IKUN: Initialization to Keep snn training and generalization great with sUrrogate-stable variaNce

Da Chang; Deliang Wang; Xiao Yang

REVIEW 5 major objections 6 minor 12 references

IKUN: Initialization to Keep snn training and generalization great with sUrrogate-stable variaNce

T0 review · 5 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read A surrogate-aware weight initialization, IKUN, claims to stabilize signal and gradient variance in spiking neural networks, reaching accuracy thresholds in up to 59% fewer epochs.

desk verdict A genuinely new initialization formula, but the proof is missing and the experiments are too thin to carry the claim. read the letter →

arxiv 2411.18250 v1 pith:7LIEVVF2 submitted 2024-11-27 cs.LG cs.AI

Da Chang , Deliang Wang , Xiao Yang This is my paper · ORCID

classification cs.LGcs.AI

keywords spikingneuralnetworksweightinitializationsurrogategradientvariancestabilizationvanishingandexplosionHessianspectrumflatminimaFashionMNIST

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

Spiking neural networks trained with surrogate gradients usually inherit ANN-style initializations that ignore how spiking changes signal statistics. This paper claims a new initialization, IKUN, can fix that by choosing each layer's weight variance so that forward signal variance stays constant and backward gradients neither vanish nor explode. The rule uses the surrogate gradient's expected squared derivative as a correction factor, replacing the plain fan-in/fan-out scaling of Xavier and Kaiming. On FashionMNIST with a two-layer convolutional SNN, IKUN reaches high-accuracy thresholds in up to roughly 59% fewer epochs under SGD and 42% fewer under Adam, reaching 95% training and 91% test accuracy, and its Hessian spectrum looks flat and nearly all positive.

What carries the argument

The load-bearing object is the surrogate-stable variance condition of Equation (8), an SNN analogue of Xavier and Kaiming initialization. The surrogate gradient $f'$ is the smooth derivative of the spiking activation used during backpropagation in place of the non-differentiable spike function. IKUN sets $\sigma_W^2 = \alpha / (\mathrm{fanin} \cdot \sigma_X^2 \cdot \mathbb{E}[f'(H)^2])$, so the scale of the random weights is inversely proportional to the expected squared surrogate gradient; IKUN v2 replaces $\mathrm{fanin}$ with $\mathrm{fanin}+\mathrm{fanout}$ in the denominator. This factor carries the argument: it converts the surrogate's effect on backward gradients into a per-layer variance-balance condition, exactly as ReLU's half-wave rectification enters Kaiming initialization.

What would settle it

Train the reported architecture at greater depth (say ten layers) or with random spike-train inputs, and measure the variance of the membrane potential at each layer and time step. IKUN predicts flat variance and bounded gradient norms; if variance grows or gradients vanish as depth or time steps increase, the balancing condition fails.

Watch

Extended reading notes

Core claim

The paper's central claim is Theorem 1: in an SNN layer with membrane potential $H[t] = \tau V[t-1] + \sum_i w_i X_i[t]$ and weights $w_i \sim \mathcal{N}(0, \sigma_W^2)$, the condition $\sigma_W^2 = \alpha / (\mathrm{fanin} \cdot \sigma_X^2 \cdot \mathbb{E}[f'(H)^2])$ keeps signal variance stable during forward propagation and prevents gradient vanishing or explosion during backpropagation. A second version, IKUN v2, uses $\mathrm{fanin}+\mathrm{fanout}$ in the denominator to balance input and output dimensions. The authors support the theorem with experiments on a two-layer convolutional SNN trained on FashionMNIST, where IKUN reaches 95% training and 91% test accuracy in fewer epochs than Xavier, Kaiming, LeCun, and normal initialization, and where trained models show Hessian eigenvalues concentrated near zero on the positive side, which they interpret as convergence to flat minima with better generalization.

Load-bearing premise

The proof assumes each layer's weighted input is a zero-mean Gaussian whose variance factorizes as fanin times weight variance times input variance, so the only effect of spiking is the scalar $\mathbb{E}[f'(H)^2]$; if temporal accumulation or non-Gaussian inputs break that, the variance condition stops holding.

