STSep: Spatial-Temporal Separable Network

• STSep is a network architecture that decouples spatial and temporal processing into specialized branches, enhancing efficiency and learning outcomes.
• It employs tailored spatial modules (e.g., 2D CNNs, graph convolutions) and dedicated temporal operators (e.g., 1D convolutions, RNNs) to capture complex dynamics.
• Fusion techniques such as gating and additive methods integrate the separate outputs, reducing parameters and improving performance over monolithic models.

A Spatial-Temporal Separable Network (STSep) is an architectural paradigm for modeling data with both spatial and temporal dependencies, in which processing is explicitly factorized into separate branches or modules for spatial and temporal handling. Rather than modeling spatial and temporal interactions as a monolithic entity, STSep architectures pursue decoupling—leveraging distinct parameterizations, neural operations, and often optimization protocols for spatial and temporal aspects, followed by carefully designed fusion mechanisms. This paradigm spans conventional deep neural models, graph neural networks, LLM-based forecasting, and spiking neural networks. The following sections present a comprehensive summary of STSep methodologies, architectural instantiations, benefits, and empirical outcomes based strictly on technical findings in the literature.

1. Core Principles and Design Strategies

STSep architectures implement an explicit separation between the spatial and temporal components of model processing. This separation can be realized at the level of convolutional layers (e.g., S3TC (El-Assal et al., 2023), StNet's TXB module (He et al., 2018)), graph convolutional affinity matrices (STS-GCN (Sofianos et al., 2021)), neural residual blocks (spiking SNN STSep (Dong et al., 5 Dec 2025)), or global dataflow (Semi-Coupled Structure (Pang et al., 2020), STH-SepNet (Chen et al., 26 May 2025)).

Key design elements include:

• Spatial Branch: Dedicated modules or operations capture semantic, location, or structural information, often with 2D convolution (video, image), spatially local graph convolution (graph data), or frame-wise computation.
• Temporal Branch: Separate units explicitly encode dynamics or evolution through temporal convolution, RNN/ConvRNN modules, temporal difference operators, or sequence models such as transformers.
• Fusion/gating: Outputs of the two branches are merged via multiplicative gating (Pang et al., 2020), additive fusion with learned weights (Dong et al., 5 Dec 2025), or a learned gating MLP (Chen et al., 26 May 2025).
• Explicit parameter decoupling: Parameter and computational savings follow from the separated approach versus dense joint operations (e.g., 2D+1D convolution vs. full 3D convolution).

This approach is contrasted with traditional joint models, such as pure 3D convolution in CNNs or monolithic spatio-temporal graphs in GNNs, with STSep reducing parameter count (up to 83× in pose-forecasting GCNs), facilitating training efficiency, and yielding improved empirical performance in complex spatio-temporal domains.

2. Formal Mathematical Frameworks

Different STSep variants employ instantiations appropriate for their data class:

• Convolutional STSep: Factorizes 3D convolution into sequential 2D spatial then 1D temporal convolutions (S3TC), reducing parameter count from $C_{in}C_{out}f_wf_hf_t$ to $C_{out}(C_{in}f_wf_h + f_t)$ and yielding increased output activity and learning efficiency in spiking networks (El-Assal et al., 2023).
• Graph-based STSep: The full spatio-temporal adjacency $A^{st}\in\mathbb{R}^{(VT)\times(VT)}$ is decomposed into Kronecker-type products or matrix multiplications of learnable $A^s \in \mathbb{R}^{V\times V}$ (joint-wise) and $A^t \in \mathbb{R}^{T\times T}$ (frame-wise) matrices. The resulting update is $H^{(l+1)} = \sigma(A^sA^tH^{(l)}W^{(l)})$, bottlenecking cross-talk and achieving drastic parameter reduction (Sofianos et al., 2021).
• Neural-sequence STSep: In semi-coupled structures, per-time-step spatial encodings $h_s(\cdot)$ are fused with temporal encodings $h_t(\cdot)$ (from ConvRNN/LSTM) via $F = \mathrm{ReLU}(h_s)\circ\mathrm{Sigmoid}(h_t)$, with training losses to encourage specialization (Pang et al., 2020).
• Modern LLM-based STSep: STH-SepNet decouples sequence modeling into a "temporal module" (lightweight LLM applied to locally aggregated tokens) and an "adaptive hypergraph spatial module," dynamically fusing representations with $$\tilde{O} = O_{temp} \odot G + O_{spat} \odot (1-G)$$, where $G$ is a learned gating vector (Chen et al., 26 May 2025).
• Spiking SNN STSep: Each residual block is split into a spatial (stateless 2D block) and a temporal (3×3 convolution over first-order temporal differences) branch. Fused as $$X^{l+1}_t = X^l_t + (1-\alpha^l)F^{s,l}_t + \alpha^lF^{t,l}_t$$ (Dong et al., 5 Dec 2025).

