Memory by Design: Probabilistic Sequence Layers

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 direct