Zentropy Semantic Configuration Fields: A Cross-Modal Framework for Analyzing Semantic Organization in Learned Representations

Representation analysis largely characterizes learned embeddings through feature similarity, linear separability, or pairwise geometry, leaving local semantic organization, i.e., how labels are composed around a point and how that composition changes with depth and neighborhood scale, without a unified measurement language. We introduce Zentropy Semantic Configuration Fields (SCF): a smoothed local class-posterior entropy, resolved as a field over network depth $l$ and neighborhood granularity $\tau$, $\mathcal{S}=\{Z(l,\tau ){\}}_{l,\tau }$. The statistic itself is a Nadaraya-Watson label posterior followed by Shannon entropy; the contribution is the field, its descriptor calculus, and a permutation-null calibration. Controlled composition experiments show the estimator closely tracks true local semantic entropy at fixed geometry ($R^2=0.977$, Pearson $r=0.994$), and four-quadrant experiments show it is complementary to distance rather than a reparameterization. Instantiating SCF across five modalities including vision, audio, time series, text, physiological signals reveals structured layer-by-granularity organization that often continues to evolve after linear probing has largely saturated, predominantly at fine granularities. A morphology benchmark shows that systems occupy clearly distinct field morphologies, with descriptors that are non-redundant and largely stable under seed, layer, bandwidth, and metric perturbations. A permutation-null calibration separates label-driven organization from a systematic label-free concentration drift, and reveals substantially stronger calibrated organization under label smoothing in a matched training comparison; in low-drift domains the observed organization is entirely label-driven. SCF thus provides a common analytical language for comparing how representation-learning systems organize semantic information.