Dual-Path Spike Fusion in SpikeSTAG

• Dual-Path Spike Fusion (DSF) is a hybrid temporal fusion module that integrates continuous LSTM dynamics with discrete spike self-attention to capture both smooth trends and abrupt events.
• DSF employs a learnable spike-gated mechanism to adaptively balance dual temporal representations, ensuring optimal fusion of spatial and temporal features.
• Ablation studies confirm DSF's effectiveness in long-sequence forecasting, demonstrating superior R² improvements and reduced error rates compared to alternative configurations.

Searching arXiv for the specified paper and closely related dual-path references to ground the article in current preprints. Dual-Path Spike Fusion (DSF) is the final and most explicitly hybrid component of SpikeSTAG, a spatial-temporal forecasting architecture that integrates graph structural learning with spike-based temporal processing for multivariate time-series forecasting (Hu et al., 4 Aug 2025). Within that system, DSF is the module that takes the spatial-temporal representation produced by the graph-spiking pipeline and turns it into a forecast by combining two different temporal views of the same signal. It is introduced on the premise that neither purely spiking graph aggregation nor purely recurrent temporal modeling is sufficient on its own, particularly when forecasting data exhibit both smooth long-term trends and abrupt event-like changes. The block is explicitly designed to “integrate spatial graph features and temporal dynamics via a spike-gated mechanism,” combining LSTM-processed sequences with spiking self-attention outputs, and is reported to improve accuracy on long-sequence datasets (Hu et al., 4 Aug 2025).

1. Placement within the SpikeSTAG pipeline

SpikeSTAG first embeds time features and an adaptive matrix, thereby eliminating the need for predefined graph structures. It then learns sequence features through the Observation (OBS) Block, which enriches node features with temporal covariates and local graph self-attention. After that, the Multi-Scale Spike Aggregation (MSSA) stage hierarchically aggregates neighborhood information through spiking SAGE layers, enabling multi-hop feature extraction while eliminating the need for floating-point operations. DSF is placed after MSSA and before the prediction head, so it functions as the final temporal consolidation module rather than as a graph-learning stage (Hu et al., 4 Aug 2025).

The manuscript summarizes the intended flow as

$$X_{\text{node},A,P}=F(Z_{\text{node},T}), \quad X_{\text{OBS}}=\text{OBS}(X_{\text{node},P}), \quad S_{\text{MSSA}}=\text{SNN}(\text{MSSA}(X_{\text{OBS},A})), \quad H_{\text{DSF}}=\text{DSF}(S_{\text{MSSA}}), \quad Y=F_{\text{predict}}(H_{\text{DSF}}).$$

Although the notation is described as somewhat garbled, the intended architecture is explicit: OBS enriches the input with temporal context and local graph relations, MSSA extracts sparse multi-hop graph-spike features, and DSF converts those features into a forecasting-oriented hidden state used by the predictor (Hu et al., 4 Aug 2025).

A common misconception is to regard DSF as a generic fusion layer appended to a temporal encoder. In SpikeSTAG it is more specific than that: it is downstream of adaptive spatial learning and spike-based neighborhood propagation, and it is introduced because the earlier representation, while already spatial-temporal, is still not sufficient to reliably capture long-horizon temporal structure.

2. Dual-path temporal refinement and temporal alignment

Mechanistically, DSF takes the MSSA output $S_{\text{MSSA}}$ as input to a dual-path temporal refinement process. One path is a lightweight LSTM, used to recover a continuous hidden-state sequence and to model longer-range, smoother dependencies. The other is a Spike Self-Attention (SSA) branch, intended to emphasize micro-scale temporal events and discontinuities in the spike domain. The paper therefore characterizes the LSTM branch as continuous and trend-aware, and the SSA branch as discrete and event-aware (Hu et al., 4 Aug 2025).

