Exploring napping paradigm for Recurrent Spiking Neural Networks

Andreas Massey; Stefano Nichele; Aliaksandr Hubin

cs.LGSep 12, 2026

Exploring napping paradigm for Recurrent Spiking Neural Networks

Authors: Andreas Massey, Stefano Nichele, Aliaksandr Hubin

Organizations: The Norwegian University of Life Sciences, Elizabeth Stephansens v. 15, 1433 Ås, Norway · Østfold University of Applied Sciences, B R A Veien 4, 1757 Halden, Norway

Abstract

Biological organisms minimize free energy by balancing two competing demands on their internal world model: it must be accurate enough to predict sensory input, yet simple enough to generalize beyond it. Two mechanisms regulate this balance offline: sleep reduces complexity through gradual synaptic downscaling, while stochastic noise attenuates precision, relaxing the constraint sensory input imposes on synaptic reorganization. Engineered Spiking Neural Networks (SNNs) leave this balance unaddressed, favoring instantaneous, noiseless weight normalization instead. This paper investigates the hypothesis that a biologically inspired micro-sleep paradigm, napping -- combining proportional weight scaling with continuous stochastic membrane activity -- can replicate the stability of normalization while shedding model complexity. We evaluate this in an unsupervised recurrent SNN trained via trace-based spike-timing-dependent plasticity (STDP) on Gabor-preprocessed MNIST. We tune napping across three regularization regimes by sweeping its duration and membrane noise level, then compare the best configuration against weight normalization. Across all three regimes, well-tuned napping matches the accuracy of normalization: accuracy peaks at brief durations and low noise, then declines monotonically as either grows. Clustering diverges, with the strongest geometric separation arising at longer durations and higher noise -- the two terms of free energy pulling apart, accuracy rewarding data fit and structure rewarding the simpler representation that gradual, noisy downscaling induces. This gain carries a simulation cost normalization avoids, so napping is most compelling where representational structure, rather than raw classification efficiency, is the priority.

Figures & tables

Panel of Figure 1 — Figure 1: Network architecture: three-layer SNN with feedforward input ( $P=5\%$ ), recurrent excitation ( $P=5\%$ ), and lateral inhibition ( $P=5\%$ ). The solid lines denote weights that change over time, and dashed lines represent static weights.

Figure 2: Effect of the three regularization regimes on synaptic weights. Unshaded is wake phase and shaded is napping session. Layer : each population converges to its layer mean. Neuron : incoming weights of each post-synaptic neuron converge to that neuron’s mean. Static : both populations decay toward fixed initialization-derived targets.

Panel of Figure 3 — Figure 3: Illustration of the Calinski–Harabasz (CH) index. Dashed lines indicate within-cluster distances (WCSS) from each point $x_{i}$ to its class centroid $c_{k}$ ; solid lines indicate between-cluster distances (BCSS) from each centroid to the grand mean $c_{E}$ .

Figure 4: Predicted accuracy (top) and clustering (bottom) vs. duration and noise variance, across layer, neuron, and static regimes. Layer/neuron accuracy falls monotonically; layer clustering peaks mid-duration. Static stays flat except for anomalous high clustering at short duration, high noise ( $\sigma^{2}=100$ ), with no accuracy gain.

	Beta (accuracy)			Gamma (clustering)
Fixed effect	Est.	z	p	Est.	z	p
$\hat{\beta}_{0}$ (intercept)	$-1.381$	$-34.43$	$<.001$	2.114	30.24	$<.001$
Main effects
$\hat{\beta}_{1}$ (dur)	.024	2.46	$.014$	$-.139$	$-8.80$	$<.001$
$\hat{\beta}_{2}$ (noise)	$-.020$	$-1.14$	$.255$	.079	2.77	$.006$	**
$\hat{\beta}_{3}$ (layer)	3.045	50.52	$<.001$	1.515	15.92	$<.001$

Table 1: Beta (accuracy) and Gamma (clustering) GLMM estimate effects.

	Beta (accuracy)			Gamma (clustering)
Fixed effect	Est.	z	p	Est.	z	p
$\hat{\beta}_{0}$ (intercept)	0 .566	$\phantom{0}.71$	$\phantom{<}.480$	3.188	$8.37$	$<.001$
$\hat{\beta}_{1}$ (napping)	.001	$.08$	$.936$	.156	$2.33$	$.020$
Random effect variances
Reg-mode	1.930			.431
Seed	$<.001$			$<.001$

Table 2: Beta (accuracy) and Gamma (clustering) GLMM results for the napping-vs-normalization comparison.

Appendix figures & tables5 assets

Supplementary material from the paper’s appendix.

Appendix

Component	Parameter	Descriptor	Value
Network
	$N_{\text{in}}$	Input neurons	784
	$N_{\text{exc}}$	Excitatory neurons	1024
	$N_{\text{inh}}$	Inhibitory neurons	225
	$P_{\text{in}\to\text{exc}}$	Wiring prob.	5%
	$P_{\text{exc}\to\text{exc}}$	Wiring prob.	5%

Appendix

Table 3: Key tuning parameters for all experiments with biosnn model

Panel of Figure 5 — Figure 5: Illustration of data transformation pipeline. First, we extract MNIST digits, then we apply Gabor filters and obtain four quadrants reflecting each orientation, and finally, we convert the data to spike-encoded arrays.

Figure 6: Beta GLMM predicted accuracy (top) and clustering (bottom) as a function of napping duration and noise level.

Napping duration	1	10	50	100	150	200	300
Noise level	1.0	2.5	5.0	7.5	10	100

Appendix

Table 4: Due to the non-linear intervals between our selected values, we log-transformed the values in Phase 1 to ensure convergence of our GLMM.

	Layer		Neuron		Static
Metric	Dur.	Noise	Dur.	Noise	Dur.	Noise
Accuracy	1	10	1	5	1	10
Clustering	100	1	1	2.5	300	100

Appendix

Table 5: Accuracy- and clustering-optimal napping configurations (duration, noise variance) selected independently per regime in the Phase 2 sweep. Static remains near chance on accuracy, so its listed optima are included only for completeness. Its clustering optimum (300 ms,

\sigma^{2}=100

) was excluded from the Phase 2 comparison, as clustering inflates there while accuracy collapses to chance.

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