For any fixed nonconstant teacher T, the best constant student has alignment cost exactly equal to the teacher mutual information I_T(X;T); a latent-only witness below this threshold with margin cannot be constant.
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A Testable Certificate for Constant Collapse in Teacher-Guided VAEs
For any fixed nonconstant teacher T, the best constant student has alignment cost exactly equal to the teacher mutual information I_T(X;T); a latent-only witness below this threshold with margin cannot be constant.