Shallow-level Temporal Feedback (STF) in SNNs

• Shallow-level Temporal Feedback (STF) is a lightweight encoding-layer mechanism that injects previous spike outputs into static image inputs to enrich temporal diversity.
• It integrates Temporal-Spatial Position Embedding (TSPE) and Temporal Feedback (TF) to capture spatio-temporal structure with minimal parameter overhead and energy cost.
• STF enhances performance by reducing latency and improving accuracy on static image tasks, while maintaining a fully spike-driven computation.

Shallow-level Temporal Feedback (STF) is a lightweight feedback mechanism for Transformer-based spiking neural networks (SNNs) introduced as a plug-and-play module for the encoding layer. It was proposed to narrow the performance gap between spiking transformers and floating-point artificial neural networks by injecting temporal feedback at a shallow stage, where feature dimensionality remains low and feedback can be implemented with lower parameter overhead, lower energy cost, and shorter inference latency than deep-level feedback designs. STF consists of two components—Temporal-Spatial Position Embedding (TSPE) and Temporal Feedback (TF)—and is designed primarily for static image classification, where repeated image inputs across timesteps otherwise induce constrained and low-diversity spike patterns (Zheng et al., 1 Aug 2025).

1. Motivation and problem setting

Transformer-based SNNs such as Spikformer, Spike-driven Transformer (SDT), and QKFormer are described as lagging behind floating-point ANN counterparts largely because spike trains are binary and information-sparse. Prior attempts to reduce this gap introduced deep-level feedback loops that propagate high-level semantic information backward from deeper layers. According to the reported characterization, these methods can improve accuracy but usually require two forward passes, operate on high-dimensional deep features, and incur increased parameter overhead, energy consumption, and latency as feature transformations become more expensive with depth (Zheng et al., 1 Aug 2025).

STF is motivated by the question of whether feedback can be constructed directly in shallow layers, where computation is cheaper and temporal spike dynamics can be exploited more naturally. Rather than transmitting abstract semantic features from deep transformer blocks, STF modifies the temporal spike generation process itself at the encoding layer. This design choice places feedback before the main transformer blocks perform heavy processing, so the module can be attached to existing Transformer-based SNN backbones without redesigning the core architecture (Zheng et al., 1 Aug 2025).

The resulting contrast is structural as well as functional. Deep-level feedback is semantic, high-dimensional, and latency-heavy; STF is shallow, temporal, spike-driven, and encoding-centric. A plausible implication is that the method targets inefficiency in prior feedback designs not by removing feedback altogether, but by relocating it to a stage where its computational footprint is smaller.

2. Architectural composition

STF consists of two components applied in the shallow encoding stage: Temporal-Spatial Position Embedding (TSPE) and Temporal Feedback (TF). The input static image is duplicated across timesteps to form a spike sequence,

$I \in \mathbb{R}^{T \times C \times H \times W},$

where $T$ is the number of timesteps and $C,H,W$ denote channels, height, and width (Zheng et al., 1 Aug 2025).

TSPE adds a spatio-temporal positional embedding

$$X_{\text{TPE}} \in \mathbb{R}^{T\times C\times H\times W},$$

initialized with a 3D trigonometric positional strategy inspired by video transformers. Two equivalent placements are explored:

$$I_{\text{embed}}[t] = W_{\text{ConvBN}} \cdot (X_{\text{TPE}}[t] + I[t]),$$

for STF-1 / STF-3 style, and

$$I_{\text{embed}}[t] = X_{\text{TPE}}[t] + W_{\text{ConvBN}} \cdot I[t],$$

for STF-2 / STF-4 style, where $W_{\text{ConvBN}}$ denotes a convolution followed by batch normalization. The stated role of TSPE is to introduce explicit temporal and spatial awareness into the encoding stage, allowing the model to distinguish timestep-specific structure even though the underlying image is static and repeated (Zheng et al., 1 Aug 2025).

TF is the defining feedback mechanism. It injects the previous timestep’s spike output $S[t-1]$ into the current timestep rather than using auxiliary hidden states or non-spiking activations. The two reported TF formulations are:

$I'[t] = I[t] + W_{\text{TF}} \cdot S[t-1],$

for STF-1 / STF-2, and

$$H[t] = \left(1 - \frac{1}{\tau_m}\right) U[t-1] + I[t] + W_{\text{TF}} \cdot S[t-1],$$

for STF-3 / STF-4, where $T$0 is a learnable convolution + BN transformation, $T$1 is the intermediate membrane state, $T$2 is the previous membrane potential, and $T$3 is the membrane time constant (Zheng et al., 1 Aug 2025).

A compact summary of the two components is given below.

Component	Mechanism	Reported role
TSPE	Adds spatio-temporal positional embedding in the encoding stage	Introduces explicit temporal and spatial awareness
TF	Feeds previous timestep spike output into current timestep	Injects temporal history while remaining fully spike-driven

The paper explicitly distinguishes TF from recurrent SNN mechanisms: it does not introduce hidden-state recurrence or non-spike activations. This suggests that STF is intended to preserve the spike-driven character of the computation while still enriching temporal dependencies at the encoder.

