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Generative deep learning techniques have demonstrated an impressive capacity for tackling biomolecular design problems in recent years. Despite their high performance, however, they still suffer from a lack of interpretability and rigorous…

An increasingly common viewpoint is that protein dynamics data sets reside in a non-linear subspace of low conformational energy. Ideal data analysis tools for such data sets should therefore account for such non-linear geometry. The…

Peptides play a crucial role in the drug design and discovery whether as a therapeutic modality or a delivery agent. Non-natural amino acids (NNAAs) have been used to enhance the peptide properties from binding affinity, plasma stability to…

The discovery of peptides having high biological activity is very challenging mainly because there is an enormous diversity of compounds and only a minority have the desired properties. To lower cost and reduce the time to obtain promising…

Symmetric Positive Definite (SPD) matrices have become popular to encode image information. Accounting for the geometry of the Riemannian manifold of SPD matrices has proven key to the success of many algorithms. However, most existing…

Peptides, short chains of amino acids, interact with target proteins, making them a unique class of protein-based therapeutics for treating human diseases. Recently, deep generative models have shown great promise in peptide generation.…

In recent years, there has been an explosion of research on the application of deep learning to the prediction of various peptide properties, due to the significant development and market potential of peptides. Molecular dynamics has…

Gaussian Process (GP) regression is a powerful nonparametric Bayesian framework, but its performance depends critically on the choice of covariance kernel. Selecting an appropriate kernel is therefore central to model quality, yet remains…

Representing graphs as sets of node embeddings in certain curved Riemannian manifolds has recently gained momentum in machine learning due to their desirable geometric inductive biases, e.g., hierarchical structures benefit from hyperbolic…

This paper proposes an innovative extension of Principal Component Analysis (PCA) that transcends the traditional assumption of data lying in Euclidean space, enabling its application to data on Riemannian manifolds. The primary challenge…

Diffusion and flow matching models have recently emerged as promising approaches for peptide binder design. Despite their progress, these models still face two major challenges. First, categorical sampling of discrete residue types…

It is proven that encoding images and videos through Symmetric Positive Definite (SPD) matrices, and considering the Riemannian geometry of the resulting space, can lead to increased classification performance. Taking into account manifold…

The Symmetric Positive Definite (SPD) matrices have received wide attention for data representation in many scientific areas. Although there are many different attempts to develop effective deep architectures for data processing on the…

In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction. This has led to the development of numerous algorithms of varying degrees of complexity that aim to recover man…

Biologists frequently desire protein inhibitors for a variety of reasons, including use as research tools for understanding biological processes and application to societal problems in agriculture, healthcare, etc. Immunotherapy, for…

Peptides, short chains of amino acid residues, play a vital role in numerous biological processes by interacting with other target molecules, offering substantial potential in drug discovery. In this work, we present PepFlow, the first…

The problem of recovering the configuration of points from their partial pairwise distances, referred to as the Euclidean Distance Matrix Completion (EDMC) problem, arises in a broad range of applications, including sensor network…

Latent space geometry provides a rigorous and empirically valuable framework for interacting with the latent variables of deep generative models. This approach reinterprets Euclidean latent spaces as Riemannian through a pull-back metric,…

Euclidean representations distort data with intrinsic non-Euclidean structure. While Riemannian representation learning offers a solution by embedding data onto matching manifolds, it typically relies on an encoder to estimate densities on…

This paper focuses on minimizing a smooth function combined with a nonsmooth regularization term on a compact Riemannian submanifold embedded in the Euclidean space under a decentralized setting. Typically, there are two types of approaches…