Editorial extensions

If this is right

IKUN reaches accuracy thresholds in up to 59.38% fewer epochs under SGD and 42.31% fewer under Adam compared with standard initializations on the reported FashionMNIST setup.
Trained models show a nearly all-positive Hessian spectrum close to zero, which the paper links to flat minima and improved generalization.
The method is designed to work with any surrogate gradient (sigmoid, tanh, or linear), so the same initialization rule transfers across surrogate choices.
IKUN v2's fanin+fanout variant explicitly accounts for both input and output dimensions, making it suitable for convolutional and other non-square layers.
The gains appear under both SGD and Adam, whereas the baselines the paper tests do not dominate on both optimizers at once.

Reading between the lines

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

Editorial inference: the variance-balance argument could be extended to deep or recurrent SNNs by replacing the static $\mathbb{E}[f'(H)^2]$ with a time-averaged or layer-dependent value, but the paper does not prove that extension.
Editorial inference: if the condition holds at scale, SNN libraries could adopt an IKUN-style default instead of Kaiming, removing a common source of instability in deep spike-based models.
Editorial inference: the flat-minima result hints that IKUN may combine well with sharpness-aware optimizers or pruning, though the paper does not test such combinations.
Editorial inference: because the condition depends on $\sigma_X^2$, input encoding (rate vs. temporal) should change the optimal initialization; testing IKUN under temporal coding would be a natural next step.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Colleague,

IKUN is a variance-preserving initialization for SNNs that folds in a surrogate-gradient term, giving formulas like sigma_W^2 = alpha / (fanin * sigma_X^2 * E[f'(H)^2]) and a fan-in+fan-out variant. That specific form does not appear in the paper's cited ANN initialization literature, and it is a natural extension of Xavier/Kaiming logic to the surrogate-gradient setting. So the core idea is new in a modest, useful way.

What the paper does well: it correctly identifies that SNNs break the forward/backward symmetry that classic init methods assume, and it tries to account for the surrogate gradient explicitly. The Hessian analysis, though limited, is a reasonable extra probe. The authors also honestly note in Section 5 that they only used a two-layer CSNN on a fixed FashionMNIST subset with constrained compute. That honesty is to their credit.

The soft spots are load-bearing. Theorem 1's proof is deferred to an appendix that is not in the preprint, so the central guarantee is unverifiable. More concerning, the stress-test argument lands: Eq. 8 balances only the instantaneous input sum wi Xi[t] and ignores the tau V[t-1] recurrence, the reset, and the threshold. LIF variance propagation is temporal; a single per-layer condition of this form cannot follow from Eq. 7 without extra assumptions about stationarity or independence that are never stated. The use of E[f'(H)^2] in a forward-variance formula is also conceptually odd, since that term comes from backpropagation, and the expectation is never defined. Alpha is a free knob that could in principle absorb the gap, which makes the formula underdetermined as a theoretical statement.

Empirically, the evidence is thin: one dataset, no seeds or error bars, and the reported speedups are threshold-dependent and not consistent across optimizers (IKUN underperforms Kaiming under Adam in some plots). The Hessian trace results are suggestive but not conclusive, and the claim about flat minima is not tied to any statistical test.

Bottom line: the idea deserves a proper treatment, but this version does not support its own claims. A revised paper with the proof made explicit, alpha and expectation specified, multi-seed experiments on at least one more dataset, and code that runs would be worth refereeing. As it stands, I would not send it to peer review; I would encourage the authors to resubmit with those gaps closed.

For us: I would only bring this to reading group as a case study in how variance-preservation arguments can silently skip temporal dynamics.

