Memory by Design: Probabilistic Sequence Layers
This work provides a unified framework for understanding and improving recurrent sequence models, which is significant for researchers and practitioners working on efficient long-context retrieval and robust memory mechanisms.
This paper introduces the design-model framework, which derives recurrent sequence maps from explicit memory assumptions using exact Bayesian filtering. Their linear-Gaussian instantiation, the Bayesian Layer, propagates both mean and covariance to track uncertainty and improve robustness across various benchmarks, including controlled collision studies and associative recall, and improves RULER long-context retrieval when distilled into a Gated DeltaNet.
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.