multi-timescale-conductance-snn

name: multi-timescale-conductance-snn description: > Multi-Timescale Conductance Spiking Networks (MTC-SNN) methodology for energy-aware temporal processing. Introduces gradient-trainable spiking neurons using fast/slow/ultra-slow conductances to shape I-V curves, enabling direct backpropagation through time (no surrogate gradients). Rich firing regimes (tonic, phasic, bursting) within single model. Outperforms LIF and AdLIF on Mackey-Glass time-series regression with substantially sparser activity. Activation: multi-timescale conductance, MTC-SNN, conductance spiking, gradient-trainable SNN, I-V curve shaping, spiking neuron dynamics, temporal processing SNN, surrogate-free SNN training

Multi-Timescale Conductance Spiking Networks (MTC-SNN)

Overview

MTC-SNN (arXiv:2605.11835) introduces a gradient-trainable spiking neural network framework where neural dynamics emerge from shaping the current-voltage (I-V) curve via tunable fast, slow, and ultra-slow conductances. Published at IEEE Neuro-Inspired Computational Elements Conference (NeuroInspire 2026, Atlanta, USA).

Authors: Alex Fulleda-Garcia, Saray Soldado-Magraner, Josep Maria Margarit-Taulé

Core Problem

Standard SNN neuron models (LIF, AdLIF) face a fundamental trade-off:

Gradient-based trainability vs dynamical richness vs activity sparsity
Acute in regression: approximation error, noise, spike discretization degrade continuous outputs
SOTA SNNs rely on simple phenomenological dynamics + surrogate gradients
Limited control over spiking diversity and sparsity

Key Innovation: Conductance-Based Neurons

Multi-Timescale Conductance Parametrization

Neural dynamics emerge from I-V curve shaping via three conductance timescales:

Fast conductance: rapid response dynamics
Slow conductance: medium-term adaptation
Ultra-slow conductance: long-term behavioral modulation

Benefits:

Systematic control over excitability
Efficient analog circuit implementation
Rich firing regimes in single model: tonic, phasic, bursting

Discrete-Time Differentiable Formulation

Derive discrete-time version of conductance dynamics
Direct backpropagation through time (BPTT) — no surrogate-gradient approximations
End-to-end gradient training of neuron parameters

Performance Results

Mackey-Glass Time-Series Regression (predictability limit)

Outperforms both LIF and SOTA AdLIF baselines
Substantially sparser activity (communication + computational perspectives)
Energy-aware temporal processing suitable for neuromorphic deployment

Sparsity Metrics

Communication sparsity: fewer spikes for equivalent task performance
Computational sparsity: sparse internal state updates

Implementation Pattern

# Conceptual structure of MTC neuron
class MTCNeuron:
    """Multi-timescale conductance neuron."""
    def __init__(self):
        self.g_fast = ...    # Fast conductance parameter
        self.g_slow = ...    # Slow conductance parameter  
        self.g_ultra_slow = ... # Ultra-slow conductance parameter
        self.v_membrane = 0.0
        self.spike_threshold = 1.0
    
    def step(self, input_current, dt):
        # Update membrane potential via conductance-based dynamics
        # Shape I-V curve through g_fast, g_slow, g_ultra_slow
        # Emit spike if v_membrane > threshold
        # Differentiable for BPTT
        pass

Training

# Standard BPTT — no surrogate gradients needed
loss = criterion(predicted, target)
loss.backward()  # gradients flow through conductance dynamics
optimizer.step()

When to Use

Temporal processing tasks (time-series, sequence modeling)
Energy-efficient / neuromorphic deployment
Regression tasks where spike discretization is problematic
Applications requiring diverse firing patterns (tonic/phasic/bursting)
Analog neuromorphic hardware implementation

Comparison with Alternatives

Model	Trainability	Firing Richness	Sparsity
LIF	Surrogate gradient	Limited (tonic only)	Low
AdLIF	Surrogate gradient	Moderate	Moderate
MTC-SNN	Direct BPTT	Rich (3 regimes)	High

Pitfalls

Conductance parameters require careful initialization
Analog circuit implementation needs precise conductance tuning
Discrete-time formulation introduces discretization error — validate timestep sensitivity