mtc-spiking-networks

name	mtc-spiking-networks
description	Multi-Timescale Conductance Spiking Networks (MTC-SN): A sparse, gradient-trainable SNN framework with rich firing dynamics for enhanced temporal processing. Uses fast/slow/ultra-slow conductances to shape I-V curves, enabling direct BPTT without surrogate gradients. Activation: multi-timescale conductance, MTC-SN, conductance-based SNN, gradient-trainable spiking, temporal regression SNN, neuromorphic regression.
category	neuroscience

MTC-SN: Multi-Timescale Conductance Spiking Networks

arXiv: 2605.11835v1 (2026-05-12) Authors: Alex Fulleda-Garcia, Saray Soldado-Magraner, Josep Maria Margarit-Taulé Affiliation: IMB-CNM CSIC (Spain), UCLA (USA) Keywords: Spiking Neural Networks, Conductance-Based Neuron Models, Multi-Timescale Dynamics, Temporal Regression, Neuromorphic Computing

Overview

MTC-SN (Multi-Timescale Conductance Spiking Networks) is a gradient-trainable spiking neural network framework that addresses the fundamental trade-off between biological plausibility, trainability, and computational efficiency in SNNs. The key innovation is using multi-timescale conductances (fast, slow, ultra-slow) to shape the current-voltage (I-V) curve, enabling rich firing dynamics while maintaining differentiability for direct backpropagation through time.

Core Innovation

Unlike traditional SNNs that rely on surrogate gradients (approximate gradients for non-differentiable spike functions), MTC-SN derives a discrete-time formulation of differentiable conductance-based dynamics, enabling exact BPTT without surrogate-gradient approximations.

Technical Details

Problem Addressed

Current SNN limitations:

• Simple neuron models (LIF) trade dynamical richness for trainability
• Surrogate gradients are approximations that may not capture true gradient information
• Regression tasks suffer from approximation error, noise, and spike discretization
• Limited control over spiking diversity and sparsity

MTC-SN Architecture

1. Multi-Timescale Conductances:

   • Fast conductance: Rapid response to input changes
   • Slow conductance: Medium-term adaptation
   • Ultra-slow conductance: Long-term dynamics and memory
   • These shape the I-V curve to produce diverse firing regimes

2. Rich Firing Regimes:

   • Tonic firing: Sustained response to constant input
   • Phasic firing: Transient response to input onset
   • Bursting: High-frequency spike clusters
   • All within a single, unified model

3. Differentiable Dynamics:

   • Discrete-time formulation enables exact gradients
   • Direct BPTT without surrogate approximations
   • Systematic control over excitability through conductance tuning

4. Hardware Compatibility:

   • Can be implemented efficiently in analog circuits
   • Suitable for neuromorphic hardware deployment

Comparison with Baselines

Feature	LIF	AdLIF	MTC-SN
Dynamical Richness	Low	Medium	High
Gradient Type	Surrogate	Surrogate	Exact
Firing Regimes	Single	Limited	Multiple
Sparsity Control	Limited	Moderate	High
Hardware Mapping	Simple	Moderate	Efficient

Evaluation

Task: Mackey-Glass Time-Series Regression

• Evaluated at the predictability limit (challenging benchmark)
• Outperforms both LIF and AdLIF networks
• Substantially sparser activity from both communication and computational perspectives

Key Results

• Better accuracy on temporal regression tasks
• Higher spike sparsity (more energy-efficient)
• Richer temporal processing capabilities
• Direct trainability without surrogate approximations

Implementation Guide

Neuron Dynamics

The MTC-SN neuron model extends the standard conductance-based formulation:

C dV/dt = -g_fast(V - E_fast) - g_slow(V - E_slow) - g_ultraslow(V - E_ultraslow) + I_ext

Where each conductance has its own timescale:

• τ_fast << τ_slow << τ_ultraslow

Discrete-Time Formulation

For gradient-based training, the continuous dynamics are discretized:

V[t+1] = V[t] + Δt/C * (sum of conductance currents + external input)

This enables exact gradient computation through the entire temporal trajectory.

Training Workflow

1. Initialize conductance parameters and time constants
2. Forward pass: Simulate spiking dynamics over time
3. Compute loss: Compare output to target (e.g., MSE for regression)
4. Backward pass: Exact BPTT through discretized dynamics
5. Update: Gradient-based optimization of conductance parameters

Practical Applications

1. Temporal Regression

• Time-series prediction
• System identification
• Signal processing

2. Neuromorphic Computing

• Energy-efficient edge inference
• Analog circuit implementation
• Low-power temporal processing

3. Biological Modeling

• Capturing diverse neuronal firing patterns
• Studying multi-timescale neural dynamics
• Bridging biological and artificial neural networks

Key Concepts

Conductance-Based Neurons

More biologically realistic than current-based models, where synaptic inputs modulate membrane conductance rather than injecting current directly.

Multi-Timescale Dynamics

Different biological processes operate at different timescales (ion channel kinetics, synaptic plasticity, adaptation). MTC-SN explicitly models this hierarchy.

Surrogate Gradient vs Exact Gradient

• Surrogate: Approximate gradient for non-differentiable spike functions (common in SNNs)
• Exact: True gradient through differentiable dynamics (MTC-SN approach)

Mackey-Glass Equation

A delay differential equation known for chaotic dynamics, used as a benchmark for temporal prediction capabilities.

Research Implications

1. Exact Gradients for SNNs: Eliminates the need for surrogate gradient approximations, providing more accurate learning signals.

2. Multi-Timescale as Inductive Bias: Incorporating biological timescale hierarchy improves temporal processing without increasing model complexity.

3. Energy Efficiency: Higher sparsity combined with better performance suggests MTC-SN is well-suited for neuromorphic hardware.

4. Unified Framework: Single model captures multiple firing regimes, reducing the need for task-specific neuron designs.

Related Concepts

• Leaky Integrate-and-Fire (LIF) neurons
• Adaptive LIF (AdLIF)
• Conductance-based neural models
• Backpropagation through time (BPTT)
• Neuromorphic hardware
• Temporal sequence learning
• Spike-based regression

Activation Triggers

• multi-timescale SNN
• conductance-based spiking
• gradient-trainable SNN
• exact gradient spiking
• temporal regression SNN
• MTC-SN
• neuromorphic regression
• multi-timescale dynamics
• conductance neuron model
• BPTT spiking network
• Mackey-Glass SNN
• spiking regression

References

• Fulleda-Garcia, A., Soldado-Magraner, S., Margarit-Taulé, J.M. (2026). "Multi-Timescale Conductance Spiking Networks: A Sparse, Gradient-Trainable Framework with Enhanced Temporal Processing." arXiv:2605.11835v1