Referee Report

5 major / 6 minor

Summary. The paper proposes IKUN, a weight-initialization scheme for spiking neural networks trained with surrogate gradients. The central theoretical claim (Theorem 1, Section 3.2) is that setting the weight variance according to Eq. (8) stabilizes forward signal variance and prevents gradient vanishing or explosion for the LIF-type dynamics in Eq. (7). The authors report experiments on a two-layer convolutional SNN on Fashion-MNIST, claiming faster convergence and better generalization than Xavier, Kaiming, LeCun, and default initialization, and support this with Hessian eigenvalue and trace analyses. The proof of Theorem 1 is deferred to an appendix that is absent from the preprint.

Significance. If the theoretical result were correct, IKUN would be a useful plug-and-play initialization for surrogate-gradient SNN training, and the paper deserves credit for open-sourcing the code and for examining multiple surrogate-gradient compatibility questions. However, the mathematical core is unverified, the variance condition as stated omits the recurrent and spike-reset structure of the neuron model, and the empirical evidence is limited to a single small dataset with no error bars. The paper also contains an inconsistency between the reported epoch-reduction percentages and the numbers in Table 1. These issues are load-bearing for the paper's central claims.

major comments (5)

[Section 3.2, Eqs. (7)-(8)] The variance condition is asserted for the recurrent dynamics H[t] = tau V[t-1] + sum_i w_i X_i[t], but Eq. (8) balances only the instantaneous input term. From Eq. (7), Var(H[t]) includes tau^2 Var(V[t-1]) and a covariance term with the input sum; neither appears in Eq. (8). The theorem also uses E[f'(H)^2], a surrogate-gradient quantity from the backward pass, to control forward variance, although the forward nonlinearity is a spike-and-reset operation whose output variance depends on the firing probability, not on f'. The proof is deferred to an appendix that is not present in the preprint, so these gaps cannot be checked.
[Section 3.2, Eq. (8)] Equation (8) is not an explicit initialization rule. The expectation E[f'(H)^2] is over an unspecified distribution of H, and H depends on sigma_W through Eq. (7), making the equation a fixed-point condition. The threshold Vthreshold = mu H introduces an additional unspecified parameter mu, and alpha is described only as a given hyperparameter with no value reported in Section 4. Without specifying these quantities, Eq. (8) cannot be instantiated or reproduced.
[Section 3.2, Theorem 1] The gradient-vanishing/explosion claim is not supported because backpropagation through time is ignored. The temporal recursion contributes products of the leakage factor tau, together with the reset mechanism, to the gradient Jacobian; any variance balance for gradients must account for these terms and the time horizon. Equation (8) contains no tau and no time dependence, so the theorem's conclusion about backpropagation does not follow from the forward-variance balance it states.
[Section 4.3, Table 1] The paper reports a 59.38% training-epoch reduction under SGD, but the listed SGD epochs are IKUN v2 = 26, Normal = 29, and Xavier = 27; the largest reduction visible in the table is 10.3%. The Adam reduction of 42.31% is consistent with the table (26 to 15 epochs), but the SGD headline number is not derivable from the printed results and needs a stated baseline.
[Section 5 and Section 4.1] The experimental evidence is too narrow for the general claims in the abstract. The model is a two-layer convolutional SNN, the data is a fixed subset of Fashion-MNIST, and no seeds, error bars, or repeated runs are reported; Section 5 explicitly concedes these limitations. This does not support broad statements about training efficiency and generalization, nor the Hessian-based generalization conclusions, without additional statistical validation.

minor comments (6)

[Section 3.2] The symbol f in Eq. (8) is never defined; specify the surrogate activation function whose derivative is used.
[Section 4.1] "LeCun Initialization (Bi & Poo, 1998)" cites the wrong reference; the correct source is LeCun et al. (2002).
[Section 4.1] The "Normal" initialization is not described; specify the distribution and scale used.
[Table 2 and Section 4.2] The text says lower absolute Hessian Trace values indicate flatter minima, but the table reports large negative traces for several methods; define the metric and its sign convention.
[Abstract and Table 1] The abstract states "up to 50%" improvement in training efficiency, while Table 1 reports 59.38%; unify these numbers.
[Eqs. (6)-(7)] Notation switches from V(t) to H[t] without defining the relationship; clarify whether H[t] is the pre-spike membrane potential and V[t] is the post-reset potential.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: IKUN's variance condition is a standard variance-preservation construction, not an input renamed as a prediction.

