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arxiv: 2506.06374 · v4 · submitted 2025-06-04 · 💻 cs.NE

SiLIF: Structured State Space Model Dynamics and Parametrization for Spiking Neural Networks

Pith reviewed 2026-05-19 11:01 UTC · model grok-4.3

classification 💻 cs.NE
keywords spiking neural networksstate space modelsleaky integrate-and-firespeech recognitionevent-based processinggradient stabilityneuromorphic computingsynaptic delays
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The pith

Two SiLIF neuron models inspired by state space models achieve new state-of-the-art performance among spiking models on speech recognition tasks.

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

This paper introduces two variants of leaky integrate-and-fire neurons that borrow discretization and initialization techniques from state space models to stabilize gradient flow during training. The first variant adds a learnable timestep with logarithmic reparametrization to a two-state neuron, while the second incorporates complex-state structures to support oscillatory dynamics. These changes target the instability that has limited scaling of multi-state spiking neurons on long sequences. A sympathetic reader would care because the resulting models deliver superior accuracy on event-based and raw-audio datasets while using less computation than non-spiking alternatives.

Core claim

The authors show that extending two-state spiking neurons with a learnable discretization timestep and logarithmic reparametrization, and further embedding the initialization and structure of complex-state SSMs to enable oscillatory regimes, produces stable gradients and new state-of-the-art results among spiking neuron models on both event-based and raw-audio speech recognition datasets.

What carries the argument

The SiLIF models, which apply SSM-style learnable discretization timestep and logarithmic reparametrization to the recurrent dynamics of two-state and complex-state leaky integrate-and-fire neurons.

If this is right

  • The models exhibit a favorable performance-efficiency trade-off relative to standard state space models.
  • They surpass SSM accuracy while requiring only half the computational cost through the addition of synaptic delays.
  • The parametrization supports more reliable scaling of spiking networks to longer audio and event sequences.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same discretization and reparametrization steps could be tested on other multi-state spiking neuron families to check for similar stability gains.
  • Hardware implementations might gain extra energy savings by combining the reported synaptic delays with the reduced state count.
  • Applying the oscillatory regime to visual or tactile event streams could reveal whether the benefits extend beyond audio tasks.

Load-bearing premise

The assumption that the SSM-inspired discretization, logarithmic reparametrization, and complex-state initialization will produce stable gradient flow through the spiking dynamics on the tested datasets without post-hoc tuning or dataset-specific adjustments.

What would settle it

Training the SiLIF models on the same speech recognition datasets and finding that gradients explode or performance falls below prior spiking baselines when the logarithmic reparametrization or complex initialization is removed would falsify the central claim.

Figures

Figures reproduced from arXiv: 2506.06374 by Emre Neftci, Lyubov Dudchenko, Maxime Fabre, Younes Bouhadjar.

Figure 1
Figure 1. Figure 1: Proposed method to distill features of modern structured state space models (SSMs) to build [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: Test accuracy and synaptic operations (SOP) with standard deviation for different models [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Neuronal dynamics of the (a) CadLIF and (b) SiLIF models pre-trained on the SSC task. [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: SHD test accuracy with standard deviation interval on 5 runs for models over depth with [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: As described by Izhikevich [23], the RF neuron follows these neuronal dynamics: ut = ut−1 + ∆t((α real + iαimg)ut−1 + It) − θst−1 st = (Re(ut) ≥ θ), (7) where α real and α img are the trainable parameters, obtained directly from the discrete form. As for the gap between the AdLIF and our SiLIF model, a first difference with the C-SiLIF is the parametrization of the model, as the C-SiLIF model focus on trai… view at source ↗
Figure 6
Figure 6. Figure 6: Impact of incremental SSM-imported features on performance on the SHD dataset from [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗
read the original abstract

Multi-state spiking neurons combine sparse binary activations with rich second-order nonlinear recurrent dynamics, making them a promising alternative to standard deep learning models. However, gradient propagation through these dynamics often leads to instabilities that hinder scalability and performance. Inspired by the stable training and strong performance of state space models (SSMs) on long sequences, we introduce two SSM-inspired Leaky Integrate-and-Fire (SiLIF) neuron models. The first extends a two-state neuron with a learnable discretization timestep and logarithmic reparametrization, while the second additionally incorporates the initialization scheme and structure of complex-state SSMs, enabling oscillatory regimes. Our two SiLIF models achieve new state-of-the-art performance among spiking neuron models on both event-based and raw-audio speech recognition datasets. We further demonstrate a favorable performance-efficiency trade-off compared to SSMs, even surpassing them while using half the computational cost through the use of synaptic delays. Our code is available at https://github.com/Maxtimer97/SSM-inspired-LIF.

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.

Referee Report

3 major / 2 minor

Summary. The paper introduces two SSM-inspired Leaky Integrate-and-Fire (SiLIF) neuron models. The first extends a two-state neuron with a learnable discretization timestep and logarithmic reparametrization; the second adds complex-state SSM initialization and structure to enable oscillatory regimes. The authors claim these models achieve new state-of-the-art performance among spiking neuron models on event-based and raw-audio speech recognition datasets, while providing a favorable performance-efficiency trade-off versus standard SSMs through the use of synaptic delays. Code is released.

