Audit Before You Interpret: Basis Freedom in Trained Neural Operators

A trained neural operator can make identical predictions in different internal bases, and those bases yield different interpretations and visualizations of its learned representation. We develop a framework for basis-consistent interpretation and visualization of trained neural operators. Its checkpoint audit applies to both purely data-driven and physics-informed models without requiring a linear decoder. We test candidate basis changes on public checkpoints from several architecture families. Each test applies a compensated reparameterization to the stored weights and includes a paired control expected to change the predictions. These tests allow interpretations to be checked across equivalent representations. For physics-informed cavity operators with low-rank linear decoders, we identify parameter-aligned subspaces using the model's own coefficients and distances between decoded physical fields. We fix these subspaces before consulting reference solutions for validation. The identified asymmetry subspace captures about 97% of the energy in the reference asymmetry component. Projections onto each fixed decoded subspace are independent of its internal basis. Embeddings built from field distances that are the same in every basis recover more reference neighbours than embeddings of standardized field-varimax coordinates. These results support physical interpretation through validated subspaces and visualization through distances that respect the audited basis freedom.