Title: PepCompass: Navigating Peptide Embedding Spaces Using Riemannian Geometry
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)
Keywords: union of manifolds, peptide optimization, riemannian geometry, geodesics, tangent space, mutation

Abstract: Antimicrobial peptide discovery is challenged by the astronomical size of peptide space and the relative scarcity of active peptides. Generative models provide continuous latent ``maps'' of peptide space, but conventionally ignore decoder-induced geometry and rely on flat Euclidean metrics, rendering exploration and optimization distorted and inefficient.
Prior manifold-based remedies assume fixed intrinsic dimensionality, which critically fails in practice for peptide data. Here, we introduce **PepCompass**, a geometry-aware framework for peptide exploration and optimization. At its core, we define a **Union of $\kappa$-Stable Riemannian Manifolds** \$\mathbb{M}^{\kappa}\$, a family of decoder-induced manifolds that captures local  geometry while ensuring computational stability. We propose two local exploration methods: **Second-Order Riemannian Brownian Efficient Sampling**, which provides a convergent second-order approximation to Riemannian Brownian motion, and **Mutation Enumeration in Tangent Space**, which reinterprets tangent directions as discrete amino-acid substitutions. Combining these yields Local Enumeration Bayesian Optimization (**LE-BO**), an efficient algorithm for local activity optimization. Finally, we introduce  Potential-minimizing Geodesic Search (**PoGS**), which interpolates between prototype embeddings along property-enriched geodesics, biasing discovery toward seeds, i.e. peptides with favorable activity. *In-vitro* validation confirms the effectiveness of PepCompass: PoGS yields four novel  seeds, and subsequent optimization with LE-BO discovers 25 highly active peptides with broad-spectrum activity, including against resistant bacterial strains. These results demonstrate that geometry-informed exploration provides a powerful new paradigm for antimicrobial peptide design.

TL;DR: PepCompass is a geometry-aware framework that leverages manifold-based exploration and optimization to efficiently design antimicrobial peptides, yielding multiple novel and highly active candidates effective against resistant bacteria.