Integrated Spike Patch Splitting (I-SPS)

• Integrated Spike Patch Splitting (I-SPS) is a method that fuses multi-timestep spike signals into a unified token set for spiking vision transformers.
• It replaces timestep-dependent tokenization with a unified representation, ensuring high temporal similarity and enabling effective adaptive computation time.
• Empirical results show that I-SPS, when paired with adaptive spiking self-attention, improves token efficiency, boosts accuracy, and reduces energy consumption.

Searching arXiv for the specified paper and closely related context. Integrated Spike Patch Splitting (I-SPS) is a static architectural module introduced within STAS, a framework for spiking vision transformers that couples input-stage redesign with adaptive computation time over both space and time. Its stated purpose is to address the low temporal similarity of SNN-based ViTs by integrating multi-timestep spike signals into a single, unified representation at the initial stage and reusing that representation for all subsequent computations. In STAS, this temporal stabilization is the architectural prerequisite that enables adaptive spiking self-attention (A-SSA) to perform two-dimensional token pruning across both spatial and temporal axes (Kang et al., 19 Aug 2025).

1. Definition and motivation

I-SPS is introduced as a replacement for vanilla spike patch splitting (SPS) in spiking vision transformers. The central distinction is that vanilla SPS operates per timestep and therefore yields different token sets at different timesteps, whereas I-SPS integrates multi-timestep spike signals into a single tokenized representation that is reused throughout the computation (Kang et al., 19 Aug 2025).

The motivation is tied directly to adaptive computation time (ACT). The source paper argues that ACT depends on the internal representation becoming stable across refinement steps. In conventional RNNs and ViTs, this condition is satisfied because successive processing stages receive highly similar representations. In SNN-based ViTs, however, each timestep receives a different input spike vector, producing low cosine similarity between consecutive temporal inputs. According to the paper, this violates the temporal-similarity prerequisite required for reliable temporal halting (Kang et al., 19 Aug 2025).

Within STAS, I-SPS is therefore not presented merely as an efficiency optimization. It is framed as the static component of a co-designed static/dynamic system. The static role is to reformulate the input stage so that temporal similarity is established; the dynamic role, assigned to A-SSA, is to exploit that stability for concurrent spatial and temporal token halting. A common misconception is to treat I-SPS itself as the adaptive mechanism. The paper instead positions it as the architectural condition that makes the dynamic mechanism effective.

2. Architectural role in spiking vision transformers

The input to the spiking ViT is given as

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

where $T$ is the number of timesteps. In the baseline formulation, the spike patch splitting module $\mathcal{S}(\cdot)$ converts the input into token embeddings separately at each timestep, producing timestep-dependent token sets $\mathcal{T}^{0,t}$ (Kang et al., 19 Aug 2025).

Under I-SPS, the multi-timestep spike input is integrated before patch splitting and self-attention, producing a single token set $\mathcal{T}^{0}$, or equivalently a temporally unified $\mathcal{T}^{0,t}$ that is identical for all $t$. The resulting tokens are then reused across all timesteps. In architectural terms, the module consumes the full spike sequence, performs temporal integration and spatial patch embedding once, and outputs a unified token representation that feeds the spiking transformer blocks (Kang et al., 19 Aug 2025).

The paper explicitly situates I-SPS before the encoder blocks and before spike self-attention. In the comparison described for Figure 1, a conventional SNN-based ViT uses vanilla SPS and SSA, while STAS uses I-SPS and A-SSA. This replacement is implementation-level rather than merely conceptual: the original SPS module in models such as Spikformer and Spikingformer is replaced with I-SPS, and the resulting model is first trained as a pre-trained backbone before applying the two-dimensional ACT mechanism (Kang et al., 19 Aug 2025).

The paper further characterizes I-SPS as a type of “one-step” approach. The computationally expensive CNN operation is reduced to a single pass, while the low-latency LIF neuron operations still iterate for $T$ timesteps. This distinction is important: I-SPS does not remove temporal recurrence from the model as a whole; it removes repeated heavy input-stage patch embedding while preserving multi-timestep spiking dynamics.

