Memory by Design: Probabilistic Sequence Layers

• URL: http://arxiv.org/abs/2605.31163v1
• Date: Fri, 29 May 2026 11:13:00 GMT
• Title: Memory by Design: Probabilistic Sequence Layers
• Abstract summary: We introduce a way to derive efficient recurrent sequence maps from explicit assumptions about memory.<n>A design model writes evidence into memory by exact Bayesian filtering.<n>A query-dependent readout produces a predictive distribution whose mean is the layer output.
• Score: 19.16406809753255
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce the design-model framework: a way to derive efficient recurrent sequence maps from explicit assumptions about memory. A design model writes evidence into memory by exact Bayesian filtering; a query-dependent readout produces a predictive distribution whose mean is the layer output. In our linear-Gaussian instantiation, the \emph{Bayesian Layer} propagates both a mean and a covariance: the covariance tracks uncertainty over stored associations, steering writes toward uncertain directions, attenuating gains as evidence accumulates, and preserving confident memories. The same framework unifies several sub-quadratic recurrences. Linear attention, GLA, and Mamba-2/SSD are exact filters under one design model, whereas DeltaNet and related Delta-rule models arise as covariance-reset reductions under another. Restoring the covariance yields closed-form predictions for retrieval dynamics, verified empirically, and improves robustness beyond the training regime across controlled collision studies, learned associative recall, and the Zoology MQAR benchmark; distilling Bayesian Layers into a pretrained 340M Gated DeltaNet improves RULER long-context retrieval at matched compute.

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