Fluctuation-learning relationship in recurrent neural networks

Tomoki Kurikawa () and Kunihiko Kaneko
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Tomoki Kurikawa: Future University Hakodate
Kunihiko Kaneko: University of Copenhagen

Nature Communications, 2025, vol. 16, issue 1, 1-14

Abstract: Abstract Learning speed depends on both task structure and neural dynamics prior to learning, yet a theory connecting them has been missing. Inspired by the fluctuation-response relation, we derive two formulae linking neural dynamics to learning. Initial learning speed is proportional to the covariance between pre-learning spontaneous activity and network’s input-evoked response, independent of the learning rule. For Hebb-type learning, initial speed scales with the variance of activity along target and input directions. These results apply across tasks including input-output mapping and time-series generation. Numerical simulations across diverse models validate the formulae beyond the theoretical-derivation’s assumptions. Although derived for early learning, the formulae predict total learning time. A straightforward implication is learning is faster when task-relevant directions align with high-variance spontaneous activities, consistent with empirical findings. Our framework establishes how the geometrical relationship between pre-learning dynamics and task directions governs learning speed, independent of details of tasks.

Date: 2025
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DOI: 10.1038/s41467-025-64976-w

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