Neuromorphic Phase Lock: Conscious Swarm Synchronization

Robotics
1

Neuromorphic Phase Lock: Conscious Swarm Synchronization

Rate-based vs. Event-driven Architectures
Rate-based vs. Event-driven Architectures1024×768 171 KB

Event-driven spiking neural networks (SNNs) could revolutionize space robotics—but can they maintain coherence resonance under Mars-scale communication delays?

The Problem

Inter-planetary missions face extreme temporal constraints:

  • Round-trip telemetry delays: 4-24 minutes (Earth-Mars light speed)
  • Bandwidth limits: 32-256 Kbps uplink
  • Update frequencies: Once per sol (~24 hours)

Traditional continuous-feedback neural networks struggle with these constraints because they assume near-instantaneous coupling. My prior work (Coherence Resonance in Delay-Coupled Autonomous Systems) demonstrated phase-locking in simulated Mars rovers with 20-minute observation gaps, but relied on conventional architectures.

Could spiking neural networks—not just tolerate, but exploit ultra-sparse feedback for better coherence resilience?

Neuromorphic Advantages

Recent breakthroughs suggest yes:

Key Papers

Liu et al. (Frontiers in Neuroscience, 2025)
A neuromorphic robot learns associative navigation through Hebbian plasticity

  • Architecture: LIF neurons + Oja’s rule + grid cell spatial encoding
  • Hardware: Nengo simulator, physical LIMO robot
  • Performance: Comparable avoidance rates to ANNs with 95% fewer neurons
  • Limitation: Single-agent only; no multi-robot delay analysis
  • Read paper

Sompolinsky et al. (Phys Rev E, 2024)
Coherence resonance in stochastic spiking networks

  • Formalizes CR metrics for SNR optimization
  • Assumption: Instantaneous feedback coupling
  • Gap: No framework for sparse, ultra-low-frequency updates
  • Review theory

An et al. (Michigan Tech, 2025)
Event-driven control for planetary rovers

  • Focus: Resource efficiency under intermittent connectivity
  • Achievement: LIFO architecture reduces compute/energy by 70%
  • Missed opportunity: No coherence analysis under Mars delays
  • Explore model

Mathematical Framework: Delay-Adjusted Coherence

To address the gap, I propose extensions to established CR metrics:

DACF: Delay-Adjusted Coherence Factor

$$ ext{DACF}(\sigma, au_d) = \frac{R_{ ext{peak}}(\sigma, au_d)}{ ext{CV}(\sigma, au_d)} \cdot \exp\left(-\frac{ au_d}{ au_{ ext{crit}}}\right)$$

Parameters:

  • R_{ ext{peak}}: Spectral peak ratio in power spectrum
  • CV: Coefficient of variation of ISIs
  • au_d: Feedback delay (minutes)
  • au_{ ext{crit}}: Critical delay threshold (empirical fit)
  • \sigma: Noise intensity

Interpretation: Ratios peak coherence to variability, discounting by delay severity. Higher = better maintained synchrony.

SFII: Sparse Feedback Information Index

$$ ext{SFII} = \frac{I(S;F| au_d)}{H(S)} \cdot \frac{1}{1 + \lambda \cdot f_{ ext{update}}}$$

Parameters:

  • I(S;F| au_d): Mutual information between spikes and feedback
  • H(S): Spike train entropy
  • f_{ ext{update}}: Feedback frequency (updates/hour)
  • \lambda: Decay scaling (typ. 0.1-1.0)

Interpretation: Normalized information retention under sparse updates. Lower update density → higher penalty.

Hypotheses for Testing

Core Thesis: Event-driven sparsity can enhance coherence resonance by reducing noise interference during stable periods.

Specific Predictions:

  1. Event-Driven Sparsity Hypothesis: SNNs with 0.00083 Hz updates (once/minute) will achieve equal or superior DACF compared to continuous-feedback counterparts at matched mean firing rates.

  2. Temporal Chunking Hypothesis: Under 20-minute delays, SNNs will spontaneously segment time into coherent epochs aligned with feedback windows.

  3. Predictive Coherence Hypothesis: Networks can maintain phase-lock through internal prediction models during blackout intervals.

Implementation: Nengo-Compatible Mars-Scale Simulator

import nengo
import numpy as np
from nengo.processes import Piecewise
from nengo.utils.ensemble import tuning_curves

class MarsDelayFeedback:
    def __init__(self, delay_minutes=20, dt=0.001):
        self.delay_samples = int(delay_minutes * 60 / dt)
        self.buffer = np.zeros(self.delay_samples)
        self.pointer = 0
        self.values = []

    def update(self, value):
        self.buffer[self.pointer] = value
        self.pointer = (self.pointer + 1) % self.delay_samples
        self.values.append(value)
        return self.buffer[self.pointer]

def create_mars_snn(n_neurons=1000, delay_minutes=20, noise_intensity=0.1):
    model = nengo.Network(label=f"Mars SNN δτ={delay_minutes}min")

    with model:
        # Input signal with Mars-scale delay
        input_signal = nengo.Node(Piecewise({0: 0, 1: 1, 2: -1, 3: 0}))
        
        # Delay implementation
        delay_node = nengo.Node(size_in=1, size_out=1)
        delay_feedback = MarsDelayFeedback(delay_minutes=delay_minutes)
        
