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REVIEW 3 major objections 5 minor 53 references

ASRC-SNN: Adaptive Skip Recurrent Connection Spiking Neural Network

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read The paper claims that LIF-based recurrent spiking networks suffer a temporal vanishing-gradient problem, and that skip recurrent connections with learned spans fix it.

desk verdict The empirical skip-connection trick is reproducible and works, but the paper's gradient-vanishing proof does not survive matrix-valued weights. read the letter →

arxiv 2505.11455 v1 pith:I4N44BEE submitted 2025-05-16 cs.NE

Shang Xu , Jiayu Zhang , Ziming Wang , Runhao Jiang , Rui Yan , Huajin Tang This is my paper · ORCID
classification cs.NE
keywords recurrentspikingneuralnetworkstemporalgradientvanishingskipconnectionadaptivespansurrogatelong-termmodelingLIFneuronsoftmaxannealing
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to establish why recurrent spiking neural networks (RSNNs) struggle with long sequences and what to do about it. Treating the LIF neuron and the recurrent connection as one dynamical system, it derives a bound: as long as the recurrent weight obeys $|W^l_2| \le V_{\mathrm{th}}$, the product of temporal Jacobians contracts, so temporal gradients vanish unless the neuron fires at every step. The proposed fix is the skip recurrent connection (SRC), which reaches back $\lambda$ time steps instead of one, and the adaptive version (ASRC), which lets each layer learn its skip span with an annealed softmax. The reason to care is practical: this architectural change improves accuracy on sequential MNIST, permuted sequential MNIST, and speech-command benchmarks, and it works across several spiking neuron models.

What carries the argument

The load-bearing object is the temporal Jacobian chain in Eqs. (7)--(8). Each adjacent-step factor is $\alpha + (W^l_2 - \alpha V_{\mathrm{th}})H(U^l[t])$, and the bound $H(U) \le 1/V_{\mathrm{th}}$ makes each factor have modulus at most $1$ when $|W^l_2| \le V_{\mathrm{th}}$, so the $k$-step product contracts toward zero. The skip recurrent connection replaces $W^l_2 S^l[t-1]$ with $W^l_2 S^l[t-\lambda]$, giving the gradient a direct path that does not multiply through the intermediate steps; the ASRC mechanism then uses a temperature-scaled softmax kernel over $T_\lambda$ candidate lags, with temperature decaying exponentially, so each layer converges to a single chosen lag at test time. This chain-bound-and-shortcut pair is what carries the argument from gradient analysis to architecture.

What would settle it

A controlled re-run with identical hidden sizes, optimizers, epochs, and per-dataset hyperparameter search across many seeds would falsify the empirical claim if SRC/ASRC do not beat the vanilla RSNN outside seed noise; separately, measuring temporal gradient norms during training would falsify the mechanism claim if SRC/ASRC do not show larger temporal gradients than vanilla RSNN.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is that in a vanilla LIF-based RSNN the temporal Jacobian $\partial U^l[t+k]/\partial U^l[t]$ factorizes into a product of per-step terms $\alpha + (W^l_2 - \alpha V_{\mathrm{th}})H(U^l[t])$, and because the surrogate spike derivative $H$ is bounded by $1/V_{\mathrm{th}}$, the whole product obeys $|\partial U^l[t+k]/\partial U^l[t]| \le \max(\alpha^k, |W^l_2/V_{\mathrm{th}}|^k) \le 1$ whenever $|W^l_2| \le V_{\mathrm{th}}$. Equality, which would keep gradients alive, forces the neuron to fire at every time step and destroys temporal discriminability. The paper therefore claims RSNNs are inherently prone to temporal gradient vanishing, and inserting a skip recurrent connection $S^l[t-\lambda]$ in place of $S^l[t-1]$ gives gradients a shortcut around the contracting chain; the ASRC variant then learns which lag each layer should use by annealing a temperature-scaled softmax over $T_\lambda$ candidate lags until it behaves as a hardmax. The empirical claim is that SRC-SNN beats vanilla RSNN by a large margin on all four benchmark datasets and that ASRC-SNN goes further, with per-layer lags that differ across layers and datasets.

Load-bearing premise

The load-bearing premise is that the reported accuracy gains of SRC/ASRC over vanilla RSNNs reflect the skip-connection mechanism and not per-dataset hyperparameter tuning or single-run noise, since the paper reports no repeated-seed statistics and takes baselines from other papers with different setups.