3. Representative Architectures

The STSep paradigm is instantiated across modalities and network families:

Model	Domain	Spatial Process	Temporal Process	Fusion
S3TC (El-Assal et al., 2023)	SNN video	2D spike conv	1D spike conv	Sequential
StNet (He et al., 2018)	Video action rec.	2D conv on "super-images"	Temporal Xception (sep convs)	Additive, then TXB
STS-GCN (Sofianos et al., 2021)	Human pose pred.	V×V learned S-matrix	T×T learned T-matrix	Matrix products
STH-SepNet (Chen et al., 26 May 2025)	Spatio-temp. pred.	Adaptive hypergraph GNN	LLM (BERT) on time-series tokens	Gated MLP
SCS/STSep (Pang et al., 2020)	Sequence tasks	Frame-wise CNNs	Conv-RNN, LSTM	Multiplicative gating
STSep-SNN (Dong et al., 5 Dec 2025)	Spiking video	Stateless spatial block	ΔX block (temporal diff + conv)	Additive, weighted

These architectures preserve spatial/temporal specializations, demonstrate superior computational or memory efficiencies compared to monolithic baselines, and frequently enable modular backbone or fusion replacements.

4. Training Protocols and Optimization Procedures

STSep models employ specialized training workflows to promote branch specialization and efficient convergence:

• Branch-specialized training/gradient scheduling: Semi-coupled structures utilize Switch Gradient Descent or Advanced STSGD, where gradient flow from the loss to spatial or temporal branch is randomly dropped with scheduled probability $p_s, p_t$, strongly decoupling early-phase learning, gradually annealed for joint optimization (Pang et al., 2020).
• Sub-task (indicating) losses: Auxiliary losses on spatial (e.g., object outline) or temporal (e.g., frame difference) tasks further encourage branch specialization (Pang et al., 2020).
• Gating/fusion learning: STSep models with learned gates (e.g., MLP-based in STH-SepNet) train the fusion as part of end-to-end optimization (Chen et al., 26 May 2025).
• Parameter initialization and knowledge transfer: StNet and STH-SepNet leverage pre-trained ImageNet or LLM weights to accelerate convergence or permit low-parameter regimes (He et al., 2018, Chen et al., 26 May 2025).
• Backbone independence: Most frameworks are modular—allowing swapping of CNN, GNN, or LLM backbones.

5. Empirical Results and Quantitative Performance Gains

STSep models achieve state-of-the-art or competitive performance in multiple empirical contexts, with pronounced efficiency advantages:

