A Non-Euclidean Approach to Generative AI and Out-of-Distribution Reasoning

A Non-Euclidean Approach to Generative AI and Out-of-Distribution Reasoning This work introduces a novel generative modeling framework based on Non-Euclidean Space Generative Models (NESGM), addressing the limitations of conventional probabilistic and Euclidean-based approaches in both creative AI and autonomous driving applications. Conventional generative models—such as Variational Autoencoders (VAE), Generative Adversarial Networks (GANs), and diffusion models—primarily operate in smooth Euclidean latent spaces, which restrict their ability to capture logical discontinuities, emergent structures, and out-of-distribution (OOD) events. The proposed NESGM embeds generative reasoning within curvature-aware manifolds (hyperbolic, spherical, and branching spaces), enabling conceptual jumps, structural novelty, and Poisson-based uniqueness constraints. This approach is further integrated with Irreversible Informational Structures (IIS) to model causal asymmetry and rare-event risk chains. Two primary application domains are explored: Creative AI: NESGM demonstrates the ability to generate metaphorical text, abstract visual art, and cross-modal conceptual blending by leveraging non-local transitions in latent space. Autonomous Driving AI: NESGM, combined with IIS, generates rare and discontinuous risk scenarios beyond the defined Operational Design Domain (ODD), supporting safety validation under SOTIF (ISO/PAS 21448) and ISO 26262. The framework feeds high-fidelity simulators with OOD scenarios, enhancing risk-oriented testing and reliability assessment. This study positions NESGM as a foundation for geometry-aware generative reasoning, bridging creative discontinuity and safety-critical scenario generation. By formalizing creativity and risk as geometric traversals in discontinuous latent spaces, it offers both a practical tool for simulation and validation and a theoretical perspective toward a Cognitive/Epistemic (CE) understanding of AI reasoning. Version History: v1.0First public preprint release of the original NESGM framework. This version introduced the core idea of moving beyond Euclidean latent spaces toward curved and non-Euclidean generative representations, together with exploratory discussions of autonomous driving, creative AI, and structural compression. v1.1Revised reference-checked edition. Bibliographic errors in the autonomous-driving section were corrected by removing incorrect citations and adding validated references on safety-critical driving scenario generation, data-driven scenario generation, and simulator-conditioned scene generation. In addition, minor terminology and notation issues were corrected, including the OOD/ODD distinction in the evaluation metrics discussion.