multi-timescale-conductance-spiking-networks

name

multi-timescale-conductance-spiking-networks

description

Multi-Timescale Conductance (MTC) Spiking Networks — gradient-trainable framework with rich firing dynamics for enhanced temporal processing. Conductance-based neuron model with fast/slow/ultra-slow timescales enables tonic, phasic, and bursting responses within a single model. Trainable via standard BPTT without surrogate gradients. Activation: multi-timescale conductance, MTC spiking network, conductance-based neuron, spiking neural network regression, surrogate-free SNN training, I-V curve shaping, neuromorphic analog circuits, Mackey-Glass forecasting SNN

Multi-Timescale Conductance (MTC) Spiking Networks

Paper: arXiv:2605.11835v1 (May 12, 2026) Authors: Alex Fulleda-Garcia, Saray Soldado-Magraner, Josep Maria Margarit-Taulé Affiliations: IMB-CNM/CSIC (Spain), UCLA (USA)

Core Problem

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

• Gradient trainability — requires smooth dynamics
• Dynamical richness — biological neurons exhibit diverse firing modes
• Activity sparsity — energy efficiency requires sparse spiking

LIF models sacrifice biophysical realism; surrogate gradients create forward-backward mismatch, especially damaging for continuous-valued temporal regression.

MTC Neuron Model

Circuit Foundation

Based on Ribar & Sepulchre (2019) conductance-based framework. Neuron excitability controlled by shaping the I-V (current-voltage) curve via parallel conductance elements at different timescales.

Governing Equations

State variables (filtered voltages):

τx · dUx/dt = -Ux + Um  (for each timescale x)
Ix±(t) = ±αx± · tanh(Ux - δx±)

Membrane potential dynamics:

τm · dUm/dt = -(Um - Urest) + R·Iin(t) - R·Σ Ix±(t)

Three Timescale Conductances

Timescale	Role	Effect
Fast (τf)	Negative conductance If−	Creates negative differential resistance → drives rapid depolarization (upstroke)
Slow (τs)	Positive conductance Is+	Damping force → recovery + refractory period
Ultra-slow (τus)	Slow negative + ultra-slow positive	Enables bursting, higher-order temporal processing

Firing Regimes

By tuning conductance parameters, the same model produces:

• Tonic Spiking — sustained firing to constant input
• Tonic Bursting — sustained clusters of spikes
• Phasic Spiking — transient response to input onset
• Phasic Bursting — transient burst responses

Key Innovation: Differentiable Spiking

Unlike LIF's hybrid continuous-discrete nature (hard threshold + reset), MTC produces spikes through fully derivable nonlinear dynamics.

Signal Conditioning (Semi-Digital Communication)

s(t) = min(ReLU(Um(t) - Uth) / (Usat - Uth), 1)

This provides:

1. Signal standardization — normalizes spike amplitudes to [0,1]
2. Semi-digital sparsity — suppresses sub-threshold activity while retaining continuous slope information during rising phase (needed for exact gradients)
3. Synaptic transduction model — approximates nonlinear neurotransmitter release

Training: No Surrogate Gradients Needed

• MTC: Standard BPTT through continuous conductance state variables
• LIF: Requires surrogate gradient (ArcTan derivative in snnTorch)
• AdLIF: Requires SLAYER surrogate gradient (α=5)

The conductance states provide smooth internal representations, avoiding the spike discretization problem that necessitates surrogate gradients.

Experimental Results: Mackey-Glass Time Series

Task: Chaotic time series forecasting at predictability horizon (1 Lyapunov time) Architecture: Feedforward SNN, 4 stages (input projection → spiking hidden layer → linear readout → low-pass filter)

Key findings:

• MTC outperforms LIF and SOTA AdLIF baselines in regression accuracy
• MTC operates in considerably sparser regime (both rate and duty-cycle dimensions)
• Dynamic sparsity emerges from single-neuron excitability tuning, not loss regularization
• Aligns with neuromorphic vision of energy-efficient intelligent perception

Hardware Implementation Advantages

1. Analog circuit compatible — conductance elements implementable with compact transconductance blocks (subthreshold MOS)
2. I-V curves need not be exact tanh — any approximately monotone nonlinearity works
3. Multi-timescale dynamics naturally map to neuromorphic hardware with different RC constants
4. No surrogate gradient overhead — eliminates backward pass approximation circuitry

Comparison with Baselines

Property	LIF	AdLIF	MTC (this work)
Firing regimes	Tonic only	Tonic + some adaptation	Tonic, phasic, bursting
Surrogate gradient needed	✓	✓	✗
Timescale control	1 (membrane)	2 (membrane + adaptation)	3+ (fast, slow, ultra-slow)
I-V curve shaping	No	No	Yes
Analog circuit mapping	Simple	Moderate	Natural
Sparsity mechanism	Threshold/loss reg	Threshold/loss reg	Intrinsic excitability

Activation Context

Use this skill when:

• Designing neuron models with rich firing dynamics for temporal processing
• Building SNNs that avoid surrogate gradient approximations
• Implementing neuromorphic circuits with conductance-based dynamics
• Tackling continuous-valued temporal regression with spiking networks
• Studying the trade-off between trainability, dynamical richness, and sparsity