Structure-Aware Scheduling Graph

• The paper demonstrates a novel formalism that maps time-evolving scheduling dynamics into graphs, enabling the detection of both typical and anomalous patterns.
• It details a methodology combining graph neural networks with multi-scale semantic aggregation and a structural-consistency loss to capture and regularize complex task dependencies.
• Experimental results show significant improvements in precision, recall, F1, and AUC over baselines such as TADDY, ANEMONE, and GCN-VAE in detecting structural, resource, and delay anomalies.

A structure-aware driven scheduling graph is a formalism and computational paradigm in which system scheduling behaviors—task executions, resource allocations, precedence constraints, and their temporal dynamics—are modeled as graphs whose nodes and edges explicitly encode evolving dependencies, resource states, execution stages, and semantic patterns. This structure-aware approach enables explicit, context-sensitive representation and detection of both typical and anomalous scheduling patterns by leveraging advanced graph neural network (GNN) architectures and semantic aggregation modules. The methodology is particularly suited for complex cyber-physical and information systems exhibiting concurrency, competition, resource stress, and nonstationary structural behaviors (Lyu et al., 21 Dec 2025).

1. Structure-Guided Construction of Scheduling Behavior Graphs

A central feature is the mapping of system scheduling dynamics at time $t$ into a graph $G_t = (V_t, E_t, X_t)$ where:

• $V_t$: Nodes, each representing an individual task at time $t$.
• $E_t \subseteq V_t \times V_t$: Directed edges encoding scheduling dependencies—including resource sharing, execution precedence, and co-execution constraints.
• $X_t \in \mathbb{R}^{|V_t| \times d}$: Node feature matrix, with features including task IDs ($x_i^{id}$), resource demand intensity ($x_i^{res}$), and temporal or stage-specific features ($x_i^{time}$).

Node embeddings are computed as $$h_i^{(0)} = \mathrm{Embed}(x_i^{id}, x_i^{res}, x_i^{time})$$. Edge weights $a_{ij}$ synthesize static and dynamic dependency signals: $$a_{ij} = \operatorname{Softmax}_{j} \left( \frac{ (W_a h_i^{(0)})^T (W_b h_j^{(0)}) }{ \sqrt{d} } + b_{ij}^t \right)$$ where $W_a, W_b \in \mathbb{R}^{d \times d}$ are trainable, and $b_{ij}^t$ is a dynamic bias term to encode temporal ordering.

Scheduling evolution is modeled via a sequence $\{G^{(1)}, \ldots, G^{(T)}\}$, with dynamic aggregation: $$G^{(t)} = \mathrm{AGG}(G^{(t-1)}, G_{\mathrm{curr}}^{(t)}, G^{(t+1)})$$ where $\mathrm{AGG}(\cdot)$ merges adjacency and feature matrices.

A structural-consistency loss $L_{\text{graph}}$ regularizes both local smoothness (encouraging connected nodes to have nearby embeddings) and global distributional alignment: $$L_{\text{graph}} = \lambda_1 \sum_{(i,j) \in E_t} \| h_i - h_j \|_2^2 - \alpha + \lambda_2 \sum_i D_{\mathrm{KL}}(p_i \| q_i)$$ with $p_i$ representing label priors from neighborhood reasoning and $q_i$ the model prediction.

2. Multi-Scale Semantic Aggregation and Global Topology Integration

The multi-scale graph semantic aggregation (MS-GSA) module augments node representations by recursively aggregating information out to $k$-hop neighborhoods ($k=1,\dots,K$), capturing both micro-local and global dependencies: $$h_i^{(k)} = \mathrm{AGG}\{ h_j^{(k-1)} : j \in N^{(k)}(i) \}$$ The $k$-scale outputs are fused by learned, scale-aware attention: $$\beta^{(k)} = \frac{ \exp(w_a^T \tanh(W_h h_i^{(k)} + b_a)) }{ \sum_{\ell=1}^K \exp(w_a^T \tanh(W_h h_i^{(\ell)} + b_a)) }$$

$$h_i^{\mathrm{fusion}} = \sum_{k=1}^K \beta^{(k)} h_i^{(k)}$$

A global residual enhancement introduces graph-level context: $$h_i^{\mathrm{final}} = h_i^{\mathrm{fusion}} + W_r \cdot \mathrm{READOUT}\left(\{h_j^{\mathrm{fusion}}\}\right)$$ where $\mathrm{READOUT}$ is typically mean-pooling.

