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Causal pieces: analysing and improving spiking neural networks piece by piece

NeurIPS 2026 · Probabilistic and scientific modeling › Causal discovery · approach: Latent-variable causal estimation

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Introduces causal pieces, regions of input/parameter space where the same causal subnetwork produces an SNN's output spikes, proves a lower bound on approximation error in terms of piece count for nLIF networks, and shows piece counts at initialisation correlate with SNN training success.

Problem

Spike-time discontinuities and event-based dynamics have made the expressivity and trainability of spiking neural networks hard to analyse rigorously, and there is no principled metric for SNN initialisation.

Approach

Partition the joint input and parameter space of feedforward single-spike SNNs into causal pieces (regions with a fixed causal subnetwork); within each piece output spike times are locally Lipschitz, and the number of pieces lower-bounds approximation error, so counting pieces on data at initialisation predicts training success.

Key results

• Log number of causal pieces at initialisation correlates with post-training test accuracy on Yin-Yang (r = 0.70, log-linear).
• Correlations of log initial piece count with final accuracy are 0.74, 0.69, 0.62, and 0.62 on Fashion-MNIST, EuroSAT and LIF variants.
• Positive-weight SNNs with evolutionary-optimised lognormal or uniform initialisation achieve performance similar to fully connected ANNs on Yin-Yang, MNIST and EuroSAT RGB.

Surprising findings

• Initialisations with non-zero mean yield the most causal pieces, contrary to the zero-mean schemes common in the literature.
• Recovering from a poor initialisation with few pieces through training is hard; piece counts often decrease during training for shallow networks.

Limitations

• Theory is proven only for nLIF neurons with large membrane time constant and single-spike coding; LIF results are empirical only.
• The number of pieces is not the sole predictor of training success; generalisation is not addressed by the theory.
• Causal pieces are limited to feedforward networks; recurrent and surrogate-gradient training are not covered.

Experimental setup

Datasets: Yin-Yang Fashion-MNIST EuroSAT RGB MNIST

Benchmarks: Yin-Yang Fashion-MNIST EuroSAT RGB MNIST

Metrics: test accuracy Pearson correlation of log piece count with accuracy number of causal pieces sum of squared residuals

Baselines: fully connected ANNs linear models Gaussian and uniform zero-mean initialisations

Builds on: linear pieces (ReLU ANN expressivity) nLIF neuron model Sparre Andersen theorem exact spike-time backpropagation

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