Beyond Low-Pass Dynamics: Frequency-Selective Spiking Reservoirs with Resonant Neurons

Aurora Micheli; Claudio Gallicchio; Nergis Tomen

cs.AIOct 27, 2026

Beyond Low-Pass Dynamics: Frequency-Selective Spiking Reservoirs with Resonant Neurons

Authors: Aurora Micheli, Claudio Gallicchio, Nergis Tomen

Organizations: Delft University of Technology · University of Pisa

Abstract

Spiking reservoir computing combines the training efficiency of fixed recurrent reservoirs with the energy efficiency of event-driven inference, where computation is triggered by sparse spikes rather than executed densely at every timestep. However, existing spiking reservoirs almost exclusively rely on Leaky Integrate-and-Fire (LIF) neurons, whose low-pass dynamics limit their ability to distinguish information encoded at different temporal frequencies. We introduce HRF-Res, a liquid state machine in which LIF neurons are replaced by a heterogeneous population of Harmonic Resonate-and-Fire (HRF) neurons. These neurons exhibit intrinsic oscillatory dynamics and selectively respond to input frequencies, enabling the reservoir to capture frequency-specific temporal patterns. The result is more discriminative representations and higher classification accuracy than LIF-based reservoirs, achieved without sacrificing the energy efficiency of spiking computation, with up to 19x lower energy consumption than an equivalent non-spiking oscillatory reservoir. Evaluated on ten benchmarks spanning time series, sequential images, audio spike trains, and neuromorphic vision, HRF-Res achieves state-of-the-art accuracy among spiking reservoir methods. These results demonstrate that introducing frequency-selective dynamics into spiking reservoirs improves representational quality and classification performance while preserving their inherent energy efficiency.

Figures & tables

Figure 1: Architecture of our proposed HRF-Res. The external input $\mathbf{u}_{t}$ is projected into a LIF encoder population (left, pink) via the fixed matrix $\mathbf{U}$ . LIF spikes $\mathbf{s}_{t}^{\text{\tiny LIF}}$ are passed to the HRF oscillatory reservoir (right, blue) via $\mathbf{V}$ ; each HRF neuron oscillates at its own resonance frequency and feeds spikes $\mathbf{s}_{t}^{\text{\tiny HRF}}$ back to the LIF layer via $\mathbf{W}$ . All weights are fixed; only the linear readout $\mathbf{r}=\mathbf{W}_{o}\mathbf{y}_{T}+\mathbf{b}_{o}$ is trained.

Figure 2: Band-pass properties of HRF-Res vs. LIF-Res. (A) Fraction of resonant neurons (

Q>0

) per dataset. HRF-Res has 4–20

\times

more resonant neurons than LIF-Res, confirming that band-pass dynamics survive in a full spiking reservoir setting. (B) Mean Q-factor among resonant neurons. HRF neurons form sharper band-pass filters on all datasets, with the largest gaps on FordA (

4.6

vs.

2.0

), DVS Gesture (

3.4

vs.

1.4

) and SHD (

2.5

vs.

0.6

). Bars show mean

\pm

std over three seeds.

Figure 3: HRF-Res produces more class-discriminative representations. (A) CKA between temporal mean reservoir states and category labels (mean

\pm

std over three seeds). HRF-Res achieves higher CKA than LIF-Res on all four datasets. (B) Distribution of per-neuron preferred frequencies (log scale). HRF neurons show distributed tuning across a range of frequencies, consistent with a heterogeneous bank of band-pass filters; LIF neurons collapse to the lowest sweep frequency, consistent with pure integration.

Dataset	Model	Acc (%)	Energy (J)
sMNIST	HRF-Res	$\mathbf{93.64\pm 0.25}$	$(1.676\pm 0.034)\times 10^{-4}$
sMNIST	LIF-Res	$67.00\pm 1.04$	$(2.352\pm 0.048)\times 10^{-4}$
FordA	HRF-Res	$\mathbf{69.72\pm 0.68}$	$(0.790\pm 0.015)\times 10^{-4}$
FordA	LIF-Res	$67.15\pm 0.66$	$(1.478\pm 0.038)\times 10^{-4}$
SHD	HRF-Res	$\mathbf{83.48\pm 0.44}$	$(1.044\pm 0.021)\times 10^{-3}$
SHD	LIF-Res	$72.95\pm 0.53$	$(1.280\pm 0.210)\times 10^{-3}$

Table 1: HRF-Res vs. LIF-Res. Both architectures are otherwise identical; hyperparameters for LIF-Res are independently re-tuned per dataset. Results are mean

\pm

std over 5 seeds with final reservoir state readout. HRF-Res outperforms or matches LIF-Res on all four datasets, with accuracy gains up to

+26.6\%

and lower energy consumption on most datasets. See Appendix A.5 for LIF-Res architecture details and Appendix A.4 for the evaluation protocol.

