rhythm-switching-adaptive-time-constants-rnn

# 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 ```python 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