3. Mathematical formulation and temporal stability

The baseline SNN-ViT is written as

$$f_T(x) = FC\Big(\frac{1}{T}\sum_{t=1}^{T}\mathcal{B}^{L}\circ \cdots \circ \mathcal{B}^{1}\circ \mathcal{S}(x)\Big),$$

with block-wise propagation

$$\mathcal{T}^{l,t} = \mathcal{B}^{l}(\mathcal{T}^{l-1,t}).$$

Under vanilla SPS, the tokenization is effectively timestep-dependent, so the initial token set varies with $T$0. Under I-SPS, the tokenization becomes timestep-independent in the sense described in the source explanation: the model conceptually replaces per-timestep tokenization with a unified token set reused across all timesteps (Kang et al., 19 Aug 2025).

The significance of this reformulation lies in what the paper calls temporal stability. In this context, temporal stability means that token embeddings at consecutive timesteps have high cosine similarity and therefore represent consistent content across time. The paper contrasts this with spatial similarity across blocks, which is already high in SNN-based ViTs because of residual connections and shared membrane states. I-SPS is designed specifically to raise similarity along the temporal axis, thereby making accumulation of halting evidence across timesteps meaningful (Kang et al., 19 Aug 2025).

The source explanation also links I-SPS to training dynamics. By reducing the temporal depth of the expensive patch-embedding path, the method shortens the temporal backpropagation path. The explanation states that this mitigates vanishing gradients and error accumulation from surrogate functions, and that improved gradient flow appears to offset the information loss from temporal compression. This suggests that I-SPS is simultaneously a representational intervention and a training-path intervention, although the paper does not introduce a separate loss term specifically for I-SPS.

4. Coupling with adaptive spiking self-attention

A-SSA is the dynamic halting mechanism that operates on the tokens produced by I-SPS. Its core object is the per-token halting score

$T$1

where $T$2 is the embedding vector of token $T$3 in block $T$4 at timestep $T$5, $T$6 is its first element, and $T$7 is the logistic sigmoid. The first element of the MLP output is trained to encode the halting score. Halting evidence is then accumulated across both blocks and timesteps:

$T$8

Tokens with $T$9 are halted and masked (Kang et al., 19 Aug 2025).

The coherence of this two-dimensional accumulation depends on I-SPS. Because I-SPS makes the tokenization unified across timesteps, the $\mathcal{S}(\cdot)$0-th token remains temporally consistent enough for cross-timestep accumulation to be meaningful. Without such stabilization, the same token index would correspond to different per-timestep spike-derived representations, weakening or destabilizing temporal halting (Kang et al., 19 Aug 2025).

The operational narrative given for Figure 2 reinforces this dependency. At the first timestep, the input passes through I-SPS to generate the unified tokenized input. At later timesteps, the same input and the same I-SPS tokens are reused, and halting scores continue to accumulate over time. This is the basis for what the paper calls two-dimensional token pruning: spatial along the block axis and temporal along the timestep axis.

5. Empirical effects on pruning, accuracy, and energy

The paper’s ablations present I-SPS as the decisive factor that makes A-SSA effective. On CIFAR-100, Table 1 reports that for Spikformer-4-384, the baseline has average tokens $\mathcal{S}(\cdot)$1 and accuracy $\mathcal{S}(\cdot)$2; A-SSA alone reduces average tokens to $\mathcal{S}(\cdot)$3 but leaves accuracy at $\mathcal{S}(\cdot)$4; I-SPS combined with A-SSA reduces average tokens further to $\mathcal{S}(\cdot)$5 and increases accuracy to $\mathcal{S}(\cdot)$6. For Spikingformer-4-384, the baseline is $\mathcal{S}(\cdot)$7 and $\mathcal{S}(\cdot)$8, A-SSA alone yields $\mathcal{S}(\cdot)$9 and $\mathcal{T}^{0,t}$0, and I-SPS plus A-SSA yields $\mathcal{T}^{0,t}$1 and $\mathcal{T}^{0,t}$2 (Kang et al., 19 Aug 2025).

These ablations support the paper’s claim that A-SSA alone is weak and becomes effective only when coupled with I-SPS. The result is not merely stronger pruning, but stronger pruning with maintained or improved accuracy. Table 5 reports the same pattern in the comparison with and without I-SPS under two-dimensional accumulation: for Spikformer, token usage moves from $\mathcal{T}^{0,t}$3 without I-SPS to $\mathcal{T}^{0,t}$4 with I-SPS, while accuracy increases from $\mathcal{T}^{0,t}$5 to $\mathcal{T}^{0,t}$6; for Spikingformer, token usage moves from $\mathcal{T}^{0,t}$7 to $\mathcal{T}^{0,t}$8, while accuracy rises from $\mathcal{T}^{0,t}$9 to $\mathcal{T}^{0}$0 (Kang et al., 19 Aug 2025).

