Editing Openai/693c0f4f-255c-8008-92e9-0cd44c6d6226 (section)

===== In the compositional paper, they prove that: =====
* If f^∈Fint\hat f \in F_{\text{int}}f^∈Fint fits the data, then it essentially must be the true generator (up to slotwise transforms).
* This is a strong structural statement about which decoders are allowed, via Jacobian/Hessian constraints. 2512.08854v1

DnD doesn’t have anything analogous:
* The hyper-convolutional decoder is chosen mostly for efficiency, not because it’s the unique class of functions that can map prompts to LoRAs “correctly.” 2506.16406v1
* For a given dataset, there may be many LoRAs that give similar performance; and for a given set of prompt batches, many mappings from text embeddings to weights will fit the training checkpoints.

So the “generator over weights” in DnD is more like a strong practical prior than a theoretically justified FintF_{\text{int}}Fint-style class.

If you were hoping to cleanly import the compositional identifiability result into DnD, that doesn’t work yet: they haven’t characterized the space of good hyper-networks the same way.