CryoKRAQEN: Kernel-Regularized Annealing for Quantized Embedding Networks in Cryo-EM Heterogeneous Reconstruction

Wenyuan Gao1,3, Yutan Wu1, Xuming He1,2
ShanghaiTech University, Shanghai, China1,
Shanghai Engineering Research Center of Intelligent Vision and Imaging2,
Zhangjiang Laboratory, Shanghai, China3
CVPR 2026
Paper Supplementary Code arXiv
First research result visualization

Main challenge in heterogeneous cryo-EM reconstruction

The key difficulty lies in unsupervisedly assigning noisy 2D particle images to unknown 3D structures. Overly hard assignments lead to mode collapse, with images concentrated into a few dominant structures, while overly soft assignments make different conformations indistinguishable, reducing reconstruction resolution. CryoKRAQEN mitigates these degenerative effects through kernel-guided annealed quantization, achieving robust and high-fidelity modeling of structural heterogeneity.

Abstract

Heterogeneous reconstruction in cryo-electron microscopy (Cryo-EM) is fundamental for understanding macromolecular structural diversity, yet remains challenging due to extreme noise, continuous conformational changes, and ambiguous image-to-structure mappings. Existing neural approaches often rely on encoder--decoder pipelines or fixed codebooks, which can be computationally demanding or struggle with complex heterogeneity. We propose CryoKRAQEN, a decoder-only framework that integrates triplane implicit representations with kernel-guided latent assignment and quantized embeddings to improve stability and structural discrimination. The method avoids encoder dependencies and mitigates collapse during training, enabling accurate modeling of both conformational and compositional variations. Across diverse Cryo-EM benchmarks, CryoKRAQEN delivers competitive performance, robust reconstructions, and interpretable latent organization compared to state-of-the-art neural and classical methods.

Architecture of CryoKRAQEN

Architecture of CryoKRAQEN

CryoKRAQEN reconstructs heterogeneous 3D structures from noisy cryo-EM images using a quantized triplane-based Fourier codebook. For each particle, a Fourier slice is extracted, compared with image features, and converted into annealed soft assignment weights via an Epanechnikov kernel. These weights combine codebook entries to form the particle’s 3D Fourier volume, which is transformed into a spatial density map.

Inference: The learned assignment weights are applied directly to the triplane codebook to generate the corresponding 3D volume and density.