Sharpness Aware Surrogate Training for Spiking Neural Networks

Maximilian Nicholson

cs.NEMar 14, 2026

Sharpness Aware Surrogate Training for Spiking Neural Networks

Authors: Maximilian Nicholson

Organizations: University of Bath, United Kingdom

Abstract

Surrogate gradients are a standard tool for training spiking neural networks (SNNs), but conventional hard forward or surrogate backward training couples a nonsmooth forward model with a biased gradient estimator. We study sharpness aware Surrogate Training (SAST), which applies sharpness aware Minimization (SAM) to a surrogate forward SNN trained by backpropagation. In this formulation, the optimization target is an ordinary smooth empirical risk, so the training gradient is exact for the auxiliary model being optimized. Under explicit boundedness and contraction assumptions, we derive compact state stability and input Lipschitz bounds, establish smoothness of the surrogate objective, provide a first order SAM approximation bound, and prove a nonconvex convergence guarantee for stochastic SAST with an independent second minibatch. We also isolate a local mechanism proposition, stated separately from the unconditional guarantees, that links per sample parameter gradient control to smaller input gradient norms under local Jacobian conditioning. Empirically, we evaluate clean accuracy, hard spike transfer, corruption robustness, and training overhead on N-MNIST and DVS Gesture. The clearest practical effect is transfer gap reduction: on N-MNIST, hard spike accuracy rises from 65.7% to 94.7% (best at $ρ=0.30$ ) while surrogate forward accuracy remains high; on DVS Gesture, hard spike accuracy improves from 31.8% to 63.3% (best at $ρ=0.40$ ). We additionally specify the compute matched, calibration, and theory alignment controls required for a final practical assessment.

Figures & tables

Panel of Figure 1 — Fig. 1: Overview of the surrogate forward SNN used during training. At inference, the final trained model can be evaluated either with the surrogate nonlinearity or by replacing it with a hard threshold according to Definition II.6 .

Setting	surrogate forward train	Smooth blocks	Covered by theory
Main N-MNIST / DVS runs	Yes	AvgPool / affine norm	Yes
MaxPool / BatchNorm extension	Yes	No	No (practical only)
hard forward / surrogate backward baseline	No	Mixed	No
hard spike inference only	Training unchanged	–	No new training guarantee

TABLE I: Which experimental settings are covered by the theory

Dataset	Method	Surrogate forward	Hard spike	Transfer gap
N-MNIST	Baseline surrogate training	0.9606 $\pm$ 0.0033	0.6572 $\pm$ 0.0974	0.3034
N-MNIST	SAST ( $\rho=0.02$ )	0.9789 $\pm$ 0.0033	0.7453 $\pm$ 0.0251	0.2336
N-MNIST	SAST ( $\rho=0.05$ )	0.9831 $\pm$ 0.0007	0.7812 $\pm$ 0.0847	0.2019
N-MNIST	SAST ( $\rho=0.10$ )	0.9786 $\pm$ 0.0009	0.8335 $\pm$ 0.0894	0.1451
N-MNIST	SAST ( $\rho=0.20$ )	0.9753 $\pm$ 0.0013	0.9018 $\pm$ 0.0496	0.0735
N-MNIST	SAST ( $\rho=0.30$ )	0.9721 $\pm$ 0.0012	0.9473 $\pm$ 0.0462	0.0248

TABLE II: Main accuracy results

Fig. 2: Robustness on N-MNIST under random event-drop corruption. Test accuracy (mean $\pm$ std over seeds) is plotted against drop probability $p$ for both surrogate forward and hard spike evaluation; SAST trained models are expected to degrade more gracefully than the baseline as corruption increases, with moderate-to-large radii typically showing the strongest gains at high drop rates.

