SIGMA: Semantic Identifier Grouping for Molecular Autoregression

Autoregressive molecular models assign probability to molecular serializations even though chemical identity is invariant to serialization. Equivalent serializations can induce different internal states along a shared molecular continuation. Randomized strings broaden exposure, but do not explicitly supervise correspondence between those states. We introduce SIGMA, a dense suffix-position objective built from chemically certified same-suffix triplets: two equivalent histories, one non-equivalent history, and a shared suffix. SIGMA aligns corresponding pre-token hidden states along the continuation and enforces a finite similarity margin over the non-equivalent history, leaving the language-model objective, decoder, and inference procedure unchanged. We compare SIGMA with canonical training, randomized-serialization training, and last-token alignment across four datasets under SMILES and SELFIES. SIGMA lowers test-reference Frechet ChemNet Distance against every control in all three training seeds on all four SELFIES datasets and on QM9 and ZINC under SMILES. Position-wise analyses show improved state correspondence, chemical discrimination, and top-1 next-token agreement while preserving between-molecule information. Full-corpus ZINC ablations under both representations identify correct state correspondence, rather than extra computation alone, as an effective ingredient. Beyond generation, a whole-molecule SIGMA extension improves mean predictive performance on all six molecular property benchmarks and reduces serialization sensitivity on every task relative to a matched randomized-serialization control.