At the full STAS level, which includes both I-SPS and A-SSA, the reported energy reductions are substantial. On ImageNet, Table 3 reports that Spikingformer-8-384 goes from $\mathcal{T}^{0}$1 mJ and $\mathcal{T}^{0}$2 in the baseline to $\mathcal{T}^{0}$3 mJ and $\mathcal{T}^{0}$4 under a moderate halting setting, and to $\mathcal{T}^{0}$5 mJ and $\mathcal{T}^{0}$6 under a more aggressive halting variant, corresponding to a $\mathcal{T}^{0}$7 energy reduction. On CIFAR-10 and CIFAR-100, Table 4 reports reductions such as $\mathcal{T}^{0}$8 mJ to $\mathcal{T}^{0}$9 mJ for Spikformer-4-384 on CIFAR-10, and $\mathcal{T}^{0,t}$0 mJ to $\mathcal{T}^{0,t}$1 mJ on CIFAR-100, with accompanying accuracy gains. The paper summarizes the overall effect as energy reductions of up to $\mathcal{T}^{0,t}$2, $\mathcal{T}^{0,t}$3, and $\mathcal{T}^{0,t}$4 on CIFAR-10, CIFAR-100, and ImageNet, respectively, while simultaneously improving accuracy over SOTA models (Kang et al., 19 Aug 2025).

6. Relation to prior work, implementation setting, and limitations

I-SPS is positioned against several baselines and adjacent ideas. Relative to vanilla SPS in Spikformer and Spikingformer, its defining difference is the creation of a unified representation rather than per-timestep token sets. Relative to prior “one-step” spiking methods such as OST and RGA, the distinction stated in the paper is one of purpose: I-SPS is introduced not primarily for latency reduction or adversarial settings, but to create the temporal similarity needed for ACT-like halting in spiking transformers (Kang et al., 19 Aug 2025).

The source explanation further places I-SPS in relation to ACT and A-ViT. ACT-style mechanisms rely on representation similarity across layers or steps in ANN settings. The paper’s novelty claim is that existing SNN-based ViT architectures inherently obstruct temporal halting, and that I-SPS re-engineers the input stage to satisfy the temporal condition required for effective adaptation. This suggests a shift from applying ACT heuristically to SNNs toward redesigning the SNN-ViT architecture so that ACT’s assumptions hold.

The implementation details reported for I-SPS are tightly coupled to this role. The module replaces the original SPS in Spikformer and Spikingformer; the model is first trained with I-SPS alone and then used as a pre-trained model for training the full two-dimensional ACT system. Reported settings include $\mathcal{T}^{0,t}$5 for CIFAR and ImageNet models, and 196 tokens in the ImageNet example corresponding to $\mathcal{T}^{0,t}$6 patches. Halting parameters such as $\mathcal{T}^{0,t}$7, $\mathcal{T}^{0,t}$8, and $\mathcal{T}^{0,t}$9 are then applied to tokens produced by I-SPS during A-SSA training (Kang et al., 19 Aug 2025).

The paper does not present a dedicated limitation section for I-SPS, but several constraints are implicit. The source explanation notes that one-step-style temporal integration sacrifices precise temporal information. This suggests a possible trade-off where temporal compression could be less suitable when fine-grained spike timing is critical. It also suggests architectural specificity: I-SPS is designed for SNN-based ViTs, and extension to other spiking architectures or tasks would require adaptation. These are best understood as plausible implications drawn from the formulation rather than as explicit experimental conclusions.

In summary, I-SPS is the static architectural mechanism in STAS that converts a multi-timestep spike sequence into a temporally unified token representation, thereby establishing the temporal stability required for reliable two-dimensional halting. Its importance lies less in tokenization alone than in making temporal ACT architecturally feasible in spiking transformers. Within STAS, it reduces repeated heavy input-stage computation, improves the conditions for training and halting, and enables A-SSA to prune tokens across both blocks and timesteps without the accuracy degradation observed when adaptive halting is used without temporal unification (Kang et al., 19 Aug 2025).