This study addresses the identifiability problem in quantum machine learning where training data lacks a preferred basis or reference frame. The authors formulate supervised learning without an external quantum reference frame, requiring classifiers to preserve unitary symmetries unbroken by the training data. They prove that if training states do not span the full Hilbert space, all pure states orthogonal to this span receive identical predictions. This limitation arises from missing reference information rather than state discrimination or computational constraints. The research establishes a robust version under weak symmetry breaking and shows that learning generic concepts requires exponentially many oriented training directions. Numerical illustrations visualize the resulting prediction collapse and its controlled relaxation. The results identify feature maps, measurement bases, and diverse training states as essential operational resources for generalization.