Editorial extensions

If this is right

  • SRC-SNN improves over vanilla RSNN on S-MNIST, PS-MNIST, SSC, and GSC by changing only the recurrent span, with no extra inference-time compute cost.
  • ASRC-SNN outperforms SRC-SNN on all four benchmarks and is less sensitive to the maximum skip span $T_\lambda$ once it exceeds a threshold, easing hyperparameter search.
  • The improvement transfers across neuron models: SRC/ASRC consistently beat vanilla recurrent versions of PLIF, GLIF, CLIF, and TC-LIF, with ASRC usually ahead.
  • On the harder SCIFAR task with six layers, SRC-SNN gains more than 8% over RSNN and ASRC-SNN gains more than 5% over SRC-SNN, with more stable accuracy.
  • Because the learned final lags vary across layers and datasets, the data-dependent optimal span is something ASRC discovers automatically, whereas SRC needs it tuned per layer.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper, the same annealed-softmax selection could learn positions in space as well as time, for instance the nonzero offsets in dilated convolution kernels, turning a manually designed dilation pattern into a learned one.
  • If the gradient mechanism is the true driver, SRC/ASRC networks should exhibit measurably larger temporal gradient norms than vanilla RSNNs early in training; the paper does not report such a measurement, so this is a testable prediction rather than a demonstrated fact.
  • The layer-wise lags in the paper's Table 5 hint that shallow layers tend to pick short lags and deep layers longer ones on speech tasks; one could test whether this pattern corresponds to the temporal receptive fields each layer needs.
  • Dropping the temperature schedule and instead penalizing the variance of the softmax output, as the paper lists as future work, could remove the decay-factor hyperparameter while preserving the hardmax limit.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper proposes a Skip Recurrent Connection (SRC) for LIF-based recurrent spiking neural networks (RSNNs), replacing the vanilla one-step recurrence with a recurrence that spans \lambda time steps, and an adaptive variant (ASRC) that learns the skip span per layer using a temperature-scaled softmax kernel. The theoretical motivation is a gradient analysis of vanilla LIF-based RSNNs (Eqs. 5-8) claiming that temporal gradients vanish when the recurrent weight satisfies |W2| <= Vth, and that this can only be avoided if every neuron fires at threshold at every step. Empirically, the authors report that SRC-SNN improves accuracy over vanilla RSNNs and prior SNN baselines on S-MNIST, PS-MNIST, SSC, GSC, and SCIFAR, and that ASRC-SNN further improves on SRC-SNN and shows robustness to the choice of the maximum skip span T_lambda.

Significance. If the empirical findings hold, the paper introduces a simple, hardware-friendly architectural modification that improves long-sequence accuracy in RSNNs, and the adaptive softmax-based selection of discrete temporal offsets is an interesting mechanism with potential extensions to spatial offsets. The authors provide code, and the experimental scope spans several benchmarks and ablations, including replacement of the LIF neuron with other neuron models and sparsity conditions. However, the theoretical gradient bound in Eqs. (5)-(8) is informal and, as shown by a matrix counterexample, not correct as stated; this weakens the central motivation for SRC. In addition, the empirical support for the superiority of ASRC over SRC is limited by the absence of multiple seeds or error bars, given that the reported differences are only 0.1-0.3 percentage points. The paper's significance therefore rests on the empirical claims, which need stronger statistical and baseline support.

