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

===== To avoid directly regressing millions of weights from prompts, you can insert δ as a bottleneck: =====

Stage 1: learn a task encoder using δ
* Train EψE_\psiEψ s.t. Eψ(Pt)≈δtE_\psi(P_t) \approx \delta_tEψ(Pt)≈δt.
* That’s a simple regression in low dimension; way easier than full LoRA.

This makes δ the “task embedding space” learned from actual finetuned behaviors.

Stage 2: learn δ → LoRA map

Now train a separate generator GθG_\thetaGθ to map δ to LoRA:

ΔW^t=Gθ(δt)\hat{\Delta W}_t = G_\theta(\delta_t)ΔW^t=Gθ(δt)
with weight-level loss:

Lstage2=∥ΔW^t−ΔWt∥2\mathcal{L}_\text{stage2} = \|\hat{\Delta W}_t - \Delta W_t\|^2Lstage2=∥ΔW^t−ΔWt∥2
At inference:
* New dataset ➜ prompts PnewP_{\text{new}}Pnew
* Stage 1: δ^new=Eψ(Pnew)\hat\delta_{\text{new}} = E_\psi(P_{\text{new}})δ^new=Eψ(Pnew)
* Stage 2: ΔW^new=Gθ(δ^new)\hat{\Delta W}_{\text{new}} = G_\theta(\hat\delta_{\text{new}})ΔW^new=Gθ(δ^new)

Now δ is both:
* A learned task representation (Stage 1), supervised by behavioral deltas;
* The bottleneck that the LoRA generator uses (Stage 2).

Pros:
* You’ve decomposed a very hard mapping “prompts → millions of weights” into: - “prompts → 4k-dim δ” (reasonable), and - “δ → weights” (pure parameter-space mapping).
* You can even pretrain Stage 2 using any LoRA–δ pairs you have, independent of prompts.

Weaknesses:
* δ is intentionally lossy. Many LoRAs can share similar δ, especially if probes are generic. So δ alone might not contain enough info to reconstruct exact LoRA.
* You’re back to weight-level MSE in Stage 2; though G has an easier job because δ already encodes “what kind of task” it is.

You can combine both worlds: in Stage 2, also add a δ-consistency loss:

∥Delta(ΔW^t)−δt∥2\|\text{Delta}(\hat{\Delta W}_t) - \delta_t\|^2∥Delta(ΔW^t)−δt∥2
so that even if weights aren’t exactly matching, their induced δ is.