Unfolded Laplacian Spectral Embedding: A Theoretically Grounded Approach to Dynamic Network Representation

Dynamic relational structures play a central role in many AI tasks, but their evolving nature presents challenges for consistent and interpretable representation. A common approach is to learn time-varying node embeddings, whose effectiveness depends on satisfying key stability properties. In this paper, we propose Unfolded Laplacian Spectral Embedding, a new method that extends the Unfolded Adjacency Spectral Embedding framework to normalized Laplacians while preserving both cross-sectional and longitudinal stability. We provide formal proof that our method satisfies these stability conditions. In addition, as a bonus of using the Laplacian matrix, we establish a new Cheeger-style inequality that connects the embeddings to the conductance of the underlying dynamic graphs. Empirical evaluations on synthetic and real-world datasets support our theoretical findings and demonstrate the strong performance of our method. These results establish a principled and stable framework for dynamic network representation grounded in spectral graph theory.

Learning Method for S4 with Diagonal State Space Layers using Balanced Truncation

We introduce a novel learning method for Structured State Space Sequence (S4) models incorporating Diagonal State Space (DSS) layers, tailored for processing long-sequence data in edge intelligence applications, including sensor data analysis and real-time analytics. This method utilizes the balanced truncation, a prevalent model reduction technique in control theory, applied specifically to DSS layers to reduce computational costs during inference. By leveraging parameters from the reduced model, we refine the initialization process of S4 models, outperforming the widely used Skew-HiPPO initialization in terms of performance. Numerical experiments demonstrate that our trained S4 models with DSS layers surpass conventionally trained models in accuracy and efficiency metrics. Furthermore, our observations reveal a positive correlation: higher accuracy in the original model consistently leads to increased accuracy in models trained using our method, suggesting that our approach effectively leverages the strengths of the original model.