arxiv: 2604.14487 · v1 · submitted 2026-04-15 · 💻 cs.LG

Recognition: unknown

Quantization of Spiking Neural Networks Beyond Accuracy

Evan Gibson Smith , Jacob Whitehill , Fatemeh Ganji

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Pith reviewed 2026-05-10 12:44 UTC · model grok-4.3

classification 💻 cs.LG

keywords spiking neural networksquantizationearth mover's distancefiring distributionaccuracydeploymentlearned quantizationuniform quantization

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The pith

Quantization of spiking networks can alter firing patterns even at unchanged accuracy

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Spiking neural networks rely on sparse firing events for efficient computation, but quantization to lower precision can disrupt those firing patterns without affecting classification accuracy. The authors argue this matters for real hardware where firing rates control memory use, energy, and processing speed. They introduce Earth Mover's Distance to quantify how much the distribution of firing rates diverges from the original network. Experiments on SEW-ResNet models show uniform quantization causes more drift than learned quantization methods. This indicates that accuracy alone is insufficient for evaluating quantized spiking networks.

Core claim

Quantization method, clipping range, and bit-width can produce substantially different firing distributions at equivalent accuracy, differences invisible to standard metrics but relevant to deployment, where firing activity governs effective sparsity, state storage, and event-processing load. Earth Mover's Distance is proposed as a diagnostic metric for firing distribution divergence. Uniform quantization induces distributional drift even when accuracy is preserved, while LQ-Net style learned quantization maintains firing behavior close to the full-precision baseline.

What carries the argument

Earth Mover's Distance applied to neuron firing rate distributions to measure behavioral divergence induced by different quantization schemes in spiking neural networks.

Load-bearing premise

That differences in firing distributions measured by Earth Mover's Distance correspond to practically relevant changes in deployment metrics such as sparsity and processing load.

What would settle it

An observation that quantized networks with high Earth Mover's Distance to the baseline show no increase in actual hardware energy use or latency compared to low-distance ones would falsify the practical importance of the metric.

Figures

Figures reproduced from arXiv: 2604.14487 by Evan Gibson Smith, Fatemeh Ganji, Jacob Whitehill.

**Figure 2.** Figure 2: Mean firing rates across layers of trained networks with various weight quantization techniques for 2-bit SEW [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 5.** Figure 5: EMD, dead neuron percentage, and mean firing rate [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗

**Figure 4.** Figure 4: EMD from FP32, mean firing rate, and dead neuron [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

read the original abstract

Quantization is a natural complement to the sparse, event-driven computation of Spiking Neural Networks, reducing memory bandwidth and arithmetic cost for deployment on resource-constrained hardware. However, existing SNN quantization evaluation focuses almost exclusively on accuracy, overlooking whether a quantized network preserves the firing behavior of its full-precision counterpart. We demonstrate that quantization method, clipping range, and bit-width can produce substantially different firing distributions at equivalent accuracy, differences invisible to standard metrics but relevant to deployment, where firing activity governs effective sparsity, state storage, and event-processing load. To capture this gap, we propose Earth Mover's Distance as a diagnostic metric for firing distribution divergence, and apply it systematically across weight and membrane quantization on SEW-ResNet architectures trained on CIFAR-10 and CIFAR-100. We find that uniform quantization induces distributional drift even when accuracy is preserved, while LQ-Net style learned quantization maintains firing behavior close to the full-precision baseline. Our results suggest that behavior preservation should be treated as an evaluation criterion alongside accuracy, and that EMD provides a principled tool for assessing it.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper shows uniform quantization shifts SNN firing distributions even at matched accuracy while learned quantization does not, measured via EMD, but never quantifies what that shift actually costs in spike rate or hardware events.

read the letter

The core observation is straightforward: on SEW-ResNet with CIFAR-10 and CIFAR-100, uniform quantization produces noticeably higher Earth Mover's Distance between full-precision and quantized firing distributions than LQ-Net style learned quantization, even when accuracy numbers line up. They treat this as a diagnostic that standard accuracy metrics miss, and they run the comparison across weight and membrane quantization at several bit widths and clipping ranges. That is the actual new piece; prior SNN quantization work has not systematically tracked distributional drift in this way.