The SSA branch requires temporal alignment between the time-series step $\Delta T$ and the SNN step $\Delta t$. The relation is stated as

$\Delta T = T_s \cdot \Delta t,$

where $T_s$ is the number of spike time steps used to discretize the continuous dynamics. After this alignment, spike attention is applied as

$$\text{SSA}(X)=\text{SpikeSoftmax}\left(\frac{QK^T}{\sqrt{d_k}}\right)V.$$

The stated intent is to preserve event sensitivity in the spike domain while keeping the branch compatible with the temporal scale of the forecasting sequence (Hu et al., 4 Aug 2025).

The sequence flow is described in a specific order. MSSA produces spike outputs; those outputs are fed into a lightweight LSTM to generate hidden temporal information; the hidden sequence is discretized again via spike encoding; and the resulting spike trains are sent into SSA. This yields two aligned hidden representations: $\mathbf{H}_{\text{LSTM}}$ for the continuous hidden-state sequence from the LSTM branch, and

$\mathbf{H}_{\text{SSA}}$

for the event-driven sequence produced by SSA. DSF then operates on these aligned temporal views rather than on raw input features (Hu et al., 4 Aug 2025).

3. Spike-gated fusion mechanism

The defining feature of DSF is its learnable gating function, which combines the two temporal representations by soft selection rather than by fixed mixing. The gate is given as

$$\mathbf{G}=\sigma\!\left(\mathbf{W}[\mathbf{H}_{\text{LSTM}};\mathbf{H}_{\text{SSA}}]\right),$$

and the fused hidden state is

$S_{\text{MSSA}}$0

Here, $S_{\text{MSSA}}$1 denotes concatenation, $S_{\text{MSSA}}$2 is the sigmoid gate, $S_{\text{MSSA}}$3 is a learnable projection, and $S_{\text{MSSA}}$4 is element-wise multiplication (Hu et al., 4 Aug 2025).

The paper assigns a concrete interpretation to the gate. When $S_{\text{MSSA}}$5, the model trusts the LSTM branch more, which is useful during stable, smooth regimes with strong periodic or trend-like structure. When $S_{\text{MSSA}}$6, it trusts SSA more, which is useful when sudden events or local irregularities dominate. This makes DSF a context-dependent arbitration mechanism between two temporal modeling paradigms rather than a simple concatenation block (Hu et al., 4 Aug 2025).

That distinction is central to the way DSF is framed. The authors explicitly interpret the gain as a reduction of feature conflict through adaptive balancing of complementary strengths. In that reading, fusion is not merely representational aggregation; it is a learned decision about which temporal inductive bias should dominate at a given point in the representation.

4. Functional role in spatial-temporal forecasting

DSF is introduced because the upstream stages of SpikeSTAG already specialize the representation in a spatial-temporal manner, yet remain under-optimized for long-range temporal synthesis. The OBS Block incorporates temporal covariates and local graph self-attention. MSSA then performs multi-scale neighborhood sampling and spiking aggregation. The resulting representation is therefore strong at spatial structure and event-driven propagation, but DSF is the stage that translates those graph-spike features into a temporally fused hidden state suitable for forecasting (Hu et al., 4 Aug 2025).

The paper emphasizes that DSF “effectively improve[s] the model accuracy of long sequence datasets.” In the full benchmark, SpikeSTAG achieves an average $S_{\text{MSSA}}$7 of $S_{\text{MSSA}}$8, surpassing iSpikformer’s $S_{\text{MSSA}}$9 and matching iTransformer’s $\Delta T$0. At 48-step prediction, the model reaches $\Delta T$1 on Electricity and $\Delta T$2 on Solar. The paper attributes this robustness to the spatial-temporal integration enabled by the graph front-end together with DSF’s temporal fusion, and argues that explicit spatial dependency modeling “effectively mitigates the performance degradation commonly observed in conventional SNNs during long-sequence modeling” (Hu et al., 4 Aug 2025).

This functional division also clarifies what DSF is not. It is not the source of graph adaptivity, which is handled earlier through adaptive matrix learning and graph aggregation. It is also not a purely spiking replacement for recurrent modeling. Rather, it is the bridge between a graph-spiking encoder and the forecasting head, preserving spike-domain event sensitivity while reintroducing continuous hidden-state dynamics where trend and periodicity matter.