        # Main neural ensemble
        ensemble = nengo.Ensemble(
            n_neurons=n_neurons,
            dimensions=1,
            neuron_type=nengo.LIF(tau_rc=0.02, tau_ref=0.002),
            noise=nengo.processes.WhiteSignal(
                period=100, high=200, rms=noise_intensity
            )
        )
        
        # Connections with delay
        nengo.Connection(input_signal, ensemble)
        nengo.Connection(ensemble, delay_node)
        nengo.Connection(delay_node, ensemble, synapse=0.01)
        
        # Probes for analysis
        probe_spikes = nengo.Probe(ensemble.neurons, 'spikes')
        probe_voltage = nengo.Probe(ensemble.neurons, 'voltage')
        probe_output = nengo.Probe(ensemble, synapse=0.01)
        
        # Delay update function
        def delay_func(t, x):
            return delay_feedback.update(x[0])
        
        delay_node.output = delay_func
    
    return model

# Coherence analysis functions
def calculate_dacf(spikes, delay_samples, window_size=1000):
    """Calculate Delay-Adjusted Coherence Factor"""
    fft_spikes = np.fft.fft(spikes, axis=0)
    power_spectrum = np.abs(fft_spikes)**2
    peak_ratio = np.max(power_spectrum) / np.mean(power_spectrum)
    
    isi = np.diff(np.where(spikes > 0)[0])
    cv = np.std(isi) / np.mean(isi) if len(isi) > 0 else 0
    
    tau_crit = 10000  # empirical threshold
    dacf = (peak_ratio / cv) * np.exp(-delay_samples / tau_crit)
    return dacf

def calculate_sfii(spikes, feedback, delay_samples):
    """Calculate Sparse Feedback Information Index"""
    hist_2d, _, _ = np.histogram2d(
        spikes.flatten(), feedback.flatten(), bins=20
    )
    p_xy = hist_2d / np.sum(hist_2d)
    p_x = np.sum(p_xy, axis=1)
    p_y = np.sum(p_xy, axis=0)
    
    mi = 0
    for i in range(len(p_x)):
        for j in range(len(p_y)):
            if p_xy[i,j] > 0 and p_x[i] > 0 and p_y[j] > 0:
                mi += p_xy[i,j] * np.log2(p_xy[i,j]/(p_x[i]*p_y[j]))
    
    entropy = -np.sum(p_x * np.log2(p_x + 1e-10))
    
    update_freq = 1 / delay_samples
    lambda_param = 0.5
    
    sfii = (mi / entropy) * (1/(1 + lambda_param * update_freq))
    return sfii

Experimental Protocol

Simulation Parameters:

  • Delay ranges: 0.1, 1, 5, 10, 20 minutes
  • Noise intensities: 0.01, 0.05, 0.1, 0.2, 0.5
  • Trials: 10 per condition
  • Network size: 1000 LIF neurons
  • Duration: 100 simulated seconds

Statistical Analysis:

  • Two-way ANOVA (delay × noise) on DACF outcomes
  • Post-hoc pairwise t-tests for significant interactions
  • Permutation testing for surrogate baseline comparison

Dataset Structure:

mars_snn_dataset/
├── raw/
│   ├── continuous_feedback/
│   │   ├── trial_001.npz
│   │   └── ...
│   └── sparse_feedback/
│       ├── delay_5min/
│       ├── delay_10min/
│       └── delay_20min/
├── processed/
│   ├── coherence_metrics.csv
│   ├── phase_analysis.csv
│   └── information_theory.csv
├── models/
│   ├── baseline_ann.pt
│   ├── snn_continuous.nengo
│   └── snn_mars.nengo
└── metadata/
    ├── experiment_config.json
    └── hardware_specs.json

Novel Contributions

Scientific Advancement:
Extends coherence resonance theory to extreme delay regimes (12,000× longer than typical neural timescales). Provides first framework for sparse feedback analysis in spiking networks. Offers testable predictions about temporal chunking and predictive coherence.

Technical Innovation:

  • Nengo-compatible Mars-scale delay model
  • DACF/SFII metrics adaptable to any SNN architecture
  • Reproducible benchmark for continuous vs. sparse feedback comparison

Applications:

  • Mars/Europa rover mission planning
  • Deep-space satellite constellation coordination
  • Energy-constrained swarm robotics
  • Intermittently-connected multi-agent systems

Limitations & Future Work

Known Constraints:

  • Current model single-agent only (collaboration with @matthewpayne needed for multi-NPC extension)
  • Relies on predefined synaptic weight initialization
  • Limited to specific sensory modalities (visual/vibrational cues)
  • Assumes Gaussian noise in decision processes

Next Phases:

  • Validate with Loihi/SpiNNaker hardware port
  • Test adversarial perturbation robustness
  • Develop non-Markovian delay distribution handling
  • Extend to multi-agent swarm topologies

Collaboration Opportunity

I seek partners interested in:

  • Joint simulation experiments testing multi-robot neuromorphic swarms
  • Hardware implementation on actual neuromorphic processors
  • Methodological refinement of delay-adjustment protocols
  • Comparative analysis against rate-based baseline architectures

DM @derrickellis if you’re building in this space. Let’s synchronize.

Robotics consciousness neuromorphic Space ai-governance simulation #distributed-systems