Control experiment	Protocol	Why it matters
Compute matched baseline	Match the total number of forward and backward passes used by SAST, either by doubling baseline updates or by extending baseline training until pass counts are comparable. Report surrogate forward accuracy, hard spike accuracy, transfer gap, robustness summary metrics, and wall clock.	Separates the effect of sharpness aware updates from the effect of extra optimization compute.
Reused second minibatch	Replace the independent second minibatch by $B^{\prime}=B$ while keeping everything else fixed.	Tests the practical cost of violating the independence assumption used in the convergence theorem.
ASAM baseline	Replace SAM by ASAM with matched optimizer settings and matched compute.	Checks whether scale adaptive perturbations outperform or match vanilla SAM in this setting.
Post training threshold calibration	With network weights fixed, tune either a single global threshold multiplier $\lambda$ or per-layer multipliers $\lambda_{\ell}$ on a validation set to maximize hard spike accuracy. Report both the best calibration-only result and the combined result when calibration is applied to SAST trained models.	Tests whether a cheaper calibration heuristic can close the transfer gap without two-pass training.
Surrogate choice and slope	Compare arctan and fast-sigmoid surrogates over a small slope grid $k$ . For each run, report $k$ , $B_{1}$ , $\hat{M}_{\theta}$ , and $\hat{\gamma}$ .	Determines whether the gains are specific to one surrogate family or one operating regime, and shows whether theorem aligned runs actually satisfy the contraction diagnostic.
Theory misaligned extension	Repeat the strongest setting with MaxPool and BatchNorm. Clearly label these as practical extensions not covered by the smoothness theory.	Separates theorem aligned evidence from broader engineering usefulness.

TABLE III: Additional controls and extra experiments required for a final assessment of SAST.

Dataset	Method	Time / epoch	Time factor	Peak memory	Mem. factor
N-MNIST	Baseline surrogate	$80.48\pm 0.25$ s	$1.00\times$	$0.40\pm 0.01$ GB	$1.00\times$
N-MNIST	SAST ( $\rho=k,k>0$ )	$167.72\pm 1.81$ s	$2.08\times$	$0.40\pm 0.01$ GB	$1.00\times$
DVS Gesture	Baseline surrogate	$2.87\pm 0.07$ s	$1.00\times$	$2.48\pm 0.01$ GB	$1.00\times$
DVS Gesture	SAST ( $\rho=k,k>0$ )	$5.09\pm 0.09$ s	$1.77\times$	$2.48\pm 0.01$ GB	$1.00\times$

TABLE IV: Training overhead measured on the hardware used for the experiments.

Spiking Neural Networks

Spiking neural networks process information through discrete, time-dependent neural events, aiming for efficient computation and biologically inspired learning.

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Sharpness-Aware Surrogate Training for On-Sensor Spiking Neural Networks

Maximilian Nicholson

University of Bath, United Kingdom

Spiking Neural Networks Event-Based Vision Sharpness-Aware Minimization

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Spiking neural networks (SNNs) are a natural computational model for on-sensor and near-sensor vision, where event driven processors must operate under strict power budgets with hard binary spikes. However, models trained with surrogate gradients often degrade sharply when the smooth surrogate nonlinearity is replaced by a hard threshold at deployment; a surrogate-to-hard transfer gap that directly limits on-sensor accuracy. We study Sharpness-Aware Surrogate Training (SAST), which applies Sharpness-Aware Minimization (SAM) to a surrogate-forward SNN so that the training objective is smooth and the gradient is exact, and position it as one gap-reduction strategy under the tested settings rather than the only viable mechanism. Under explicit contraction assumptions we provide state-stability, input-Lipschitz, and smoothness bounds, together with a corresponding nonconvex convergence result. On two event-camera benchmarks, swap-only hard-spike accuracy improves from 65.7% to 94.7% on N-MNIST and from 31.8% to 63.3% on DVS Gesture. Under a hardware-aware inference simulation (INT8/INT4 weight quantization, fixed-point membrane potentials, discrete leak factors), SAST remains strong: on N-MNIST, hard-spike accuracy improves from 47.6% to 96.9% (INT8) and from 43.2% to 81.0% (INT4), while on DVS Gesture it improves from 25.3% to 47.6% (INT8) and from 26.0% to 43.8% (INT4). SynOps also decrease under the same hardware-aware setting, including 1734k

\rightarrow

1315k (N-MNIST, INT8) and 86221k

\rightarrow

4323k (DVS Gesture, INT8). These results suggest that SAST is a promising component in a broader toolbox for on-sensor spiking inference under the tested settings.

Abstract

Spiking Neural Networks

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