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PreprintCC BYChemRxiv

An unlearnable target: diagnosing the orientation gauge in PXRD-conditioned molecular-crystal flow matching

  • Frank Cai1
  1. 1Purdue University West Lafayette
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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

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Cite

BibTeXRIS
BibTeX
@misc{cai2026unlearnable,
  title = {{An unlearnable target: diagnosing the orientation gauge in PXRD-conditioned molecular-crystal flow matching}},
  author = {Frank Cai},
  howpublished = {ChemRxiv},
  year = {2026},
  month = sep,
  doi = {10.26434/chemrxiv.15008251/v1},
  url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15008251/v1},
  note = {CC BY},
}
RIS
TY  - UNPB
TI  - An unlearnable target: diagnosing the orientation gauge in PXRD-conditioned molecular-crystal flow matching
AU  - Frank Cai
PY  - 2026
DA  - 2026/09/03
PB  - ChemRxiv
DO  - 10.26434/chemrxiv.15008251/v1
UR  - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15008251/v1
AB  - 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
ER  -