Oleg Presnyakov | Searcharxiv

arXiv2026

Read Between the Hyperplanes: On Spectral Projection and Sampling Approaches to Randomized Kaczmarz

Among recent developments centered around Randomized Kaczmarz (RK), a row-sampling iterative projection method for large-scale linear systems, several adaptions to the method have inspired faster convergence. Focusing solely on ill-conditioned and overdetermined linear systems, we highlight inter-row relationships that can be leveraged to guide directionally aware projections. In particular, we find that improved convergence rates can be made by (i) projecting onto pairwise row differences, (ii) sampling from partitioned clusters of nearly orthogonal rows, or (iii) more frequently sampling spectrally-diverse rows.

math.NA↗

arXiv2025

Conformational Rank Conditioned Committees for Machine Learning-Assisted Directed Evolution

Machine Learning-assisted directed evolution (MLDE) is a powerful tool for efficiently navigating antibody fitness landscapes. Many structure-aware MLDE pipelines rely on a single conformation or a single committee across all conformations, limiting their ability to separate conformational uncertainty from epistemic uncertainty. Here, we introduce a rank -conditioned committee (RCC) framework that leverages ranked conformations to assign a deep neural network committee per rank. This design enables a principled separation between epistemic uncertainty and conformational uncertainty. We validate our RCC-MLDE approach on SARS-CoV-2 antibody docking, demonstrating significant improvements over baseline strategies. Our results offer a scalable route for therapeutic antibody discovery while directly addressing the challenge of modeling conformational uncertainty.

cs.LG↗