major comments (3)
  1. [Section 4.2, Table 1 and Figures 2-4] The bound on the temporal Jacobian product is derived by treating the factor (alpha + (W2 - alpha Vth) H(U)) as a scalar or as a product of commuting terms, but W2 is a matrix and H(U) is a diagonal matrix of surrogate derivatives. The spectral norm of a product of non-commuting matrices is not bounded in the manner claimed. A concrete counterexample is alpha=1, Vth=1, W2 = [[0,1],[1,0]] (so ||W2|| = Vth), and H(U) = diag(1,0). The per-step Jacobian in Eq. (5) becomes [[0,0],[1,1]], whose spectral norm is sqrt(2) > 1. Thus temporal gradients can grow across a single step even when ||W2|| <= Vth, and the conclusion that gradients necessarily vanish unless every neuron fires at threshold does not follow. Since this analysis is the stated motivation for the SRC architecture, it must be corrected (for example, by using appropriate spectral-norm conditions or by weakening the claim) before the theoretical contribution can be accepted.
  2. [Section 4.1, Table 1] No standard deviations or multiple seeds are reported for any result. The claimed advantage of ASRC over SRC is only 0.19 points on S-MNIST (99.57 vs 99.38), 0.10 points on SSC (81.93 vs 81.83), and 0.11 points on GSC (96.29 vs 96.18). These differences are likely within the run-to-run variance of SNN training with surrogate gradients. Without repeated trials and a paired significance test, the statement in the abstract and Section 4.3.2 that ASRC consistently outperforms SRC is not supported. Please report mean and standard deviation over at least five seeds for all main results and key ablations.
  3. [Section 4.1] The baseline numbers in Table 1 are copied from prior publications with different architectures, parameter counts, data preprocessing, and training setups (e.g., TC-LIF [21], PMSN [27], DCLS-Delays [29]). The only controlled vanilla RSNN baseline appears in Figure 2 for PS-MNIST and SSC, but it is not included in Table 1 for all datasets, and its hyperparameters are not specified. Without a same-protocol vanilla RSNN trained under identical settings (same optimizer, epochs, hidden sizes, and preprocessing as SRC-SNN/ASRC-SNN), the claim that SRC significantly outperforms vanilla RSNN is not fully established. Please add such baselines for all datasets, or clearly report the existing RSNN numbers in Table 1.
minor comments (5)
  1. [Section 3.4.1] There are several typos and inconsistent abbreviations: 'Resluts' in Section 4.2, 'hyparameter' in Section 4.3.1, 'diffirent' in the caption of Figure 4, and inconsistent spelling of 'SCIFAR' / 'SCFAR' in Appendix A.1. These should be corrected.
  2. [Section 5] The text says that during the testing phase Eq. (11) is used to compute p_l, but Eq. (11) is a limit expression, not an algorithm. The implementation should be described precisely, including how ties in the argmax are resolved when the temperature goes to zero.
  3. [Section 4.3.2] The related work and discussion should more explicitly position the contribution with respect to [40], which already analyzed skip recurrent connections, and to [47] on dilated convolutions with learnable spacings, since ASRC learns a discrete position in a similar spirit. Currently this is only mentioned as future work, which understates the prior art and should be clarified in Related Work.
  4. [Appendix A.2] The 'robustness' claim for ASRC is based on insensitivity to T_lambda in Figures 2c and 2d, but the fluctuations across different T_lambda are still several tenths of a percent and no error bars are shown. Please clarify what 'robustness' means and support it with quantitative variability measures.
  5. [Appendix A.2] The description of the learning rate schedule for the softmax kernel would benefit from clarification: the text says the learning rate is set to 100x the global learning rate, while Table 2 gives specific values; please reconcile these and describe the schedule precisely.

Circularity Check

0 steps flagged · score 0.0 of 10

No meaningful circularity found: the gradient analysis is self-contained and the empirical claims do not reduce to fitted inputs or self-citations.

full rationale

The paper's only formal derivation is the temporal gradient analysis in Section 3.2. It starts from the LIF update equations (Eqs. 1-4) and surrogate gradient definition (Eq. 6), then derives the temporal Jacobian product (Eq. 7) and uses Eq. (8) to motivate skip recurrent connections. This is a self-contained mathematical chain, not a quantity fitted to benchmark labels and then relabeled as a prediction. The proposed SRC and ASRC architectures are not defined in terms of the target accuracies: λ and Tλ are selected by hyperparameter search (Tables 2-3), which affects how strong the empirical claims are but is ordinary tuning rather than circularity. The citation of [40] for the effectiveness of skip recurrent connections is not a self-citation, and it is not load-bearing because the paper explicitly distinguishes its SRC from [40] by relying on the LIF neuron's intrinsic self-connection for adjacent time steps. Self-references in the paper ([15], [16]) appear only in background statements about SNN performance, not in the derivation of the central claim. No step reduces an output equation to an input equation by construction, and no fitted parameter is renamed as a prediction. Possible mathematical weakness in Eq. (8) for matrix-valued recurrent weights would be a correctness concern, not circularity.

Assumptions & free parameters 4 free parameters · 4 assumptions · 1 invented entities

The paper relies on the standard LIF neuron model and surrogate-gradient training; it adds no new physical entities. The main free choices are the recurrence skip span lambda in SRC and the kernel length T_lambda in ASRC, both tuned per dataset, plus the temperature schedule. ASRC is a new mechanism, though its softmax-to-hardmax selection is a known discrete-selection trick used in delay-learning works.