5. Ablation evidence and reported performance

The paper presents an ablation study across METR-LA, PEMS-BAY, Solar, and Electricity with four DSF-related configurations: W1 removes SSA and uses only the lightweight LSTM; W2 uses SSA only, directly from MSSA outputs; W3 stacks LSTM and SSA without gating; and W4 is the full DSF with gated fusion. The reported outcome is unambiguous: W4 is best on every dataset (Hu et al., 4 Aug 2025).

Dataset	$\Delta T$3 (W4)	$\Delta T$4 (W4)
METR-LA	0.868	0.375
PEMS-BAY	0.874	0.384
Solar	0.973	0.246
Electricity	0.987	0.207

The comparative pattern is as important as the absolute numbers. On METR-LA, W3 reaches $\Delta T$5, but W4 improves to $\Delta T$6 and lowers $\Delta T$7 from $\Delta T$8 to $\Delta T$9. On PEMS-BAY, W4 improves over W3 from $\Delta t$0 to $\Delta t$1 in $\Delta t$2, and from $\Delta t$3 to $\Delta t$4 in $\Delta t$5. The paper explicitly interprets this as evidence that gating reduces feature conflict and adaptively balances the complementary strengths of LSTM and SSA (Hu et al., 4 Aug 2025).

The ablation also shows that SSA-only outperforms LSTM-only on several datasets by roughly $\Delta t$6–$\Delta t$7 on $\Delta t$8, indicating that spike-based temporal representations are themselves strong. At the same time, those representations still benefit from recurrent smoothing and long-range trend modeling. Conversely, ungated stacking can perform well on periodic datasets such as Solar and Electricity, but can degrade on more complex traffic datasets such as PEMS-BAY. The paper presents this as evidence that unconstrained feature mixing is less stable than learned gating (Hu et al., 4 Aug 2025).

6. Relation to other dual-path architectures

DSF in SpikeSTAG belongs to a broader family of dual-path architectures, but its specific formulation is tied to spike-based forecasting. In speech enhancement, DPT-FSNet proposes a dual-path transformer-based full-band and sub-band fusion network in the frequency domain. There, the intra-transformer models sub-band information along time within each frequency bin, and the inter-transformer models full-band information across frequency at each time step; the two paths are applied alternatively rather than in parallel, and the representation is framed as more interpretable because it remains a complex spectrogram (Dang et al., 2021).

In spiking language modeling, SymbolicLight V1 introduces a spike-gated dual-path architecture centered on Dual-Path SparseTCAM. That model combines binary Leaky Integrate-and-Fire spikes with a continuous residual stream, and fuses an exponential-decay aggregation path with a spike-gated local attention path through

$\Delta t$9

The paper explicitly states that this mechanism can be viewed as a form of Dual-Path Spike Fusion, while also emphasizing that it is not a pure-spike SNN but a hybrid model in which spikes gate and organize continuous computation (Liu, 20 May 2026).

A further adjacent formulation appears in multimodal emotion recognition, where Dual-Path Conflict Resolution (DCR) separates a fusion/calibration path from an arbitration path that can select fusion or a unimodal prediction depending on conflict severity. That work is presented as a strong candidate for a DSF-like interpretation, but it does not define DSF and does not implement a spike-based gate in the sense of spiking neural networks (Yu et al., 6 May 2026).

This suggests that “dual-path” has become a general architectural template for combining complementary inductive biases, but DSF in the strict sense refers most directly to the SpikeSTAG block that fuses continuous trend-aware dynamics and discrete event-aware spike attention after graph-spiking aggregation. Within that narrower meaning, DSF denotes a forecasting-specific temporal fusion mechanism whose core operation is gated arbitration between $\Delta T = T_s \cdot \Delta t,$0 and $\Delta T = T_s \cdot \Delta t,$1, and whose reported benefit is most visible in longer-horizon multivariate forecasting (Hu et al., 4 Aug 2025).