Figure 4: Readout strategy ablation. Test accuracy (%, mean

\pm

std over 5 trials) for six readout strategies across four datasets. Blue bars: membrane-based readouts operating on the HRF position state

\mathbf{y}_{t}

, using the final state (

\mathbf{y}_{T}

), temporal mean, root mean square (RMS), or standard deviation (Std). Green bar: combined membrane-based readout concatenating RMS, Std, and final state (

3N

-dimensional). Orange bar: spike-based readout using the mean HRF spike rate. Bold outline marks the best accuracy per dataset. The best membrane-based readout outperforms the spike-based alternative on every dataset, and the combined readout achieves the best or near-best accuracy on all datasets.

Dataset	Method	Neurons	Acc (%)
SHD	HRF-Res	6,000	$\mathbf{89.78\pm 0.35}$
	Deckers et al. [ 12 ]	16,000	$89.30$
	Biswas et al. [ 14 ]	3,000	$77.80$
FordA	HRF-Res	800	$73.91\pm 0.74$
	HRF-Res (large)	2,500	$\mathbf{82.05\pm 0.55}$
	Dey et al. [ 13 ]	2,500	$80.37$

Table 3: Comparison with spiking reservoir baselines. Neurons: number of reservoir units. HRF-Res results: mean

\pm

std over 5 seeds. HRF-Res achieves competitive or state-of-the-art accuracy across all modalities, in most cases with fewer neurons than prior methods.

Appendix figures & tables7 assets

Supplementary material from the paper’s appendix.

Appendix

	RON			HRF-Res
Dataset	Synaptic	State	Total	Synaptic	State	Total	Reduction
sMNIST	23.11	0.09	23.20	1.676	0.115	1.791	$13.0\times$
psMNIST	22.64	0.09	22.73	1.884	0.115	1.999	$11.4\times$
FordA	14.74	0.06	14.80	0.790	0.074	0.864	$17.1\times$
npCIFAR-10	32.97	0.11	33.08	3.450	0.147	3.597	$9.2\times$

Appendix

Table 4: Energy including neuron state updates (

\times 10^{-4}

J per sequence,

N=800

). “Synaptic” is the energy reported in Table 2 ; “State” is the cost of the

\mathcal{O}(N)

neuron state updates, computed as MACs.

Dataset	$f_{\min}$ (Hz)	$f_{\max}$ (Hz)	$T_{\mathrm{sweep}}$	$\Delta t$ [HRF-Res]	$\Delta t$ [LIF-Res]
sMNIST	0.01	2.0	6,000	0.042	0.034
FordA	0.01	2.0	6,000	0.051	0.068
SHD	0.001	2.0	50,000	0.223	0.084
DVS Gesture	0.001	2.0	50,000	0.259	0.056

Appendix

Table 8: Frequency sweep parameters and model

\Delta t

values per dataset.

Dataset	Model	Resonant (%)	Mean $Q$	Std of $f^{*}$ (Hz)
sMNIST	HRF-Res	$89.0\pm 1.1$	$4.38\pm 0.04$	$0.0829\pm 0.0029$
sMNIST	LIF-Res	$16.7\pm 2.8$	$3.67\pm 0.14$	$0.0018\pm 0.0001$
FordA	HRF-Res	$100.0\pm 0.1$	$4.62\pm 0.03$	$0.0395\pm 0.0012$
FordA	LIF-Res	$3.8\pm 0.6$	$1.02\pm 0.03$	$0.0030\pm 0.0005$
SHD	HRF-Res	$60.5\pm 0.7$	$2.49\pm 0.02$	$0.0238\pm 0.0001$
SHD	LIF-Res	$5.7\pm 0.1$	$0.63\pm 0.01$	$0.0075\pm 0.0005$

Appendix

Table 9: Frequency-selectivity analysis with a Hann window applied before the DFT (mean

\pm

std over three seeds).

	FordA		sMNIST		SHD		DVS Gesture
$n$	HRF-Res	LIF-Res	HRF-Res	LIF-Res	HRF-Res	LIF-Res	HRF-Res	LIF-Res
100	$.0555\pm.0217$	$.0211\pm.0104$	$.2628\pm.0244$	$.2238\pm.0267$	$.2632\pm.0236$	$.2380\pm.0359$	$.3552\pm.0333$	$.3245\pm.0286$
200	$.0357\pm.0115$	$.0101\pm.0044$	$.2298\pm.0244$	$.1922\pm.0264$	$.2294\pm.0149$	$.2049\pm.0174$	$.3253\pm.0125$	$.2989\pm.0120$
500	$.0274\pm.0039$	$.0053\pm.0025$	$.2217\pm.0101$	$.1781\pm.0135$	$.2063\pm.0084$	$.1838\pm.0137$	–	–
1000	$.0268\pm.0035$	$.0034\pm.0009$	$.2166\pm.0081$	$.1761\pm.0102$	$.2018\pm.0072$	$.1804\pm.0069$	–	–
Full	$.0263$	$.0029$	$.2111$	$.1729$	$.1959$	$.1732$	$.3203$	$.2914$

Appendix

Table 10: CKA as a function of the number of test samples

n

(mean

\pm

std over repeated random subsamples; one fixed reservoir per model). “Full”: entire test set (1,320 / 10,000 / 2,264 / 264 samples for FordA / sMNIST / SHD / DVS Gesture), for which only one sample is possible. DVS Gesture has fewer than 500 test samples.

