# GSF-chi: Global Stereochemical Fields for Chiral Graph Transformers

arXiv: https://arxiv.org/abs/2609.12532 · HTML: https://mlsanity.com/paper/2609.12532/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 26 references that are in the map.
- First posted on arXiv 11 Sep 2026.

## Builds on (most cited first, 13 of 13)

- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Molecules](https://mlsanity.com/paper/2011.14115/) (2020)
- [Spherical Message Passing for 3D Graph Networks](https://mlsanity.com/paper/2102.05013/) (2021)
- [Learning 3D Representations of Molecular Chirality with Invariance to Bond Rotations](https://mlsanity.com/paper/2110.04383/) (2021)
- [LieRE: Lie Rotational Positional Encodings](https://mlsanity.com/paper/2406.10322/) (2024)
- [Message Passing Networks for Molecules with Tetrahedral Chirality](https://mlsanity.com/paper/2012.00094/) (2020)
- [Algebraic Positional Encodings](https://mlsanity.com/paper/2312.16045/) (2023)
- [Difficulty in chirality recognition for Transformer architectures learning chemical structures from string](https://mlsanity.com/paper/2303.11593/) (2023)
- [ChiENN: Embracing Molecular Chirality with Graph Neural Networks](https://mlsanity.com/paper/2307.02198/) (2023)
- [E(3)-equivariant models cannot learn chirality: Field-based molecular generation](https://mlsanity.com/paper/2402.15864/) (2024)
- [Learning Molecular Chirality via Chiral Determinant Kernels](https://mlsanity.com/paper/2602.07415/) (2026)

## Abstract (arXiv)

Enantiomers share atoms, bonds, and pairwise distances yet can behave differently in chiral environments, so molecular encoders must respect atom relabelings and proper rotations without becoming blind to reflection. We introduce GSF-chi, a graph transformer in which stereogenic units modulate all pairwise interactions rather than single out one atom as special. Each central or axial stereogenic unit creates a reflection-even phase field over all atoms, a handedness pseudoscalar chi sets the direction of a relative rotation on latent query--key blocks, giving a Chiral-RoPE that reflection inverts rather than leaves fixed. A C2 projection separates mirror-even ECD peak counts and positions from mirror-odd peak signs. We prove the operator's even--odd decomposition and its annotation-inversion, permutation, and unit-order identities under explicit canonical-role conditions; property tests and a coordinate-reflection audit verify the laws end to end. GSF-chi leads every central-ECD output and improves axial Rotation and Symbol by 12.6% and 7.9% over the strongest baseline. Equal-budget controls attribute the Rotation advantage to global signed support rather than parameter or edge count; the C2 projection yields exact enantiomer-pair consistency at a small raw-accuracy cost under complete supervision and becomes predictive when mirror supervision is scarce.