DCGR-3D: Tensorized Sequence Modeling with Multilinear Content Addressing and Cross-Axis-Validated Multi-Axis State

Standard state-space (SSM) and attention sequence models update a vectorized hidden state h_t ∈ R^D, so the number of independently addressable state entries grows linearly with width. We propose DCGR-3D, a tensorized architecture that organizes the hidden state as a third-order tensor H_t ∈ Rd×d×d, giving cubic growth of state capacity (d^3) at matched parametrization and enabling multi-axis write/read. Two mechanisms are introduced. First, cross-axis-validated multi-axis gating (AGG_3D); the forget gate along each axis is computed from cross-sections of the other two axes, so retention decisions are made jointly by independent latent coordinates. Second, multilinear content addressing (SEL3D): a poly-3 kernel sim_3D(q,k) = (a_q·a_k)(b_q·b_k)(c_q·c_k) that fires only when all three structural axes match—in sharp contrast to a 1D dot product, which responds to partial overlap and is therefore fooled by near-miss keys. On a synthetic long-range key–value recall benchmark (MQAR) over structured composite keys, DCGR-3D attains ≥98% recall across every distance (d=1,...,20, including extrapolation beyond the training window), whereas an equal-capacity 1D state (512 cells) and a standard transformer both collapse to near-random (≲8%). The poly-3 kernel is additionally immune to near-miss distractors sharing two of three axes. We further diagnose a subtle trainability failure: a discrete arg max routing gate yields zero gradient to its own logits and caps performance; a soft gate fully restores convergence. We complement the empirical study with capacity and selectivity guarantees, a complexity–parameter analysis, and a measured-efficiency comparison.