What DNA Foundation Models Learn Beyond Sequence Composition

Do genomic foundation models (FMs) provide predictive information beyond simple sequence composition? We evaluate frozen representations from five DNA FMs against normalized k-mer frequencies across 57 genomic classification datasets and two exploratory gene-expression regression tasks. Simple k-mer features remain competitive with most models, whereas NTv3 shows a consistent advantage; the ranking is robust to globally fixed and multi-scale k-mer baselines and alternative downstream probes. To test incremental predictive utility directly, we compare global 6-mer features with their concatenation with each FM embedding under a matched Random Forest protocol. NTv3 improves 46 of 57 datasets (mean DeltaMCC = +0.072), while Caduceus provides smaller gains and the other models do not improve mean MCC. We separately decompose embeddings into a component linearly predictable from 6-mer frequencies and a ridge residual, finding that linear recoverability does not reliably indicate downstream utility. Exact 6-mer-preserving shuffles further reveal task-relevant sequence-order sensitivity, most pronounced for NTv3, although order sensitivity alone does not guarantee predictive improvements. Our results establish compositional features as essential controls and offer complementary diagnostics for evaluating the added value of frozen genomic representations, without making claims about fine-tuning capacity.