maps the resulting dynamics back to the original state space. This design enhances cross-dimensional communication while preserving the linear-time recurrent structure of Mamba. Experiments on long-sequence extrapolation, language modeling benchmarks, and brain--computer interface decoding show consistent improvements over Mamba backbones, suggesting that motif-guided low-rank dynamics provide an effective structural prior for long-range sequence modeling.
State Space Models (SSMs) have emerged as a powerful paradigm for efficient long-sequence modeling, offering parallel training and fast linear-time recurrent inference. However, like other recurrent architectures, SSMs must compress an unbounded history into a fixed-size state, which limits context retention and makes precise retrieval over long-range context inherently difficult. To overcome this limitation, we propose Delay State Space Models (DSSMs), a delay differential equation (DDE)-inspired extension of diagonal SSMs that augments discrete SSM recurrences with explicit delayed-state feedback. Making explicit delayed feedback practical requires new stability parameterization, history management, and FFT-training tools. We address these challenges with a practical discretization and parameterization grounded in a simple delay-independent stability condition. To bypass direct time-domain kernel construction, we derive the DSSM transfer function and compute kernels in the frequency domain, using a kernel contour shift to suppress aliasing and recover accurate FFT training. Empirically, DSSMs substantially improve targeted delayed-retrieval tasks while outperforming S4D on most standard sequence metrics and remaining close on the others.