You're right that the headline table compares checkpoints with unequal training. The 60B bf16 checkpoint got one distillation pass (the recovery); the 60B MXFP4 checkpoint got that pass plus a second one against the 120B teacher. We describe that second pass in the approach section, but we should have been explicit that the table therefore doesn't, on its own, separate "distilling under quantization" from "distilling for longer." We'll add that caveat to the text.
A bit of context on what the paper is: it's an applied case study, not a theoretical claim. The question we set out to answer is the one a deployment team faces: Given a compressed model that has to ship in 4 bits, what's the best way to run the quantization step? The result we stand behind is narrow and reproducible: the shipped 4-bit checkpoint scores above the bf16 checkpoint it was quantized from, rather than below it, which is the usual outcome of direct post-training quantization. What we shouldn't have leaned into is the stronger causal reading, that quantization itself is "free training", and you're right that the current table doesn't isolate that.
The comparison that would settle it is the one you describe: the bf16 60B given the identical second pass. same data, steps, teacher and, separately, that continued bf16 checkpoint post-training-quantized to MXFP4. The second is really the decision anyone deploying faces: heal under quantization, or quantize afterwards. If we extend this for a revised version, those are the arms we'd add; either way we're flagging them as a limitation of the current version rather than claiming the table resolves the question.
We don't think retraction is the right call. The reported numbers are real and reproducible, and the practical result stands. But we agree the causal framing needs that control, and we'd rather correct it in the open than argue it. Appreciate the push.
