Probabilistic Geometric Alignment via Bayesian Latent Transport for Domain-Adaptive Foundation Models

Adapting large-scale foundation models to new domains with limited supervision remains a fundamental challenge due to latent distribution mismatch, unstable optimization dynamics, and miscalibrated uncertainty propagation. This paper introduces an uncertainty-aware probabilistic latent transport framework that formulates domain adaptation as a stochastic geometric alignment problem in representation space. A Bayesian transport operator is proposed to redistribute latent probability mass along Wasserstein-type geodesic trajectories, while a PAC-Bayesian regularization mechanism constrains posterior model complexity to mitigate catastrophic overfitting. The proposed formulation yields theoretical guarantees on convergence stability, loss landscape smoothness, and sample efficiency under distributional shift. Empirical analyses demonstrate substantial reduction in latent manifold discrepancy, accelerated transport energy decay, and improved covariance calibration compared with deterministic fine-tuning and adversarial domain adaptation baselines. Furthermore, bounded posterior uncertainty evolution indicates enhanced probabilistic reliability during cross-domain transfer. By establishing a principled connection between stochastic optimal transport geometry and statistical generalization theory, the proposed framework provides new insights into robust adaptation of modern foundation architectures operating in heterogeneous environments. These findings suggest that uncertainty-aware probabilistic alignment constitutes a promising paradigm for reliable transfer learning in next-generation deep representation systems.

A Real-Time Neuro-Symbolic Ethical Governor for Safe Decision Control in Autonomous Robotic Manipulation

Ethical decision governance has become a critical requirement for autonomous robotic systems operating in human-centered and safety-sensitive environments. This paper presents a real-time neuro-symbolic ethical governor designed to enable risk-aware supervisory control in autonomous robotic manipulation tasks. The proposed framework integrates transformer-based ethical reasoning with a probabilistic ethical risk field formulation and a threshold-based override control mechanism. language-grounded ethical intent inference capability is learned from natural language task descriptions using a fine-tuned DistilBERT model trained on the ETHICS commonsense dataset. A continuous ethical risk metric is subsequently derived from predicted unsafe action probability, confidence uncertainty, and probabilistic variance to support adaptive decision filtering. The effectiveness of the proposed approach is validated through simulated autonomous robot-arm task scenarios involving varying levels of human proximity and operational hazard. Experimental results demonstrate stable model convergence, reliable ethical risk discrimination, and improved safety-aware decision outcomes without significant degradation of task execution efficiency. The proposed neuro-symbolic architecture further provides enhanced interpretability compared with purely data-driven safety filters, enabling transparent ethical reasoning in real-time control loops. The findings suggest that ethical decision governance can be effectively modeled as a dynamic supervisory risk layer for autonomous robotic systems, with potential applicability to broader cyber-physical and assistive robotics domains.