Beyond Perturbation Robustness: Biological Equivalence in Genomic Foundation Models

Genomic foundation models are commonly evaluated through predictive benchmarks or perturbation sensitivity, but neither directly tests whether learned representations respect known task-relative biological equivalences. We study translation-preserving equivalence in protein-coding DNA, where synonymous codon substitutions change nucleotide sequence while preserving the encoded amino-acid sequence. Using 91 human coding sequences, we generate 10 independent synonymous transformation paths per source at depths $k=1,2,3$, paired with edit-matched nonsynonymous controls. We evaluate frozen Omni-DNA-20M, Omni-DNA-116M, NucEL-93M, and JEPA-DNA-NTv3-100M using representation geometry, matched equivalence retrieval, and downstream amino-acid-composition stability. Omni-DNA remains at chance on matched retrieval (0.496 and 0.500) despite smaller absolute representation distances at the larger scale. NucEL shows clearer equivalence structure, with retrieval of 0.596 (95% CI [0.572, 0.621]) and a positive downstream stability margin of 0.00382 (95% CI [0.00290, 0.00486]); JEPA-DNA shows weaker evidence. These results suggest that smaller perturbation distances should not be interpreted as evidence of more biologically coherent representations, and that equivalence-based evaluation can complement conventional robustness metrics.