  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.
