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Accuracy-Efficiency Trade-Offs in Spiking Neural Networks: A Lempel-Ziv Complexity Perspective on Learning Rules

Zofia Rudnicka, Janusz Szczepanski, Agnieszka Pregowska

TL;DR

This paper uses Lempel-Ziv complexity (LZC) as a compact, decision-relevant descriptor of spike-train temporal organization to quantify how different learning rules reshape class-conditional temporal structure.

Abstract

Training spiking neural networks (SNNs) remains challenging due to temporal dynamics, non-differentiability of spike events, and sparse event-driven activations. This paper studies how the choice of learning paradigm (unsupervised, supervised, and hybrid) affects classification performance and computational cost in temporal pattern recognition. Building on our earlier study [Rudnicka et al., 2026], we use Lempel-Ziv complexity (LZC) as a compact, decision-relevant descriptor of spike-train temporal organization to quantify how different learning rules reshape class-conditional temporal structure. The pipeline combines a leaky integrate-and-fire (LIF) SNN with an LZC-based decision rule. We evaluate learning rules on synthetic sources with controlled temporal statistics (Bernoulli, two-state Markov, and Poisson spike processes) and on two-class subsets of MNIST and N-MNIST. Across datasets, gradient-based learning achieves the highest accuracy but at high computational cost, whereas bio-inspired rules (e.g., Tempotron and SpikeProp) offer favorable accuracy--efficiency trade-offs. These results highlight that selecting a learning rule should be guided by application constraints and the desired balance between separability and computational overhead.

Accuracy-Efficiency Trade-Offs in Spiking Neural Networks: A Lempel-Ziv Complexity Perspective on Learning Rules

TL;DR

This paper uses Lempel-Ziv complexity (LZC) as a compact, decision-relevant descriptor of spike-train temporal organization to quantify how different learning rules reshape class-conditional temporal structure.

Abstract

Training spiking neural networks (SNNs) remains challenging due to temporal dynamics, non-differentiability of spike events, and sparse event-driven activations. This paper studies how the choice of learning paradigm (unsupervised, supervised, and hybrid) affects classification performance and computational cost in temporal pattern recognition. Building on our earlier study [Rudnicka et al., 2026], we use Lempel-Ziv complexity (LZC) as a compact, decision-relevant descriptor of spike-train temporal organization to quantify how different learning rules reshape class-conditional temporal structure. The pipeline combines a leaky integrate-and-fire (LIF) SNN with an LZC-based decision rule. We evaluate learning rules on synthetic sources with controlled temporal statistics (Bernoulli, two-state Markov, and Poisson spike processes) and on two-class subsets of MNIST and N-MNIST. Across datasets, gradient-based learning achieves the highest accuracy but at high computational cost, whereas bio-inspired rules (e.g., Tempotron and SpikeProp) offer favorable accuracy--efficiency trade-offs. These results highlight that selecting a learning rule should be guided by application constraints and the desired balance between separability and computational overhead.

Paper Structure

This paper contains 24 sections, 17 equations, 1 figure, 9 tables.

Table of Contents

  1. Introduction
  2. Relation to Prior Work
  3. Background on Learning Rules in Spiking Neural Networks
  4. Notation
  5. Unsupervised Learning Algorithms
  6. Spike Timing Dependent Plasticity
  7. Symmetric Spike-Driven Spike-Based Plasticity
  8. Supervised Learning Algorithms
  9. Backpropagation Algorithm
  10. Spike-Timing-Dependent Backpropagation
  11. Tempotron Learning Rule
  12. SpikeProp Algorithm
  13. Chronotron Learning Rule
  14. Remote Supervised Method
  15. Hybrid Learning Algorithms
  16. ...and 9 more sections

Figures (1)

  • Figure 1: The architecture of the considered neural network.