3. Relation to leaky integrate-and-fire dynamics and spike-pattern diversity

The STF formulation is embedded in standard leaky integrate-and-fire (LIF) dynamics:

$T$4

$T$5

$T$6

In this notation, $T$7 is the membrane state before thresholding, $T$8 is the generated spike, and $T$9 is the updated membrane potential after reset. STF changes how the current input $C,H,W$0 and prior spike $C,H,W$1 are combined before spike generation proceeds through this LIF process (Zheng et al., 1 Aug 2025).

A central claim is that STF improves performance primarily by increasing the diversity of spike patterns. On static datasets the same image is repeated over timesteps,

$C,H,W$2

Without STF, the paper derives a spike-generation time

$C,H,W$3

This is presented as showing that for fixed $C,H,W$4, threshold, and static input, the neuron tends to produce only a limited set of spike patterns (Zheng et al., 1 Aug 2025).

By incorporating $C,H,W$5 into the current timestep computation, STF breaks this constraint: spike generation is no longer determined solely by the repeated image input, but also by the evolving temporal state. The reported consequences are that more binary spike combinations become reachable, spike entropy increases, temporal codes become richer, and representation capacity improves. The paper states that STF can activate all 16 possible patterns at $C,H,W$6, whereas direct coding and GAC are biased toward a few patterns and IMP is better but still incomplete (Zheng et al., 1 Aug 2025).

Spike entropy is defined as

$C,H,W$7

where $C,H,W$8 is the frequency of each spike pattern. Higher entropy is interpreted as higher spike-pattern diversity. The paper links this diversity to improved information capacity, better propagation through the network, reduced pattern collapse, and more expressive binary representations. It also reports that TF contributes more strongly than TSPE, although the combination performs best (Zheng et al., 1 Aug 2025).

4. Empirical evaluation across datasets and backbones

The reported evaluation covers three static image classification datasets—CIFAR-10, CIFAR-100, and ImageNet-1K—and also includes CIFAR10-DVS as a neuromorphic dataset. STF is tested on three Transformer-based SNN backbones: Spikformer, SDT, and QKFormer. For CIFAR experiments, results are reported at $C,H,W$9; for ImageNet-1K, the main reported setups are SDT-6-512 at $$X_{\text{TPE}} \in \mathbb{R}^{T\times C\times H\times W},$$0 and QKFormer HST-10-768 at $$X_{\text{TPE}} \in \mathbb{R}^{T\times C\times H\times W},$$1. The implementation uses PyTorch 2.0.1, CUDA 11.8, and SpikingJelly 0.0.0.0.12, with standard augmentation including RandAugment, random crop, flip, jitter, and Mixup/CutMix on ImageNet (Zheng et al., 1 Aug 2025).

On CIFAR-10 and CIFAR-100, STF is reported to improve all three backbones across timesteps. Representative values are shown below.

Backbone	CIFAR-10 improvement	CIFAR-100 improvement
Spikformer-4-384	93.20 → 94.95 at $$X_{\text{TPE}} \in \mathbb{R}^{T\times C\times H\times W},$$2; 95.24 → 95.99 at $$X_{\text{TPE}} \in \mathbb{R}^{T\times C\times H\times W},$$3	75.17 → 76.94 at $$X_{\text{TPE}} \in \mathbb{R}^{T\times C\times H\times W},$$4; 78.22 → 79.14 at $$X_{\text{TPE}} \in \mathbb{R}^{T\times C\times H\times W},$$5
SDT-2-512	95.01 → 95.24 at $$X_{\text{TPE}} \in \mathbb{R}^{T\times C\times H\times W},$$6; 96.24 → 96.41 at $$X_{\text{TPE}} \in \mathbb{R}^{T\times C\times H\times W},$$7	77.47 → 78.21 at $$X_{\text{TPE}} \in \mathbb{R}^{T\times C\times H\times W},$$8; 79.87 → 80.61 at $$X_{\text{TPE}} \in \mathbb{R}^{T\times C\times H\times W},$$9
QKFormer HST-4-384	95.79 → 96.02 at $$I_{\text{embed}}[t] = W_{\text{ConvBN}} \cdot (X_{\text{TPE}}[t] + I[t]),$$0; 96.35 → 96.61 at $$I_{\text{embed}}[t] = W_{\text{ConvBN}} \cdot (X_{\text{TPE}}[t] + I[t]),$$1	79.79 → 80.07 at $$I_{\text{embed}}[t] = W_{\text{ConvBN}} \cdot (X_{\text{TPE}}[t] + I[t]),$$2; 81.64 → 81.89 at $$I_{\text{embed}}[t] = W_{\text{ConvBN}} \cdot (X_{\text{TPE}}[t] + I[t]),$$3

On ImageNet-1K, the paper reports consistent gains with small overhead. For SDT-6-512, accuracy increases from 72.41% to 73.01%, with a parameter increase of 0.17% and an energy increase of 12.08%. For QKFormer HST-10-768, accuracy increases from 84.22% to 84.97%, with a parameter increase of 0.32% and an energy increase of approximately 7.2%. At higher resolutions, QKFormer improves from 85.20 to 85.89 at $$I_{\text{embed}}[t] = W_{\text{ConvBN}} \cdot (X_{\text{TPE}}[t] + I[t]),$$4 and from 85.65 to 86.26 at $$I_{\text{embed}}[t] = W_{\text{ConvBN}} \cdot (X_{\text{TPE}}[t] + I[t]),$$5 (Zheng et al., 1 Aug 2025).

