Memory by Design: Probabilistic Sequence Layers
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866913172567359488 |
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| author | Dowling, Matthew Jeon, Hyungju Savin, Cristina Park, Il Memming |
| author_facet | Dowling, Matthew Jeon, Hyungju Savin, Cristina Park, Il Memming |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_31163 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Memory by Design: Probabilistic Sequence Layers Dowling, Matthew Jeon, Hyungju Savin, Cristina Park, Il Memming Machine Learning 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. |
| title | Memory by Design: Probabilistic Sequence Layers |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2605.31163 |