Consistency is enforced through MS-GSA-specific loss terms: $$L_{\mathrm{MS-GSA}} = \gamma_1 \sum_{i,k} \| h_i^{(k)} - h_i^{\mathrm{fusion}}\|_2^2 + \gamma_2 \sum_{i} \| h_i^{\mathrm{final}} - h_i^{(0)} \|_2^2$$ This hierarchical semantic integration enables the disentangling of local versus global anomaly signatures.

3. Anomaly Detection Methodology and Quantitative Evaluation

Final node embeddings $h_i^{\mathrm{final}}$ are scored for anomaly likelihood via an MLP and sigmoid output ($s_i \in [0,1]$). The system models and evaluates three canonical anomaly modalities:

• Structural shifts: Edge rewiring events reflecting changes in dependency structures.
• Resource changes: Perturbations in node resource vectors $x_i^{res}$.
• Task delays: Abnormal stretches in $x_i^{time}$ features to reflect latency.

Comprehensive benchmarking was performed on a real-world cloud workload dataset, with key metrics including precision, recall, F1, and area under the ROC curve (AUC). Baseline comparisons include TADDY, ANEMONE, GCN-VAE, and AT-GTL. The structure-aware driven approach demonstrably outperforms all baselines:

Method	Precision	Recall	F1	AUC
TADDY	0.87	0.84	0.85	0.90
ANEMONE	0.89	0.86	0.87	0.91
GCN-VAE	0.82	0.79	0.80	0.88
AT-GTL	0.85	0.83	0.84	0.89
Ours	0.91	0.88	0.89	0.93

Ablation experiments show that both the structure-guided construction (GSG-SGC) and multi-scale aggregation (MS-GSA) are critical, with the full model yielding the strongest anomaly separability. Optimal performance is achieved at neighborhood scale $k=3$, which balances local and global context.

4. Visualization, Representation, and Separability of Scheduling Patterns

t-SNE embedding analysis reveals the representational enhancement provided by structure-aware design:

• Baseline embeddings: Significant overlap between normal and anomalous classes, poor discriminability.
• GSG-SGC module only: Improved separation for structural anomalies, insufficient discrimination for resource/delay anomalies.
• MS-GSA module only: Clarified distinction for delay anomalies, but structural anomalies remain entangled.
• Full model: All anomaly classes become cleanly clustered and well separated, capturing both global structural and local semantic irregularities.

This demonstrates the necessity of combining explicit structure representation (scheduling stages, resources, paths) with multi-scale semantic fusion for disentangled, robust pattern recognition.

5. Significance for Scheduling Anomaly Detection in Complex Systems

The structure-aware driven scheduling graph paradigm advances anomaly detection by jointly modeling:

• Temporal evolution and global relationships in scheduling (via dynamically evolving graphs and structural bias in graph construction).
• Hierarchically aggregated semantics (via multi-scale, attention-weighted fusion).
• Direct incorporation of system execution context—resource usage, competition, concurrency—into the detection model.

Empirically, this enables sensitive detection of structural disruptions, resource-contention events, and scheduling delays. The approach is adaptive, robust to multiple classes of nonstationarity, and enables explicit interpretation of anomalous graph structures (Lyu et al., 21 Dec 2025).

6. Perspectives and Further Directions

Structure-aware driven scheduling graphs represent a general strategy applicable beyond anomaly detection, supporting advanced scheduling, adaptive resource management, and event pattern recognition in time-evolving, resource-constrained environments. Key future challenges include:

• Scaling to massive, long-lived dynamic graphs under adversarial operational conditions.
• Generalization across diverse domains with varying structural regularities.
• Integration with reinforcement learning or domain-knowledge-guided optimization loops.

Ongoing research explores extensions to learning-based scheduling, hybrid semantic-logic pattern recognition, and explainable anomaly reasoning grounded in topological graph dynamics.