rhythm-switching-adaptive-time-constants-rnn

name

rhythm-switching-adaptive-time-constants-rnn

description

Methodology for analyzing how recurrent neural networks with neuron-specific adaptive time constants switch between multiple frequency band rhythms. Covers rhythm-switching mechanisms, time constant-frequency relationships, and degeneracy of learned solutions. Activation: rhythm switching RNN, adaptive time constants, frequency band switching, RNN neural dynamics, multi-band rhythms, cortical rhythm mechanisms.

Rhythm Switching in RNNs with Adaptive Time Constants

Analysis of multiple coexisting mechanisms by which RNNs with learnable neuron-specific time constants switch between frequency band rhythms (theta, alpha, beta, gamma).

Metadata

• Source: arXiv:2605.14388
• Authors: Yutaka Yamaguti, Shota Nakamura
• Published: 2026-05-14

Core Methodology

Key Innovation

RNNs trained on multi-band rhythm-switching tasks deploy multiple coexisting mechanisms for switching, not a single canonical approach. The mechanisms vary across independently trained runs, exposing a degeneracy of learned solutions.

Three Rhythm-Switching Mechanisms

1. Subpopulation Turnover

   • Active neuron subpopulation changes between rhythm modes
   • Different neurons dominate output for different frequency bands

2. Network-Wide Baseline Shifts

   • Global shift in operating point repositions network near distinct unstable fixed points
   • Each fixed point corresponds to a different rhythm mode
   • Switching = jumping between basins of attraction

3. Inter-Neuronal Phase Reorganization

   • Selective cancellation or support of band components in population output
   • Phase relationships between neurons reorganize to favor specific frequencies

Time Constant-Frequency Relationship

• Negative correlation between neuron time constant and matched-mode amplitude
• Correlation strengthens monotonically with frequency
• Low-frequency rhythms: distributed participation of many neurons
• High-frequency rhythms: dominated by small subpopulation of short-time-constant neurons

Experimental Framework

1. Train leaky integrator RNNs with neuron-specific learnable time constants
2. Task: four-band (theta, alpha, beta, gamma) rhythm switching
3. Analyze 20+ independently trained networks
4. Identify switching mechanisms via spectral decomposition and phase analysis

Implementation Guide

Analysis Steps

1. Train RNN with adaptive time constants on rhythm-switching task
2. Spectral analysis: compute power spectra for each trained network
3. Time constant mapping: correlate learned time constants with rhythm participation
4. Mechanism identification:
   • Subpopulation analysis: which neurons active per mode
   • Fixed point analysis: linearize around operating points
   • Phase analysis: compute phase relationships between neurons

Code Skeleton

import numpy as np

# Leaky integrator RNN with adaptive time constants
class AdaptiveTimeConstantRNN:
    def __init__(self, n_units, dt=0.001):
        self.tau = np.ones(n_units)  # learnable time constants
        self.W = np.random.randn(n_units, n_units) * 0.1
        self.b = np.zeros(n_units)
        
    def step(self, x, h, u):
        # dh/dt = (-h + f(Wh + u)) / tau
        pre = self.W @ h + u + self.b
        dh = (-h + np.tanh(pre)) / self.tau
        return h + dh * dt
    
    def analyze_rhythm(self, output, fs):
        from scipy.signal import welch
        freqs, psd = welch(output, fs=fs)
        bands = {'theta': (4,8), 'alpha': (8,13), 'beta': (13,30), 'gamma': (30,80)}
        powers = {}
        for band, (lo, hi) in bands.items():
            mask = (freqs >= lo) & (freqs <= hi)
            powers[band] = np.trapz(psd[mask], freqs[mask])
        return powers, freqs, psd

Applications

• Interpreting frequency-band-specific functional differentiation in biological neural systems
• Understanding degeneracy in learned neural representations
• Designing RNNs with controllable rhythm generation capabilities
• Modeling cortical circuit mechanisms for multi-band neural oscillations

Pitfalls

• Mechanism degeneracy: different training runs yield different switching mechanisms
• Time constant initialization can bias which mechanism emerges
• Spectral analysis requires sufficient sequence length for reliable band estimates
• Biological plausibility of learned time constants may vary

Related Skills

• rhythm-snn-temporal-processing — complementary: Rhythm-SNN adds oscillatory dynamics to SNNs for temporal processing and noise robustness (Nature Communications 2025)
• neuromodulation-rhythmic-pattern-control
• neural-dynamics-decision-making
• working-memory-rsnn-delays