Fast Weight Attention for Continual Learning

Abstract:Recurrent fast-weight memories and selective state-space models compress an expanding context into a fixed-size recurrent state, making the state transition an online learning rule. We study this rule under read-after-write autoregressive semantics. For the prefix-prediction objective considered here, the local fast-memory example revealed at step $t$ is the prefix-aligned pair $(\mathbf{x}_t,\mathbf{y}_t)=(\phi(\mathbf{k}_{t-1}),\mathbf{v}_t)$. The common same-step association $(\phi(\mathbf{k}_t),\mathbf{v}_t)$ remains causal, but optimizes a different internal objective. We derive normalized first-order updates for squared-error regression and negative inner-product objectives. The regression family comprises Falcon-1 (a scalar NLMS update), Falcon-2 (its per-column extension), and Falcon-3 (a sliding-window mini-batch update); Falcon-1A/Falcon-2A/Falcon-3A are the corresponding inner-product variants. We provide recurrent, masked-parallel, and chunk-parallel forms, together with numerically stable positive-decay renormalization. Representative variants remain competitive in language modeling and improve length extrapolation on variable-digit addition. This framework separates temporal alignment, plasticity, forgetting, and bounded rehearsal in recurrent sequence models.

Machine Learning (cs.LG); Computation and Language (cs.CL); Machine Learning (stat.ML)

arXiv:2608.27763 [cs.LG]

(or arXiv:2608.27763v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2608.27763 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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