full rationale

The paper's central step, Theorem 1 in Section 3.2, proposes the weight-variance condition sigma_W^2 = alpha / (fanin * sigma_X^2 * E[f'(H)^2]) and claims it stabilizes forward variance and avoids gradient vanishing/explosion. This is the standard variance-matching construction used by Xavier and Kaiming initialization: one writes the variance-propagation equation, imposes the stability goal, and solves for sigma_W. The condition is not by construction identical to the theorem's conclusion; the conclusion concerns the LIF recursion H[t] = tau V[t-1] + sum_i w_i X_i[t], which involves the recurrent term, reset, and threshold, none of which appear explicitly in Eq. 8. Thus the theorem would require a real proof, not a definitional rewriting. The proof is deferred to an appendix that is referenced but absent, and the expectation E[f'(H)^2] depends on H and hence on the weight distribution, making Eq. 8 an implicit self-consistency condition rather than a fitted parameter renamed as a prediction. Those are correctness and rigor concerns, not circularity. The paper contains no load-bearing self-citations: the cited prior initialization methods and datasets are external, and the experimental comparisons are against standard baselines rather than against values produced by the paper's own formulas. The limitation passage in Section 5, stating that experiments used a two-layer convolutional SNN on a fixed subset of Fashion-MNIST, is an honest scope restriction and does not smuggle any input into an output. Under the required standard of quoting a specific reduction, no circular step can be exhibited. Score 0.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central formula rests on variance-propagation math, a Gaussian-like distributional assumption for H, and a temporal independence assumption for the membrane recurrence. None of these are stated as assumptions or proven in the included text; the missing appendix is the only place they could be checked. The method also introduces two unconstrained scale choices (alpha and E[f'(H)^2]).

free parameters (3)

alpha
Hyperparameter in Eq. 8 and Eq. 9 that scales initialization variance directly; no value or selection rule is reported, so the scale of sigma_W^2 is underdetermined.
E[f'(H)^2]
Expected squared surrogate gradient appears in the denominator of both IKUN formulas, but the paper gives no analytic value, empirical estimator, or distributional assumption for it.
mu threshold coefficient (Vthreshold=mu H)
The threshold is set as Vthreshold=mu H but mu is never defined; threshold choice controls firing rate and therefore the variance the theorem claims to stabilize.

assumptions (4)

standard math Layer inputs and weights are zero-mean and mutually independent so that Var(sum w_i X_i)=fan_in sigma_W^2 sigma_X^2.
Eq. 8 requires this variance propagation identity, but the paper never states the independence or zero-mean assumption for spiking inputs.
ad hoc to paper The recurrent membrane potential term tau V[t-1] can be ignored in the variance balance, so the network behaves like a memoryless feedforward layer.
Theorem 1 writes H[t]=tau V[t-1]+sum w_i X_i[t] but Eq. 8 contains no time-step or leakage term; the accumulation of variance over T timesteps is not analyzed.
ad hoc to paper The effect of the spiking nonlinearity on gradient variance is fully captured by E[f'(H)^2].
The theorem's variance condition uses only this expectation, without justifying that the surrogate gradient and reset mechanism are summarized by it.
domain assumption A two-layer convolutional SNN on FashionMNIST is representative of SNN training behavior.
The conclusion restricts the evidence to that architecture and dataset, yet the abstract makes general claims about SNN training and generalization.