	FordA		sMNIST		SHD		DVS Gesture
Washout	HRF-Res	LIF-Res	HRF-Res	LIF-Res	HRF-Res	LIF-Res	HRF-Res	LIF-Res
0%	.0399	.0078	.2708	.2144	.2143	.1836	.3509	.2835
10%	.0414	.0084	.2707	.2144	.2145	.1829	.3509	.2832
25%	.0365	.0086	.2723	.2155	.2143	.1832	.3509	.2825
50%	.0301	.0069	.2720	.2200	.2142	.1881	.3507	.2819

Appendix

Table 11: CKA after discarding an initial fraction of each trajectory (washout; one fixed reservoir per model). Washout steps at 10/25/50%: FordA 50/125/250; sMNIST 78/196/392; SHD 25/62/125; DVS Gesture 20/50/100.

	FordA		sMNIST
$\sigma$	HRF-Res	LIF-Res	HRF-Res	LIF-Res
0.00	$69.72\pm 0.68$	$67.15\pm 0.66$	$93.64\pm 0.25$	$67.00\pm 1.04$
0.05	$69.42\pm 0.90$	$67.07\pm 0.95$	$77.22\pm 4.07$	$12.46\pm 1.19$
0.10	$70.10\pm 0.81$	$66.39\pm 0.95$	$73.82\pm 3.01$	$12.16\pm 0.63$
0.20	$68.03\pm 0.75$	$62.67\pm 0.80$	$67.14\pm 1.52$	$12.15\pm 0.91$
0.30	$67.25\pm 1.12$	$57.73\pm 0.27$	$59.90\pm 1.34$	$12.04\pm 0.70$

Appendix

Table 12: Test accuracy (%) under additive Gaussian input noise of standard deviation

\sigma

(mean

\pm

std over three reservoirs). The

\sigma=0

row reproduces the clean results of Table 1 (five seeds).

	FordA		sMNIST
Rate	HRF-Res	LIF-Res	HRF-Res	LIF-Res
0.70	$52.02\pm 0.55$	$49.80\pm 1.33$	$7.37\pm 2.83$	$11.22\pm 1.41$
0.80	$53.11\pm 3.04$	$50.66\pm 1.60$	$9.04\pm 1.42$	$13.48\pm 2.86$
0.90	$55.23\pm 1.08$	$53.64\pm 3.73$	$13.06\pm 4.20$	$18.68\pm 1.65$
1.00	$69.72\pm 0.68$	$67.15\pm 0.66$	$93.64\pm 0.25$	$67.00\pm 1.04$
1.10	$57.80\pm 1.50$	$55.68\pm 5.84$	$10.22\pm 0.46$	$25.35\pm 8.25$

Appendix

Table 13: Test accuracy (%) under sampling-rate shifts (rate

=1.0

: original sampling rate; mean

\pm

std over three reservoirs). The rate

=1.0

row reproduces the clean results of Table 1 (five seeds).

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Frequency-Based Reservoir computing

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Open paper AskPDF arXiv

Reservoir computing has emerged as an efficient machine learning framework for predicting time series generated by dynamical systems. In contrast to other machine and deep learning approaches, a reservoir computing trains only the output layer via linear regression, leaving the reservoir (recurrent layer) untrained. This simplification makes reservoir computers easier to train and more amenable to experimentation. However, because current reservoirs consist of networks of randomly connected nodes and require the optimization of numerous hyperparameters, a framework that precisely explains how reservoir computing operates and how it can be optimized remains missing. Here, we propose a frequency-based reservoir inspired by the brain's oscillatory dynamics and its hierarchy of timescales. The frequency-based reservoir can be interpreted as an ensemble of independent oscillatory units, each processing a portion of the input's frequency content. This allows us to understand the reservoir's internal behavior by modeling it as a single unit driven by an external input. Borrowing from the theory of a nonlinear oscillator forced by complex periodic inputs, we found that units of the frequency-based reservoir selectively amplify and store specific input frequencies, which are then used for prediction. The frequency-based reservoir performs as well as or better than equivalent random reservoirs. Furthermore, the frequency-based approach can be optimized to improve short-term prediction, a property that random reservoirs lack. Finally, we show that the frequency-based reservoir can also predict complex spatiotemporal dynamics. Our results show that reservoir computing can be designed using brain properties and theoretical insights borrowed from the physics of forced nonlinear oscillators.

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