Equivariant amortized inference of poses for cryo-EM

Cryo-EM is a vital technique for determining 3D structure of biological molecules such as proteins and viruses. The cryo-EM reconstruction problem is challenging due to the high noise levels, the missing poses of particles, and the computational demands of processing large datasets. A promising solution to these challenges lies in the use of amortized inference methods, which have shown particular efficacy in pose estimation for large datasets. However, these methods also encounter convergence issues, often necessitating sophisticated initialization strategies or engineered solutions for effective convergence. Building upon the existing cryoAI pipeline, which employs a symmetric loss function to address convergence problems, this work explores the emergence and persistence of these issues within the pipeline. Additionally, we explore the impact of equivariant amortized inference on enhancing convergence. Our investigations reveal that, when applied to simulated data, a pipeline incorporating an equivariant encoder not only converges faster and more frequently than the standard approach but also demonstrates superior performance in terms of pose estimation accuracy and the resolution of the reconstructed volume. Notably, $D_4$-equivariant encoders make the symmetric loss superfluous and, therefore, allow for a more efficient reconstruction pipeline.