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Cite this review

Pith. "Pith review of IKUN: Initialization to Keep snn training and generalization great with sUrrogate-stable variaNce." pith.science (2026). https://pith.science/paper/7LIEVVF2

@misc{pith2026241118250,
  author       = {Pith},
  title        = {Pith review of: IKUN: Initialization to Keep snn training and generalization great with sUrrogate-stable variaNce},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7LIEVVF2}},
  note         = {Machine review of arXiv:2411.18250}
}

read the original abstract

Weight initialization significantly impacts the convergence and performance of neural networks. While traditional methods like Xavier and Kaiming initialization are widely used, they often fall short for spiking neural networks (SNNs), which have distinct requirements compared to artificial neural networks (ANNs). To address this, we introduce \textbf{IKUN}, a variance-stabilizing initialization method integrated with surrogate gradient functions, specifically designed for SNNs. \textbf{IKUN} stabilizes signal propagation, accelerates convergence, and enhances generalization. Experiments show \textbf{IKUN} improves training efficiency by up to \textbf{50\%}, achieving \textbf{95\%} training accuracy and \textbf{91\%} generalization accuracy. Hessian analysis reveals that \textbf{IKUN}-trained models converge to flatter minima, characterized by Hessian eigenvalues near zero on the positive side, promoting better generalization. The method is open-sourced for further exploration: \href{https://github.com/MaeChd/SurrogateVarStabe}{https://github.com/MaeChd/SurrogateVarStabe}.

Figures

Figures reproduced from arXiv: 2411.18250 by the authors.

**Figure 1.** Mechanism of the LIF neuron. This diagram illustrates the working principle of an LIF neuron, modeled as an RC circuit with leakage. When an input spike I(t) causes the membrane potential V (t) to accumulate and reach the threshold Vth, the neuron emits a spike and resets its potential to the resting value Vreset. If the threshold is not reached, the membrane potential gradually decays to the resting level, governed… view at source ↗

**Figure 2.** Temporal logic in SNNs, adapted from (Wu et al., 2018). The figure illustrates the basic principles of temporal logic in SNNs. Multiple neurons are connected via weighted synapses to form a layered network structure. Input signals are encoded before being fed into the network, with common encoding methods including temporal encoding and rate encoding. Temporal encoding represents information through spike intervals… view at source ↗

**Figure 3.** Activation function curve of σ(x, α) = 1 1+exp(−αx) . As α increases, the function gradually approaches a step function. 2.3. Analysis of Existing Methods for Improving SNN Training Existing research has made some progress in alleviating the challenges of SNN training, but exploration of weight initialization remains limited. Below are several typical approaches and their limitations: 4 [PITH_FULL_IMAGE:figures/ful… view at source ↗

Figures from the paper (6 more)

**Figure 4.** Figure 4: Network architecture. The diagram illustrates the twolayer convolutional SNN architecture, where each layer comprises convolution, pooling, and spiking activation functions for efficient extraction and processing of temporal features in input data. Comparison Methods …

**Figure 6.** Figure 6: (a) and (c) show the training and testing accuracy curves under the Adam optimizer, while (b) and (d) illustrate the loss curves. Although IKUN initialization achieves faster loss reduction in the early stages, it underperforms compared to Kaiming and LeCun initializat…

**Figure 5.** Figure 5: (a) and (c) show the changes in training and testing accuracy under the SGD optimizer, while (b) and (d) depict the training and testing loss curves. IKUN initialization achieves faster loss reduction in the early training stages and maintains higher stability, but in…

**Figure 7.** Figure 7: (a) shows the top 50 ranked Hessian eigenvalues using the SGD optimizer. Both IKUN and Kaiming initialization yield eigenvalues close to 0 and positive, indicating a flat optimization region with good curvature characteristics, better generalization, and robustness. (b…

**Figure 9.** Figure 9: Hessian eigenvalue density distribution with the Adam optimizer. The figure shows the density distribution of Hessian eigenvalues under the Adam optimizer. The IKUN initialization method demonstrates a compact distribution of positive values, further supporting its sup…

**Figure 8.** Figure 8: Hessian eigenvalue density distribution with the SGD optimizer. The figure compares the density distribution of Hessian eigenvalues for different initialization methods under the SGD optimizer. IKUN and Kaiming initialization exhibit concentrated distributions close to…

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Reference graph

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