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Anatomy of Associative Recall in Fixed-State Recurrences: A Matched-State Decomposition, an Interference Wall, and a Curriculum That Breaks It

arXiv · AI, language, vision and robotics · article · Sep 14, 2026 · UTC

Fixed-state recurrences--linear attention and state-space models--are reported to lag behind attention on associative recall, but whole-architecture comparisons cannot say which ingredient is responsible. We decompose masked multi-query recall at a fixed state budget along three single-knob axes: a short causal convolution, the transition structure (rank-1 delta rule vs. diagonal), and decay. The convolution dominates (~+0.5 recall in both families under matched training): comparisons that pit convolution-free cells against a convolution-equipped Mamba measure the missing convolution, not the

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