Referee Report

1 major / 3 minor

Summary. The paper claims that quantization of spiking neural networks (SNNs) should be evaluated not only on accuracy but also on preservation of firing behavior, as different methods can induce distributional drift in spike rates even at matched accuracy. Using SEW-ResNet architectures on CIFAR-10 and CIFAR-100, systematic experiments compare uniform quantization against learned quantization (LQ-Net style) for both weights and membrane potentials. The authors propose Earth Mover's Distance (EMD) as a diagnostic metric and report that uniform quantization produces substantially larger EMD divergences from the full-precision baseline than learned quantization, while accuracies remain comparable. They conclude that behavior preservation merits consideration alongside accuracy for deployment on resource-constrained hardware.

Significance. If the central empirical findings hold, the work could usefully broaden SNN quantization evaluation beyond accuracy-centric benchmarks by highlighting how quantization choices affect the sparse, event-driven nature of SNN computation. The proposal of EMD as a principled, distribution-sensitive metric is a concrete contribution that could be adopted in future studies. The experiments are systematic across bit-widths and quantization targets, providing a useful reference point for the community.

major comments (1)

[Abstract and Results] Abstract and Results section: The motivation that firing-distribution differences (via EMD) are relevant to deployment because 'firing activity governs effective sparsity, state storage, and event-processing load' is asserted but not supported by any direct measurements or correlations with concrete metrics such as average spike rate, layer-wise event density, effective sparsity, or simulated hardware event-processing cost. This leaves the practical significance of the reported EMD gaps dependent on an untested assumption.

minor comments (3)

[Experimental evaluation] The manuscript should report error bars, standard deviations, or statistical significance tests for the EMD and accuracy values across multiple runs or seeds.
[Methods] Clarify the precise construction of the firing distributions used for EMD (e.g., binning of spike times, normalization, or per-layer vs. network-wide aggregation).
[Discussion] Add a short discussion of potential limitations in generalizing the SEW-ResNet/CIFAR results to other SNN architectures or larger-scale datasets.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful and constructive review. The feedback identifies a valuable opportunity to strengthen the empirical grounding of our motivation. We address the comment in detail below and will revise the manuscript accordingly.

read point-by-point responses

Referee: [Abstract and Results] Abstract and Results section: The motivation that firing-distribution differences (via EMD) are relevant to deployment because 'firing activity governs effective sparsity, state storage, and event-processing load' is asserted but not supported by any direct measurements or correlations with concrete metrics such as average spike rate, layer-wise event density, effective sparsity, or simulated hardware event-processing cost. This leaves the practical significance of the reported EMD gaps dependent on an untested assumption.

Authors: We agree that the manuscript would benefit from explicit empirical support for the deployment relevance of the observed EMD differences. While the link between spike-rate distributions and hardware metrics such as effective sparsity and event-processing load is standard in the neuromorphic literature, we did not include direct correlations in the original submission. In the revised version we will add a dedicated analysis subsection that reports (i) layer-wise average spike rates and their standard deviations for each quantization method, (ii) the Pearson correlation between per-layer EMD and the resulting spike-rate shift, and (iii) a simple event-count-based estimate of processing load derived from the measured spike densities. These additions will make the practical significance of the EMD gaps concrete rather than assumed. revision: yes

Circularity Check

0 steps flagged

No circularity: purely empirical comparison of quantization methods via standard metrics

full rationale

The paper reports experimental results on SEW-ResNet models trained on CIFAR-10/100, comparing uniform vs. learned (LQ-Net) quantization for weights and membrane potentials. It measures accuracy and applies the standard Earth Mover's Distance (EMD) to observed spike-count histograms. No equations, derivations, or first-principles claims are present that could reduce to fitted parameters, self-definitions, or self-citations by construction. The EMD usage is a direct, non-circular diagnostic on empirical distributions; deployment relevance is asserted but not derived mathematically. This matches the expected non-circular outcome for an empirical evaluation paper.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No explicit free parameters, axioms, or invented entities stated in the abstract; the work rests on standard ML assumptions about quantization and the relevance of firing rates to hardware cost.

pith-pipeline@v0.9.0 · 5486 in / 976 out tokens · 23471 ms · 2026-05-10T12:44:23.945093+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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