# PepCompass: Navigating peptide embedding spaces using Riemannian Geometry

arXiv: https://arxiv.org/abs/2510.01988 · HTML: https://mlsanity.com/paper/2510.01988/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 32 of its 64 references that are in the map.
- First posted on arXiv 2 Oct 2025.

## Builds on (most cited first, 30 of 32)

- [Interpreting the Latent Space of GANs for Semantic Face Editing](https://mlsanity.com/paper/1907.10786/) (2019)
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- [Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Models](https://mlsanity.com/paper/2103.04922/) (2021)
- [Riemannian Score-Based Generative Modelling](https://mlsanity.com/paper/2202.02763/) (2022)
- [Latent Space Oddity: on the Curvature of Deep Generative Models](https://mlsanity.com/paper/1710.11379/) (2017)
- [Biological Sequence Design with GFlowNets](https://mlsanity.com/paper/2203.04115/) (2022)
- [Protein Design with Guided Discrete Diffusion](https://mlsanity.com/paper/2305.20009/) (2023)
- [High-Dimensional Bayesian Optimization with Sparse Axis-Aligned Subspaces](https://mlsanity.com/paper/2103.00349/) (2021)
- [Understanding the Latent Space of Diffusion Models through the Lens of Riemannian Geometry](https://mlsanity.com/paper/2307.12868/) (2023)
- [Conditioning by adaptive sampling for robust design](https://mlsanity.com/paper/1901.10060/) (2019)
- [Vanilla Bayesian Optimization Performs Great in High Dimensions](https://mlsanity.com/paper/2402.02229/) (2024)
- [The Riemannian Geometry of Deep Generative Models](https://mlsanity.com/paper/1711.08014/) (2017)
- [Adaptive and Safe Bayesian Optimization in High Dimensions via One-Dimensional Subspaces](https://mlsanity.com/paper/1902.03229/) (2019)
- [AdaLead: A simple and robust adaptive greedy search algorithm for sequence design](https://mlsanity.com/paper/2010.02141/) (2020)
- [Verifying the Union of Manifolds Hypothesis for Image Data](https://mlsanity.com/paper/2207.02862/) (2022)
- [Low-Rank Subspaces in GANs](https://mlsanity.com/paper/2106.04488/) (2021)
- [Deep Generative Models through the Lens of the Manifold Hypothesis: A Survey and New Connections](https://mlsanity.com/paper/2404.02954/) (2024)
- [Geometrically Enriched Latent Spaces](https://mlsanity.com/paper/2008.00565/) (2020)
- [Variational Autoencoders with Riemannian Brownian Motion Priors](https://mlsanity.com/paper/2002.05227/) (2020)
- [Discovering Many Diverse Solutions with Bayesian Optimization](https://mlsanity.com/paper/2210.10953/) (2022)
- [A survey and benchmark of high-dimensional Bayesian optimization of discrete sequences](https://mlsanity.com/paper/2406.04739/) (2024)
- [What is a meaningful representation of protein sequences?](https://mlsanity.com/paper/2012.02679/) (2020)
- [Improved Off-policy Reinforcement Learning in Biological Sequence Design](https://mlsanity.com/paper/2410.04461/) (2024)
- [Counterfactual Explanations via Riemannian Latent Space Traversal](https://mlsanity.com/paper/2411.02259/) (2024)
- [Accelerating Antimicrobial Discovery with Controllable Deep Generative Models and Molecular Dynamics](https://mlsanity.com/paper/2005.11248/) (2020)
- [Navigating Chemical Space with Latent Flows](https://mlsanity.com/paper/2405.03987/) (2024)
- [Mario Plays on a Manifold: Generating Functional Content in Latent Space through Differential Geometry](https://mlsanity.com/paper/2206.00106/) (2022)
- [Internal Representations of Vision Models Through the Lens of Frames on Data Manifolds](https://mlsanity.com/paper/2211.10558/) (2022)
- [Artificial intelligence-driven antimicrobial peptide discovery](https://mlsanity.com/paper/2308.10921/) (2023)
- [On the generalization of Tanimoto-type kernels to real valued functions](https://mlsanity.com/paper/2007.05943/) (2020)

## Abstract (arXiv)

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 mathbbMkappa, 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.