Attending to Memory Writes Reduces Seed Variability in Recurrent Length Generalization

Abstract:Recurrent memory requires learning useful updates, but attention added to assist learning can also compromise length generalization. We study bounded delta attention: causal attention over uncorrected update proposals whose bounded correction enters the recurrent update. Its implementation in TraceRelay combines additive phase recurrence with attention computed before a parallel scan. On prefix-supervised modulo-5, trained at lengths 1--40, three findings characterize its behavior at length 80. First, upper delta attention attains $70.81\pm8.26$% accuracy across seven seeds, versus $69.21\pm22.42$% for the local-attention recurrent baseline (mean $\pm$ sample SD): a 63.2% reduction in SD with a similar mean. Upper state attention also reduces variation, reaching $74.75\pm6.24$%, so this benefit is not unique to update-level attention. Disabling the upper delta correction retains $70.62\pm8.60$%. Second, blocking gradients at the delta-attention inputs changes accuracy to $65.25\pm12.40$% in the matched seven-seed comparison, increasing SD by 50.2%. It also delays a 99% validation threshold on average among the same six seeds that reach it; the 95% threshold is reached earlier on average with input-gradient blocking across all seven seeds. Third, lower delta attention exhibits substantially less extrapolation degradation than lower state attention: 62.60% versus 19.40%, against a 71.06% baseline. Removing its correction reduces accuracy to 22.56%; its advantage over lower state attention also persists under input-gradient blocking. These observations motivate bounded update-level attention as a recurrent learning scaffold, combining reduced seed variation with less severe degradation in a placement where state attention fails.

Machine Learning (cs.LG)

arXiv:2611.04902 [cs.LG]

(or arXiv:2611.04902v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2611.04902 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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