# Cryo-em images are intrinsically low dimensional

arXiv: https://arxiv.org/abs/2504.11249 · HTML: https://mlsanity.com/paper/2504.11249/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 61 references that are in the map.
- First posted on arXiv 15 Apr 2025.

## Builds on (most cited first, 17 of 17)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Benchmarking Simulation-Based Inference](https://mlsanity.com/paper/2101.04653/) (2021)
- [Validating Bayesian Inference Algorithms with Simulation-Based Calibration](https://mlsanity.com/paper/1804.06788/) (2018)
- [Manifold learning: what, how, and why](https://mlsanity.com/paper/2311.03757/) (2023)
- [Detecting Model Misspecification in Amortized Bayesian Inference with Neural Networks](https://mlsanity.com/paper/2112.08866/) (2021)
- [Learning Robust Statistics for Simulation-based Inference under Model Misspecification](https://mlsanity.com/paper/2305.15871/) (2023)
- [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)
- [Non-linear dimensionality reduction: Riemannian metric estimation and the problem of geometric discovery](https://mlsanity.com/paper/1305.7255/) (2013)
- [Multi-Resolution A*](https://mlsanity.com/paper/2004.06684/) (2020)
- [Selecting the independent coordinates of manifolds with large aspect ratios](https://mlsanity.com/paper/1907.01651/) (2019)
- [Detecting Model Misspecification in Amortized Bayesian Inference with Neural Networks: An Extended Investigation](https://mlsanity.com/paper/2406.03154/) (2024)
- [Improved graph Laplacian via geometric self-consistency](https://mlsanity.com/paper/1406.0118/) (2014)
- [Deep learning based mixed-dimensional GMM for characterizing variability in CryoEM](https://mlsanity.com/paper/2101.10356/) (2021)
- [On Manifold Learning in Plato's Cave: Remarks on Manifold Learning and Physical Phenomena](https://mlsanity.com/paper/2304.14248/) (2023)

## Built on by (most cited first, 2 of 2)

- [Minimum Distance Summaries for Robust Neural Posterior Estimation](https://mlsanity.com/paper/2602.09161/) (2026)
- [cryoSENSE: Compressive Sensing Enables High-throughput Microscopy with Sparse and Generative Priors on the Protein Cryo-EM Image Manifold](https://mlsanity.com/paper/2511.12931/) (2025)

## Abstract (arXiv)

Simulation-based inference provides a powerful framework for cryo-electron microscopy, employing neural networks in methods like CryoSBI to infer biomolecular conformations via learned latent representations. This latent space represents a rich opportunity, encoding valuable information about the physical system and the inference process. Harnessing this potential hinges on understanding the underlying geometric structure of these representations. We investigate this structure by applying manifold learning techniques to CryoSBI representations of hemagglutinin (simulated and experimental). We reveal that these high-dimensional data inherently populate low-dimensional, smooth manifolds, with simulated data effectively covering the experimental counterpart. By characterizing the manifold's geometry using Diffusion Maps and identifying its principal axes of variation via coordinate interpretation methods, we establish a direct link between the latent structure and key physical parameters. Discovering this intrinsic low-dimensionality and interpretable geometric organization not only validates the CryoSBI approach but enables us to learn more from the data structure and provides opportunities for improving future inference strategies by exploiting this revealed manifold geometry.