# SOLVAR: Fast covariance-based heterogeneity analysis with pose refinement for cryo-EM

arXiv: https://arxiv.org/abs/2602.17603 · HTML: https://mlsanity.com/paper/2602.17603/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 45 references that are in the map.
- First posted on arXiv 19 Feb 2026.

## Builds on (most cited first, 8 of 8)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Deep Generative Modeling for Volume Reconstruction in Cryo-Electron Microscopy](https://mlsanity.com/paper/2201.02867/) (2022)
- [CryoBench: Diverse and challenging datasets for the heterogeneity problem in cryo-EM](https://mlsanity.com/paper/2408.05526/) (2024)
- [cuFINUFFT: a load-balanced GPU library for general-purpose nonuniform FFTs](https://mlsanity.com/paper/2102.08463/) (2021)
- [Cryo-EM reconstruction of continuous heterogeneity by Laplacian spectral volumes](https://mlsanity.com/paper/1907.01898/) (2019)
- [Continuously heterogeneous hyper-objects in cryo-EM and 3-D movies of many temporal dimensions](https://mlsanity.com/paper/1704.02899/) (2017)
- [Covariance estimation using conjugate gradient for 3D classification in Cryo-EM](https://mlsanity.com/paper/1412.0985/) (2014)

## Abstract (arXiv)

Cryo-electron microscopy (cryo-EM) has emerged as a powerful technique for resolving the three-dimensional structures of macromolecules. A key challenge in cryo-EM is characterizing continuous heterogeneity, where molecules adopt a continuum of conformational states. Covariance-based methods offer a principled approach to modeling structural variability. However, estimating the covariance matrix efficiently remains a challenging computational task. In this paper, we present SOLVAR (Stochastic Optimization for Low-rank Variability Analysis), which leverages a low-rank assumption on the covariance matrix to provide a tractable estimator for its principal components, despite the apparently prohibitive large size of the covariance matrix. Under this low-rank assumption, our estimator can be formulated as an optimization problem that can be solved quickly and accurately. Moreover, our framework enables refinement of the poses of the input particle images, a capability absent from most heterogeneity-analysis methods, and all covariance-based methods. Numerical experiments on both synthetic and experimental datasets demonstrate that the algorithm accurately captures dominant components of variability while maintaining computational efficiency. SOLVAR achieves state-of-the-art performance across multiple datasets in a recent heterogeneity benchmark. The code of the algorithm is freely available at https://github.com/RoeyYadgar/SOLVAR.