Privileged basis — is absent from → Residual stream

The paper's own definition of a privileged basis is a coordinate system 'in which we would expect changes to be unusually meaningful, such as the standard basis after a non-linearity in an MLP' -- and it explicitly states the residual stream 'can usually be treated as a vector space with no privileged basis,' unlike that MLP example. Structurally this is because the residual stream is a running sum of additive layer outputs rather than the output of an elementwise nonlinearity, so no single coordinate system is singled out by the architecture the way the standard basis is singled out immediately after a ReLU. This absence is exactly what licenses treating individual residual-stream coordinates, the default-basis baseline, as no more principled a unit of analysis than an arbitrary random direction, which the paper then checks directly.