Pros: - Use functional maps framework to motivate an a data-driven pipeline - First fully-differentiable functional maps pipeline, in which both the probe functions and the functional basis are learned from data - Well motivated two stage architecture that seems to bring clear benefits - Very well written Cons: - Benchmarks are not standard: missing FAUST official benchmark and partiality is shown on their own test set instead of more common projections or "cuts and holes" - Ablations missing: they don’t explain why they use small number of points (1K), nor why the number of basis is quite small (20) (which could limit applicability to real scans) R1 and R4 were satisfied with the answers provided by the authors and decided to increase their scores to marginally above acceptance threshold. R2 maintains his/her score as marginally above acceptance threshold. He/She considers that the direction proposed in this work is good and the results are promising, but considers that is not yet ready for publication (see the updated review for a detailed description). The AC considers that the paper has merit, is very elegant and shows very promising results. The AC recommends acceptance and encourages the authors to incorporate the suggestions by R2, most importantly the missing ablations (explanations) regarding the number of points and basis functions used.