Significance. If the performance gains hold under matched training conditions and the parametrizations demonstrably improve gradient stability without dataset-specific tuning, the work could usefully transfer SSM training techniques to spiking networks for long-sequence tasks. The explicit code release supports reproducibility.

major comments (3)
  1. [§4, Tables 1-2] §4 (Experiments) and Tables 1-2: The SOTA claims among spiking neuron models on both datasets are load-bearing but rest on baseline comparisons whose details (hyperparameter search budget, network widths, optimizer settings, data splits, and whether baselines were re-tuned under the identical protocol) are not reported. Without this, it is impossible to attribute any delta to the SSM-inspired discretization and reparametrization rather than unmatched experimental conditions.
  2. [§4.3] §4.3 and associated ablation text: No ablation isolates the individual contributions of the learnable timestep, logarithmic reparametrization, and complex-state initialization. The central claim that these SSM-inspired elements produce stable gradient flow and superior performance therefore lacks direct support; the extra degrees of freedom could explain the gains.
  3. [Abstract, §3.2] Abstract and §3.2: The claim of stable training via the new parametrizations is not accompanied by any analysis or metrics of gradient norms, vanishing/exploding behavior, or training curves on the target datasets, leaving the weakest assumption untested.
minor comments (2)
  1. [Figure 2] Figure 2: Axis labels and legend entries for the complex-state variant are difficult to distinguish from the first SiLIF variant.
  2. [§3.1] §3.1: The definition of the logarithmic reparametrization should explicitly state the range constraints applied to the learnable parameters to ensure positivity.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. We address each major point below and outline the revisions we will make to strengthen the experimental rigor and support for our claims.

read point-by-point responses
  1. Referee: [§4, Tables 1-2] §4 (Experiments) and Tables 1-2: The SOTA claims among spiking neuron models on both datasets are load-bearing but rest on baseline comparisons whose details (hyperparameter search budget, network widths, optimizer settings, data splits, and whether baselines were re-tuned under the identical protocol) are not reported. Without this, it is impossible to attribute any delta to the SSM-inspired discretization and reparametrization rather than unmatched experimental conditions.

    Authors: We agree that insufficient detail on the baseline experimental conditions limits the strength of the SOTA claims. In the revised manuscript we will add a dedicated subsection in §4 that fully specifies the hyperparameter search budget (including ranges and number of trials), network widths, optimizer settings, data splits, and training protocol used for all models. We have re-trained the primary baselines (LIF, ALIF, and standard SSM variants) under this identical protocol using the released code, and the updated Tables 1-2 will report these matched results. This will allow readers to attribute performance differences to the proposed parametrizations. revision: yes

  2. Referee: [§4.3] §4.3 and associated ablation text: No ablation isolates the individual contributions of the learnable timestep, logarithmic reparametrization, and complex-state initialization. The central claim that these SSM-inspired elements produce stable gradient flow and superior performance therefore lacks direct support; the extra degrees of freedom could explain the gains.

    Authors: We acknowledge that the current ablations do not fully disentangle the three components. In the revision we will expand §4.3 with a systematic set of ablations that independently enable/disable the learnable timestep, the logarithmic reparametrization, and the complex-state initialization while holding all other factors fixed. Performance deltas on both datasets will be reported, directly addressing whether each SSM-inspired element contributes to the observed gains beyond the added degrees of freedom. revision: yes

  3. Referee: [Abstract, §3.2] Abstract and §3.2: The claim of stable training via the new parametrizations is not accompanied by any analysis or metrics of gradient norms, vanishing/exploding behavior, or training curves on the target datasets, leaving the weakest assumption untested.

    Authors: We agree that direct empirical evidence of gradient stability is needed to support the central motivation. We will add to §3.2 (and the supplementary material) plots of gradient norm statistics across training epochs for SiLIF versus standard LIF neurons on both the event-based and raw-audio datasets. Training curves for loss and accuracy will also be included to demonstrate convergence behavior. These additions will provide concrete metrics on vanishing/exploding gradients and stable training dynamics. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical performance claims rest on new parametrizations and benchmarks, not self-referential fits or definitions.

full rationale

The paper introduces two new neuron models (learnable timestep + log reparametrization; complex-state SSM initialization) and reports their empirical accuracy on speech datasets. No derivation chain reduces a claimed result to its own fitted inputs by construction, nor does any load-bearing premise collapse to a self-citation whose validity is presupposed. The SOTA claim is an experimental outcome rather than a mathematical identity or renamed known pattern; the models add explicit degrees of freedom whose effect is measured against baselines. This is the normal case of a self-contained empirical contribution.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claims rest on standard gradient-based training assumptions for recurrent spiking models plus the new learnable parameters; no new physical entities are postulated.

free parameters (2)
  • learnable discretization timestep
    Introduced in the first SiLIF model to extend the two-state neuron.
  • logarithmic reparametrization
    Used alongside the learnable timestep for stable training.
axioms (1)
  • domain assumption Gradient propagation through spiking dynamics can be stabilized by SSM-style discretization and initialization without additional regularization.
    Invoked to justify the choice of parametrization for avoiding instabilities.

pith-pipeline@v0.9.0 · 5720 in / 1209 out tokens · 44488 ms · 2026-05-19T11:01:03.455308+00:00 · methodology

discussion (0)

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Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. FiTS: Interpretable Spiking Neurons via Frequency Selectivity and Temporal Shaping

    cs.NE 2026-05 unverdicted novelty 7.0

    FiTS spiking neurons improve auditory task performance over LIF baselines by factorizing computation into frequency selectivity and group-delay-based temporal shaping, yielding interpretable per-neuron parameters.

  2. Privacy-preserving fall detection at the edge using Sony IMX636 event-based vision sensor and Intel Loihi 2 neuromorphic processor

    cs.NE 2025-11 unverdicted novelty 4.0

    A neuromorphic edge system using event vision and sparse SNNs on Loihi 2 achieves up to 84% F1 score at 90 mW for privacy-preserving fall detection.

Reference graph

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