Beyond Euclidean Latents: A Geometric and Logic-Aware Framework for Emergence, OOD Reasoning, and AI Safety

This paper argues that several persistent problems in modern AI—emergence without explanation, weak concept structure, out-of-distribution (OOD) failure, AI safety fragmentation, and degradation under recursive synthetic-data reuse—are not isolated issues, but consequences of a shared representational limitation. In particular, current AI systems continue to rely heavily on flat Euclidean latent spaces and statistically smooth assumptions that are effective for interpolation within observed regimes, yet structurally inadequate for discontinuity, semantically distant transition, rare-event preservation, and controllable behavior under novelty. In response, the paper proposes a geometric and logic-aware framework that moves beyond Euclidean latents by treating emergence, OOD reasoning, and AI safety as coupled phenomena governed by the geometry, logical coherence, and boundary-preserving structure of internal representation. Rather than framing robustness and safety as downstream patches, this work argues that the next stage of AI requires representational reformulation itself as a foundation for more coherent, robust, and safety-aware intelligence.