Multiscale Euclidean Network Trajectories: Second-Moment Geometry, Attribution, and Change Points

arXiv:2605.04589 · stat.ML, cs.LG, math.ST, stat.TH · Submitted 2026-05-06 · Read on arXiv

stat.ML, cs.LG, math.ST, stat.TH

Submitted: 2026-05-06

Updated: 2026-09-25

Code: https://github.com/hisanor013/ment

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Trace — 67× in this paper · explained in 2 episodes
• Embeddings — 47× in this paper · explained in 2 episodes
• Consistency — 35× in this paper · explained in 3 episodes
• Alignment — 11× in this paper · explained in 1 episode
• Accuracy — 8× in this paper · explained in 1 episode
• Modularity — 5× in this paper · explained in 9 episodes
• Multiscale Euclidean Network Trajectories — 5× in this paper
• Adjacency Matrix — 4× in this paper · explained in 1 episode
• Spectral Gap — 4× in this paper · explained in 5 episodes
• F1 Score — 3× in this paper · explained in 3 episodes
• Generative Model — 3× in this paper · explained in 2 episodes
• Hypergraph — 3× in this paper · explained in 2 episodes
• Interpretability — 3× in this paper · explained in 15 episodes
• Latent Space — 3× in this paper · explained in 7 episodes
• Actor — 2× in this paper · explained in 3 episodes
• Adam — 2× in this paper · explained in 2 episodes
• Laplacian Anomaly Detection — 2× in this paper
• Latent Representation — 2× in this paper · explained in 2 episodes
• Robustness — 2× in this paper · explained in 5 episodes
• Verification — 2× in this paper · explained in 2 episodes
• Abstraction — 1× in this paper · explained in 1 episode
• Aggregation — 1× in this paper · explained in 1 episode
• Benchmark — 1× in this paper · explained in 2 episodes
• Clustering — 1× in this paper · explained in 2 episodes
• Commentary — 1× in this paper · explained in 2 episodes
• Core — 1× in this paper · explained in 2 episodes
• Fingerprinting — 1× in this paper · explained in 2 episodes
• Hilbert Space — 1× in this paper · explained in 2 episodes
• Latent Representations — 1× in this paper · explained in 3 episodes
• Objective Function — 1× in this paper · explained in 2 episodes
• Synthetic Data Generation — 1× in this paper · explained in 5 episodes
• Theoretical Guarantees — 1× in this paper · explained in 2 episodes

Sources

• The multilayer random dot product graph
• Euclidean mirrors and first-order changepoints in network time series
• Dynamic networks clustering via mirror distance
• NetSimile: A Scalable Approach to Size-Independent Network Similarity
• Change-point detection in dynamic networks via graphon estimation
• Doubly unfolded adjacency spectral embedding of dynamic multiplex graphs

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