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.

Antimicrobial peptides are short proteins that can kill bacteria and may help combat antibiotic resistance. Discovering new antimicrobial peptides is extremely difficult because the number of possible peptide sequences is enormous — there are roughly $10^{33}$ possible peptides of length up to 25. Only a tiny fraction of them are actually effective against bacteria. Machine learning methods can help by organizing peptides into a “map” where similar peptides are placed close together. However, most existing methods assume that this map is flat, meaning that moving the same distance in any direction leads to similar changes in peptide properties. Real peptide data do not behave this way, making exploration inaccurate and inefficient. We developed a new framework, called PepCompass, that explores peptide space while accounting for its curved geometry. First, PepCompass performs global exploration to identify promising unexplored regions between known antimicrobial peptides. It then performs local optimization within these regions to design improved peptides with stronger antimicrobial activity. We experimentally tested the generated peptides in the laboratory. PepCompass successfully identified 29 novel peptides with strong broad-spectrum antibacterial activity. These results show that geometry-aware machine learning can provide a powerful new strategy for antimicrobial peptide discovery.