General Aspects Internal Noise Spiking Neural

Core Concepts

Noise Sources in SNNs

Internal noise arises from multiple biological mechanisms:

1. Channel noise: Stochastic opening/closing of ion channels (thermal fluctuations)
2. Synaptic noise: Probabilistic neurotransmitter release (vesicle stochasticity)
3. Threshold noise: Variability in spike threshold due to channel state
4. Background activity: Ongoing spontaneous network activity (synaptic bombardment)

Additive vs Multiplicative Noise

import numpy as np

class NoisyLIFNeuron:
    """
    Leaky Integrate-and-Fire neuron with configurable internal noise.
    """
    
    def __init__(self, tau_m=20e-3, v_rest=-65e-3, v_thresh=-50e-3,
                 noise_type='additive', noise_std=1e-3):
        self.tau_m = tau_m
        self.v_rest = v_rest
        self.v_thresh = v_thresh
        self.v_reset = v_rest
        self.noise_type = noise_type
        self.noise_std = noise_std
        self.v_membrane = v_rest
        
    def step(self, input_current, dt=1e-3):
        # LIF membrane dynamics
        dv = (-(self.v_membrane - self.v_rest) + input_current * 1e6) / self.tau_m * dt
        
        # Internal noise
        if self.noise_type == 'additive':
            # State-independent: dV = f(V)dt + sigma*dW
            noise = np.random.normal(0, self.noise_std)
        elif self.noise_type == 'multiplicative':
            # State-dependent: dV = f(V)dt + g(V)*dW
            noise = np.random.normal(0, self.noise_std * abs(self.v_membrane - self.v_rest))
        else:
            noise = 0
        
        self.v_membrane += dv + noise
        
        if self.v_membrane >= self.v_thresh:
            self.v_membrane = self.v_reset
            return True
        return False

Noise Characterization

def characterize_noise_regime(spike_times):
    """
    Determine noise regime from spike train statistics.
    
    - Additive noise: CV approx 1 (Poisson-like), Fano factor approx 1
    - Multiplicative noise: CV != 1, Fano factor != 1
    - Sub-Poisson: CV < 1 (regular firing)
    - Super-Poisson: CV > 1 (bursty firing)
    """
    isi = np.diff(spike_times)
    if len(isi) < 2:
        return {'CV': np.nan, 'fano_factor': np.nan}
    
    cv = np.std(isi) / np.mean(isi)
    
    # Fano factor from spike counts in windows
    window = 0.1
    counts = []
    for t in np.arange(spike_times[0], spike_times[-1] - window, window):
        counts.append(np.sum((spike_times >= t) & (spike_times < t + window)))
    
    fano = np.var(counts) / (np.mean(counts) + 1e-10)
    
    return {'CV': cv, 'fano_factor': fano}

Practical Applications

1. Neuromorphic hardware: Design noise-robust SNN chips
2. Stochastic computing: Leverage noise for probabilistic inference
3. Robustness testing: Validate SNN under realistic noise conditions
4. Neurological modeling: Excessive noise linked to disorders

Activation Keywords

• SNN internal noise
• spiking neural network noise
• additive multiplicative noise
• neuromorphic noise
• spike timing jitter
• stochastic SNN