Structural Loss in Multi-Temporal Networks: A Projection-Based Perspective on Observation-Dependent Variability.

This is a preprint version of a paper accepted at the CAS Conference. A camera-ready version will follow.

Variability in predictive performance and explanatory outcomes across observational scales is a persistent feature of complex network analysis. In multi-layered and non-stationary systems, identical underlying structures can produce divergent observations depending on temporal resolution, aggregation procedures, or observation range. Such variability is typically treated as noise or as a limitation of specific models, leaving its structural origin insufficiently explained.

This study introduces structural loss as a projection-induced loss of rule-origin causal distinguishability. We conceptualize networks as layered relational structures governed by heterogeneous transition constraints and model observation as an integrative projection that maps multi-temporal relational spaces onto a single observational representation. Under such projection, causally distinct transitions across layers may become observationally indistinguishable.

From this perspective, observation-dependent variability is reinterpreted not as error, but as information generated through projection. The framework provides a structural explanation for scale-sensitive analytical behavior and enables fluctuations previously regarded as noise to be understood as meaningful signals of underlying relational heterogeneity. Without assuming a privileged observational scale, this approach offers a foundation for analyzing multi-layered, multi-temporal complex adaptive systems.