What Your Benchmark Cannot See: Non-Identifiability of Backbone Symmetry Under Invariant Readouts

Standard benchmark scores can make a structural collapse look like an ordinary performance drop. We show that this ambiguity is fundamental: under a fixed invariant readout, the score alone cannot reveal whether directional information is absent from the backbone or erased by the readout, making backbone symmetry non-identifiable. For targets that swap under reverse complementation, this mismatch forces orbit-paired accuracy to exactly zero on orbit-closed free orbits, independent of loss, optimisation, decoding, or readout capacity, even while Matthews correlation coefficient (MCC), accuracy, and macro-F1 remain non-zero. We characterise how channel symmetrisation and position-symmetric pooling jointly remove directional information at readout, and test the predictions with parameter-matched readouts across three DNA foundation models on a new direction-aware promoter benchmark. Linear probes recover directionality from Caduceus representations; a symmetry-matched equivariant readout restores positive orbit-paired accuracy and exact equivariant agreement across all three models; and a matched invariant control exhibits no structural obstruction. Thus the problem is not symmetry itself, but using a readout symmetry that the target does not obey—and benchmark scores alone need not expose the mistake.