RNNs with adaptive time constants reveal multiple rhythm-switching mechanisms

Yamaguti and Nakamura from Kyushu University trained leaky integrator recurrent neural networks (RNNs) with learnable, neuron-specific time constants on a cognitively motivated rhythm-switching task spanning four frequency bands: theta (4–8 Hz), alpha (8–12 Hz), beta (12–30 Hz), and gamma (30–80 Hz). By analyzing 20 independently trained networks, they uncovered a systematic relationship between neuronal time constants and rhythm generation. Low-frequency rhythms emerged from widespread, distributed participation of many neurons, whereas high-frequency rhythms were dominated by a small subpopulation of neurons with short time constants. The negative correlation between time constant and matched-mode amplitude strengthened monotonically with frequency, revealing a clear computational hierarchy.

Crucially, the networks used multiple coexisting mechanisms to switch between rhythms: (1) turnover of the active subpopulation—different neurons activate for different rhythms—(2) network-wide baseline shifts that reposition the operating point near distinct unstable fixed points, and (3) inter-neuronal phase reorganization that selectively cancels or supports band components in the population output. The specific mechanism deployed for each mode pair varied across training runs, exposing a degeneracy of learned solutions. This parallels biological findings where both rhythm-specific and multi-rhythm interneurons coexist, and provides a computational framework for understanding frequency-band-specific functional differentiation in neural systems. The paper offers a bridge between RNN-based models of cognition and biological neural circuit dynamics.