This paper investigates the limitations of canonicalization and frames in equivariant learning, showing that unweighted frames can disrupt the continuity of functions. It introduces robust frames, which are weighted and preserve continuity, and demonstrates their effectiveness for group actions such as permutations, rotations, and orthogonal transformations. The study proves that for certain groups, no continuous canonicalization exists, and that only the Reynolds operator preserves continuity for permutations. Robust frames are constructed for these groups, ensuring continuity and efficiency. The paper also shows that weighted frames can achieve this with significantly smaller sizes than traditional frames. The results highlight the importance of continuity in equivariant learning and provide a theoretical foundation for the use of probabilistic or weighted frames in practice. The work contributes to the development of more robust and efficient equivariant models in geometric deep learning.This paper investigates the limitations of canonicalization and frames in equivariant learning, showing that unweighted frames can disrupt the continuity of functions. It introduces robust frames, which are weighted and preserve continuity, and demonstrates their effectiveness for group actions such as permutations, rotations, and orthogonal transformations. The study proves that for certain groups, no continuous canonicalization exists, and that only the Reynolds operator preserves continuity for permutations. Robust frames are constructed for these groups, ensuring continuity and efficiency. The paper also shows that weighted frames can achieve this with significantly smaller sizes than traditional frames. The results highlight the importance of continuity in equivariant learning and provide a theoretical foundation for the use of probabilistic or weighted frames in practice. The work contributes to the development of more robust and efficient equivariant models in geometric deep learning.