An unlearnable target: diagnosing the orientation gauge in PXRD-conditioned molecular-crystal flow matching
Year: 2026
Type: preprint
Abstract: Rigid-body flow matching reduces a molecular crystal to a lattice, fractional cen-troids and per-molecule orientations on SO(3), and is an attractive route to structure determination from powder X-ray diffraction (PXRD). We report a negative result and its root cause. Our PXRD-conditioned rigid-body flow recovered 0 of 160 held-out structures, and the failure was neither the lattice nor the sampler: a frame-preserving oracle substitution shows that installing the ground-truth unit cell into the generated packing yields 0/10 matches, while a component decomposition on held-out data puts the lattice head at 91.6% of variance explained and both packing heads at their no-information floors (centroid −0.1%, orientation 3.7%). The orientation loss sat at ∼4.7 against an analytic predict-nothing floor of π2/3+2 = 5.290, because the training target was the absolute molecular pose, which factorises as
Source: ChemRxiv
Author: Frank Cai
Institution: Purdue University West Lafayette
Language: English
Subfield: Materials Chemistry
Field: Materials Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7207678806