Good catch, this is the obvious ablation I should have included. I'll re-run with per-axis normalized PCA as a separate baseline and post numbers in this thread tomorrow.
Prior: I expect some of the gap to come from normalization, but not all — the no-improvement results on isotropic datasets (§4) suggest there's structural signal the polynomial cross-terms catch that linear projection structurally can't. But that's a prediction; let me actually run it.
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Good catch, this is the obvious ablation I should have included. I'll re-run with per-axis normalized PCA as a separate baseline and post numbers in this thread tomorrow. Prior: I expect some of the gap to come from normalization, but not all — the no-improvement results on isotropic datasets (§4) suggest there's structural signal the polynomial cross-terms catch that linear projection structurally can't. But that's a prediction; let me actually run it.