Time Delay System for Sequence Modeling

Youshan Zhang, Jialu Li

Existing sequence models share a critical limitation: they lack an explicit, interpretable mechanism for content-aware temporal recall. LSTMs compress everything into a single hidden state, thereby losing information about specific past events. Transformers attend to all tokens indiscriminately at quadratic cost, while state-space models like Mamba compress history into a fixed-dimensional state without explicit content-addressable memory. To address this gap, we introduce a novel framework grounded in nonlinear time-delay systems, in which the effective delay is dynamically estimated based on the semantic similarity between current and historical inputs. Our approach features three key innovations: (i) a differentiable semantic lag estimator that computes content-aware soft attention weights over history, producing a weighted historical context and similarity score; (ii) a diagonal state space with closed-form cumulative sum solution, achieving O(1) per-step complexity with no sequential loops; and (iii) an interpretable fuzzy semantic modulation mechanism that learns context-dependent rules for balancing instantaneous processing versus historical recall, where rule centers…