This paper explores the limitations of canonicalization and frames in equivariant learning, particularly in preserving continuity. It demonstrates that for commonly used groups, there is no efficiently computable choice of frame that preserves the continuity of the function being averaged. Specifically, unweighted frame-averaging can transform a smooth, non-symmetric function into a discontinuous, symmetric function. To address this issue, the authors introduce weighted frames, which assign non-uniform, input-dependent weights to group elements. They define weak equivariance to relax the requirement of equivariance at points with non-trivial stabilizers and introduce the concept of robust frames, which preserve continuity. The paper provides constructions of robust frames for the actions of $SO(d)$, $O(d)$, and $S_n$ on point clouds, showing that these frames can be efficiently implemented and preserve continuity. The results are supported by theoretical proofs and empirical experiments, highlighting the advantages of using robust frames over traditional methods in terms of both continuity and robustness.This paper explores the limitations of canonicalization and frames in equivariant learning, particularly in preserving continuity. It demonstrates that for commonly used groups, there is no efficiently computable choice of frame that preserves the continuity of the function being averaged. Specifically, unweighted frame-averaging can transform a smooth, non-symmetric function into a discontinuous, symmetric function. To address this issue, the authors introduce weighted frames, which assign non-uniform, input-dependent weights to group elements. They define weak equivariance to relax the requirement of equivariance at points with non-trivial stabilizers and introduce the concept of robust frames, which preserve continuity. The paper provides constructions of robust frames for the actions of $SO(d)$, $O(d)$, and $S_n$ on point clouds, showing that these frames can be efficiently implemented and preserve continuity. The results are supported by theoretical proofs and empirical experiments, highlighting the advantages of using robust frames over traditional methods in terms of both continuity and robustness.