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About this paper
Floor Eijkelboom, Grigory Bartosh, Christian Andersson Naesseth, Max Welling, Jan-Willem van de Meent
CatFlow generates categorical molecular graphs by predicting distributions over atom and bond endpoints, then using expected endpoints to define velocities in a continuous flow trained with cross-entropy. On QM9, it reports validity 99.81%, uniqueness 99.95%, and FCD 0.441, versus Dirichlet Flow Matching’s 99.10%, 98.15%, and 0.888. These reported scores concern categorical graphs and do not establish universal superiority.
Key insights
- Flow matching's vector field can be expressed as an expectation over a posterior path, allowing its reformulation as a variational inference problem (VFM).
- For conditional vector fields linear in the target, a fully-factorized (mean-field) variational approximation is sufficient to learn the correct marginal vector field, simplifying the problem significantly.
- CatFlow's use of a categorical variational distribution leads to a cross-entropy loss, which provides an advantageous inductive bias for discrete data, enhancing training stability and robustness.
Summary by alphaXiv.
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