• Video Action Recognition: StNet (He et al., 2018) achieves 71.4% top-1 on Kinetics400 (ResNet101, 311 GFLOPs) vs 64.7% for C3D, 70.2% for I3D, with strong generalization to UCF101.
• Pose Forecasting: STS-GCN (Sofianos et al., 2021) yields up to 34% error reductions in mid- to long-term MPJPE versus DCT-RNN-GCN, with just 1.7% of its parameter count.
• Spatio-Temporal Prediction: STH-SepNet (Chen et al., 26 May 2025) outperforms 18 baselines on benchmarks across traffic and climate—e.g., BIKE-Inflow MAE 5.18 vs. 5.54 (TimesNet), with 25–30% GPU memory reduction and >1.7× speedup.
• SNN Video Understanding: STSep (Dong et al., 5 Dec 2025) consistently exceeds non-separated SNNs: e.g., on Something-Something V2, “STSep (ImageNet↑)” achieves 34.4% top-1 (val, 16×128 frames) versus TSN at 24.9%; S3TC (El-Assal et al., 2023) attains parameter reductions (7× lower) and accuracy improvements over 3D spiking convolutions.
• Semantic Sequencing, Forecasting, and Annotation: SCS/STSep (Pang et al., 2020) achieves ~61.7% top-1 on Kinetics, 71% IoU on Cityscapes outline annotation, and improved auto-driving, object-outlining, and radar-echo forecasting metrics vs. conventional LSTM and ConvLSTM baselines.

Ablation studies repeatedly confirm that strict or gated separation is essential for these gains; deactivating gating, hybridization, or specialized training typically decreases performance or leads to collapse (over-integration).

6. Architectural Variations and Theoretical Considerations

Multiple lines of evidence point to the efficacy and subtleties of STSep separation:

• Parameter efficiency: Decomposing spatial and temporal operators achieves reductions from $O(V^2T^2)$ adjacency parameters (full spatio-temporal GCN) to $O(V^2 + T^2)$ (STS-GCN).
• Expressivity vs. Inductive Bias: While strict separability can limit the learning of features with entangled spatio-temporal semantics (El-Assal et al., 2023), empirical ablations repeatedly show performance benefits when data exhibit low-rank temporal or modular spatial structure, as in traffic, pose, or edge-dominated video domains.
• Resource competition in SNNs: In deep SNNs, temporal state maintenance consumes capacity for spatial learning; separation ensures freed representational power for both, with moderate decoupling outperforming both extremes (Dong et al., 5 Dec 2025).
• Adaptivity and fusion: STH-SepNet dynamically constructs hypergraphs and fuses branch outputs with a gating network, enabling adaptive modeling of spatial and temporal drift, as empirically validated by ablations (Chen et al., 26 May 2025).
• Unsupervised and neuromorphic viability: STSep methods such as S3TC preserve event-driven, local unsupervised learning (STDP) and significantly reduce hardware mapping costs on neuromorphic substrates (El-Assal et al., 2023).

7. Limitations, Open Questions, and Future Directions

While STSep methods consistently demonstrate empirical, computational, and architectural advantages, several caveats are documented:

• Loss of Joint Spatio-Temporal Entanglement: Full 3D filters or dense adjacencies can, in principle, capture higher-order correlations that strict separation may miss (El-Assal et al., 2023).
• Hyperparameter Sensitivity: The optimal division of kernel sizes or the degree of separation is highly task- and data-dependent (El-Assal et al., 2023, Dong et al., 5 Dec 2025).
• Scalability and Generalization: While STH-SepNet (Chen et al., 26 May 2025) confirms scalability on large-scale datasets and tasks, deeper, more complex architectures integrating STSep at multiple stages require further validation, especially in unsupervised and neuromorphic contexts.
• Branch Specialization Schedules: Advanced training protocols (e.g., ASTSGD) require careful design of gradient dropping and sub-task supervision, and the dynamics of such schedules remain under investigation (Pang et al., 2020).

• "S3TC: Spiking Separated Spatial and Temporal Convolutions with Unsupervised STDP-based Learning for Action Recognition" (El-Assal et al., 2023)
• "StNet: Local and Global Spatial-Temporal Modeling for Action Recognition" (He et al., 2018)
• "Space-Time-Separable Graph Convolutional Network for Pose Forecasting" (Sofianos et al., 2021)
• "Decoupling Spatio-Temporal Prediction: When Lightweight Large Models Meet Adaptive Hypergraphs" (Chen et al., 26 May 2025)
• "Complex Sequential Understanding through the Awareness of Spatial and Temporal Concepts" (Pang et al., 2020)
• "Unleashing Temporal Capacity of Spiking Neural Networks through Spatiotemporal Separation" (Dong et al., 5 Dec 2025)