A Structure-Preserving Geometric Mapping Algorithm for Safe Representation Learning and Latent Space Optimization

Geometric structure plays a critical role in representation learning for safety-sensitive recognition, where latent distortion may weaken both task discrimination and unsafe-sample rejection. Existing methods often optimize prediction, manifold preservation, or out-of-distribution detection separately, leaving the interaction between structural fidelity and safety-boundary stability insufficiently modeled. This paper proposes SPG-SafeMap, a structure-preserving geometric safe learning framework that jointly learns latent representations, task predictors, and safety boundaries. The method integrates local neighborhood preservation, landmark-based geodesic consistency, graph Laplacian smoothness, geometric safety-margin learning, adversarial safety consistency, and prototype-based compactness into a unified optimization objective. Experiments on multiple public benchmarks show that SPG-SafeMap consistently improves task performance, OOD safety detection, safety-risk suppression, and latent structure preservation compared with representative manifold, anomaly-detection, and contrastive-learning baselines. These results indicate that explicitly coupling geometric mapping with safety-aware representation optimization provides a more reliable latent space for robust and interpretable safe learning.