PepCompass: Navigating Peptide Embedding Spaces Using Riemannian Geometry

Antimicrobial peptide discovery is challenged by the astronomical size of peptide space and the relative scarcity of active peptides. While generative models provide latent maps of this space, they typically ignore decoder-induced geometry and rely on flat Euclidean metrics, making exploration distorted and inefficient. Existing manifold-based approaches assume fixed intrinsic dimensionality, which fails for real peptide data. We introduce **PepCompass**, a geometry-aware framework based on a **Union of $\kappa$-Stable Riemannian Manifolds** that captures local decoder geometry while maintaining computational stability. PepCompass performs global interpolation via **Potential-minimizing Geodesic Search (PoGS)** to bias discovery toward promising seeds and enables local exploration through **Second-Order Riemannian Brownian Efficient Sampling** and **Mutation Enumeration in Tangent Space**, which together form **Local Enumeration Bayesian Optimization (LE-BO)**. PepCompass achieves a 100% *in-vitro* validation rate: PoGS identifies four novel seeds and LE-BO optimizes them into 25 highly active, broad-spectrum peptides, demonstrating that geometry-informed exploration is a powerful paradigm for antimicrobial peptide design.