The paper further notes that QKFormer with STF reaches performance competitive with the much larger E-SpikFormer while using far fewer parameters and only half the timesteps. The explicit quantitative pattern across datasets and models supports the paper’s claim that the gains are systematic rather than backbone-specific.

5. Efficiency, robustness, and temporal sensitivity

STF is reported to add overhead, but substantially less than traditional deep feedback. On CIFAR, the latency overhead is about +5% to +8% for Spikformer + STF, about +3% to +6% for SDT + STF, and about +3% to +9% for QKFormer + STF. By comparison, SpiLiFormer adds around +15% to +27% latency on CIFAR (Zheng et al., 1 Aug 2025).

Appendix ImageNet latency values further illustrate the cost profile: SDT increases from 26.987 ms to 28.375 ms (+5.14%), QKFormer from 57.316 ms to 60.942 ms (+6.33%), and SpiLiFormer from 58.990 ms to 66.302 ms (+12.40%). This supports the paper’s conclusion that STF roughly halves the latency penalty associated with deep-level feedback (Zheng et al., 1 Aug 2025).

The paper also evaluates adversarial robustness using FGSM and PGD on QKFormer at $$I_{\text{embed}}[t] = W_{\text{ConvBN}} \cdot (X_{\text{TPE}}[t] + I[t]),$$6 for CIFAR-10 and CIFAR-100. The stated conclusion is that STF improves robustness under both attacks without hurting clean accuracy. This is used to argue that STF is not merely fitting the training set more aggressively, but is producing a more informative and stable encoding (Zheng et al., 1 Aug 2025).

Temporal sensitivity is examined by shuffling spike trains and measuring the resulting accuracy drop. For QKFormer without STF, CIFAR-100 accuracy changes from 79.79 to 79.01 at $$I_{\text{embed}}[t] = W_{\text{ConvBN}} \cdot (X_{\text{TPE}}[t] + I[t]),$$7, 81.15 to 80.38 at $$I_{\text{embed}}[t] = W_{\text{ConvBN}} \cdot (X_{\text{TPE}}[t] + I[t]),$$8, 81.35 to 80.76 at $$I_{\text{embed}}[t] = W_{\text{ConvBN}} \cdot (X_{\text{TPE}}[t] + I[t]),$$9, and 81.64 to 81.12 at $$I_{\text{embed}}[t] = X_{\text{TPE}}[t] + W_{\text{ConvBN}} \cdot I[t],$$0. With STF, the corresponding drops are 80.07 to 79.10, 81.26 to 80.06, 81.51 to 80.76, and 81.89 to 81.05. The larger drops under temporal shuffling are interpreted as evidence that STF encodes more temporal structure and is more sensitive to disruption of that structure (Zheng et al., 1 Aug 2025).

6. Scope, limitations, and terminological context

The main practical implication presented for STF is that it can function as a new spike encoding scheme for static scenarios. Its reported advantages are that it is lightweight, plug-and-play, compatible with existing spiking transformers, accuracy-improving under modest parameter and energy overhead, and fully spike-driven. The method is described as being especially effective for static image tasks, where repeated inputs across timesteps otherwise lead to overly deterministic spike-generation behavior (Zheng et al., 1 Aug 2025).

The principal limitation reported is that STF does not generalize well to neuromorphic or event-based data such as CIFAR10-DVS; performance degrades in that setting. The explanation given is task-structural: static images benefit because STF injects temporal diversity into an otherwise repetitive signal, whereas event-based data already contains natural temporal structure, and adding STF may disturb that structure. A plausible implication is that the mechanism is specialized to compensate for missing temporal variation rather than to model arbitrary temporal dynamics (Zheng et al., 1 Aug 2025).

A separate terminological issue arises because the phrase “shallow” also appears in LLM-for-time-series work, where it refers to shallow temporal conditioning such as positional embeddings, prefix prompts, or input-only temporal injection. In "Deep TPC: Temporal-Prior Conditioning for Time Series Forecasting," the authors explicitly critique such input-stage temporal integration as limited because temporal information is injected only once and degrades through the layers of a frozen decoder (Bellos et al., 18 Feb 2026). That usage is conceptually distinct from STF in spiking transformers. STF is a formal method name for shallow encoding-layer temporal feedback in SNNs, whereas the time-series literature uses “shallow” to describe input-only temporal conditioning in transformer decoders. The shared adjective therefore does not indicate a shared mechanism.

Within its intended scope, STF is defined by an encoding-layer intervention: it modifies spike generation early, preserves spike-driven computation, and seeks performance gains through increased spike-pattern diversity rather than through deep semantic feedback. The reported findings collectively position it as an encoding-centric alternative to deep-level feedback for static image classification in Transformer-based SNNs (Zheng et al., 1 Aug 2025).