free parameters (4)
  • lambda (skip coefficient in SRC-SNN) = 16 (S-MNIST), 12 (PS-MNIST), 3 (SSC), 4 (GSC), 16 (SCIFAR)
    Selected by validation search per dataset (Table 3); the paper notes sensitivity on SSC.
  • T_lambda (softmax kernel length in ASRC-SNN) = 41 (S-MNIST), 51 (PS-MNIST), 6 (SSC), 21 (GSC), 11 (SCIFAR)
    Chosen per dataset (Table 3); the robustness claim is that sensitivity is low once T_lambda is large.
  • Temperature decay factor = 0.96 per epoch
    Set by hand; controls the annealing schedule from soft to hard selection (Section 3.4.1).
  • Softmax kernel learning rate multiplier = 0.1, 0.25, or 0.05 (100x global learning rate)
    Hyperparameter for the logits wl used in the softmax kernel (Table 2).
assumptions (4)
  • domain assumption LIF neuron dynamics with soft reset (Eqs. 1-3) describe the temporal behavior of each layer.
    Standard in the SNN literature; the paper's gradient analysis is built on this model.
  • domain assumption The surrogate gradient triangle function (Eq. 6) with width gamma=Vth approximates the Heaviside derivative for training.
    Training relies on this surrogate; the bound |dSl/dUl| <= 1/Vth follows from it.
  • standard math The worst-case temporal Jacobian product can be bounded by treating the surrogate gradient as maximized at every step (Eqs. 7-8).
    Used to conclude gradient vanishing; the extreme case requires the neuron to fire at every time step.
  • domain assumption The low-temperature softmax converges to hardmax (Eq. 11), and using hardmax at test time preserves or improves performance.
    Justifies replacing the annealed softmax with one-hot spans during testing (Section 3.4.1).
invented entities (1)
  • Adaptive Skip Recurrent Connection (ASRC) with temperature-scaled softmax kernel independent evidence
    purpose: Selects per-layer temporal skip span by annealing a softmax over candidate lags to a hardmax.
    The learned final spans are documented in Table 5 and benchmark accuracy provides an external handle. The mechanism is a method rather than a new physical entity.

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Cite this review

Pith. "Pith review of ASRC-SNN: Adaptive Skip Recurrent Connection Spiking Neural Network." pith.science (2026). https://pith.science/paper/I4N44BEE

@misc{pith2026250511455,
  author       = {Pith},
  title        = {Pith review of: ASRC-SNN: Adaptive Skip Recurrent Connection Spiking Neural Network},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/I4N44BEE}},
  note         = {Machine review of arXiv:2505.11455}
}
read the original abstract

In recent years, Recurrent Spiking Neural Networks (RSNNs) have shown promising potential in long-term temporal modeling. Many studies focus on improving neuron models and also integrate recurrent structures, leveraging their synergistic effects to improve the long-term temporal modeling capabilities of Spiking Neural Networks (SNNs). However, these studies often place an excessive emphasis on the role of neurons, overlooking the importance of analyzing neurons and recurrent structures as an integrated framework. In this work, we consider neurons and recurrent structures as an integrated system and conduct a systematic analysis of gradient propagation along the temporal dimension, revealing a challenging gradient vanishing problem. To address this issue, we propose the Skip Recurrent Connection (SRC) as a replacement for the vanilla recurrent structure, effectively mitigating the gradient vanishing problem and enhancing long-term temporal modeling performance. Additionally, we propose the Adaptive Skip Recurrent Connection (ASRC), a method that can learn the skip span of skip recurrent connection in each layer of the network. Experiments show that replacing the vanilla recurrent structure in RSNN with SRC significantly improves the model's performance on temporal benchmark datasets. Moreover, ASRC-SNN outperforms SRC-SNN in terms of temporal modeling capabilities and robustness.

Figures

Figures reproduced from arXiv: 2505.11455 by the authors.

Figure 1
Figure 1. This figure demonstrates the flow of temporal information within the LIF neurons of the [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Effects of λ/Tλ on SRC-SNN/ASRC-SNN in SSC and PS-MNIST benchmarks. (a)-(b): Impact of λ on SRC-SNN; (c)-(d): Impact of Tλ on ASRC-SNN. All results are shown on PS-MNIST and SSC datasets respectively. (GSC) and Spiking Google Speech Commands (SSC). We use a simple model architecture consisting of three hidden layers. Furthermore, we evaluate the effectiveness of SRC and ASRC on the more challenging sequential CIFAR … view at source ↗
Figure 3
Figure 3. The impact of the membrane potential decay factor [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: The comparison between SRC-SNN and ASRC-SNN under complex datasets and sparse [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: These plots present heatmaps of the weight distributions of the Softmax kernels across [PITH_FULL_IMAGE:figures/full_fig_p016_5.png]
Figure 6
Figure 6. Figure 6: The accuracy change plot during the training of ASRC-SNN. [PITH_FULL_IMAGE:figures/full_fig_p017_6.png]

Discussion (0). Continue with ORCID to comment.

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.