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

=== Assistant: Nice, this is a really reasonable incremental project. ===
Nice, this is a really reasonable incremental project. I’ll write this as a research-plan skeleton you could almost paste into a proposal.

==== Tentative Title ====

Behavior-Aware Data-to-LoRA Generation via Delta Activations

==== 1. Background ====

===== 1.1 Parameter-efficient finetuning and data-to-LoRA generation =====

Large language models (LLMs) are commonly adapted via LoRA: low-rank adapters ΔW=BA\Delta W = BAΔW=BA added to a frozen base model, trained on task data DDD. 2506.16406v1

Recent work like Drag-and-Drop LLMs (DnD) treats LoRA updates themselves as generative targets: a hyper-network takes a batch of unlabeled prompts from a dataset and directly outputs the LoRA weights for that dataset. This collapses the classical data→gradients→weights loop into a single forward pass and removes per-task finetuning.

DnD trains the hyper-network with MSE on tokenized LoRA weights between generated and reference adapters. 2506.16406v1

Limitations of current data-to-LoRA training:
* The target space (LoRA weights) is huge, so pure MSE is noisy and high-variance.
* Weight space is multi-modal: many different LoRAs can yield similar task behavior, but MSE to a single reference penalizes all but one.
* The supervision is purely parametric, not directly aligned with model behavior.

This makes training the generator harder, and probably limits generalization to unseen tasks.

===== 1.2 Delta Activations as behavioral model embeddings =====

Delta Activations propose a compact, behavior-based representation for finetuned models. For a base model fbasef_\text{base}fbase and a finetuned model fff, they define:
* For each probe input xxx from a small generic probe set DprobeD_\text{probe}Dprobe, compute the last-layer hidden state for the final token: - hf(x)h_f(x)hf(x) for the finetuned model, - hbase(x)h_\text{base}(x)hbase(x) for the base model.
* The delta activation for that input is: Δf(x)=hf(x)−hbase(x)\Delta_f(x) = h_f(x) - h_\text{base}(x)Δf(x)=hf(x)−hbase(x)
* Aggregate over the probe set: vf=1∣Dprobe∣∑x∈DprobeΔf(x)v_f = \frac{1}{|D_\text{probe}|} \sum_{x\in D_\text{probe}} \Delta_f(x)vf=∣Dprobe∣1x∈Dprobe∑Δf(x) giving a single vector vf∈Rdv_f \in \mathbb{R}^dvf∈Rd.

They show that:
* vfv_fvf clusters finetuned models by domain (math, coding, legal, etc.).
* The embedding is approximately additive: combining finetuning datasets corresponds to vector addition in the delta space. 2509.04442v1
* A few-shot finetuned model can serve as a task embedding via its Delta Activations.

So Delta Activations give a low-dimensional, behavior-aligned representation of how a LoRA modifies a model.

===== 1.3 Gap and opportunity =====

DnD learns a mapping:

: prompts from dataset → LoRA weights,
: supervised only in weight space.

Delta Activations gives:

: finetuned model (or LoRA) → behavioral embedding δ.

These two lines almost meet, but not quite:
* DnD knows how to go from data to weights, but doesn’t explicitly use any behavioral summary.
* Delta Activations knows how to go from weights to behavior, but doesn’t feed back into adapter generation.

Idea: use Delta Activations as auxiliary behavioral supervision for the data→LoRA generator, to make training easier and improve generalization.

You won’t replace weight-level supervision with δ (good instinct) – you’ll add δ as an extra, low-dimensional, behavior-aligned target.

==== 2. Goals and Research Questions ====

Goal: Improve data-to-LoRA generation by incorporating Delta Activations as an auxiliary task, making the generator more behavior-aware and easier to train.

RQ1 – In-domain reconstruction:
Does delta-based auxiliary supervision improve how well a prompt-conditioned generator reproduces known LoRAs and their behavior on the same tasks?

RQ2 – Zero-shot cross-task generalization:
Given only prompts from a new dataset, does the delta-augmented generator produce LoRAs that perform better (or at least more robustly) than a DnD-style baseline?

RQ3 – Robustness and sample efficiency:
Does δ supervision help when training data (number of prompt–checkpoint pairs) is small, or when LoRA targets are noisy?

RQ4 – Compositional task behavior:
If we interpolate or add deltas (e.g., δ_math + δ_code), and decode them into LoRAs, do we get meaningful joint capabilities?

==== 3. Proposed Method ====

===== 3.1 Setup and data =====

Start from a DnD-like setup:
* Base LLM (e.g., LLaMA-3.1-8B or a smaller variant).
* A pool of finetuned LoRA adapters over diverse domains (e.g., LEGAL, MATH, MEDICAL, COMMONSENSE, CODING) as in the Delta paper. 2509.04442v1
* For each LoRA ΔWt\Delta W_tΔWt, you have: - its training prompts / dataset, - the finetuned adapter weights, - and you can compute its Delta Activation vector δt\delta_tδt.

Generator architecture:
* Reuse DnD’s macro-architecture: frozen text encoder over prompt batches, feeding a hyper-convolutional decoder that outputs tokenized LoRA weights.

===== 3.2 Computing Delta Activations =====

For each LoRA ttt:
# Fix a small generic probe set DprobeD_\text{probe}Dprobe (e.g., 5 Alpaca-style generic instructions as in the Delta paper). 2509.04442v1
# For each probe x∈Dprobex\in D_\text{probe}x∈Dprobe: - Run base model → hbase(x)h_\text{base}(x)hbase(x), - Run base+LoRA_t → ht(x)h_t(x)ht(x), - Compute Δt(x)=ht(x)−hbase(x)\Delta_t(x) = h_t(x) - h_\text{base}(x)Δt(x)=ht(x)−hbase(x).
# Average to get the embedding δt\delta_tδt.

We’ll treat δt\delta_tδt as the behavioral target for LoRA ttt.

===== 3.3 Core model variants =====

You can define a few variants—one as your main method, the rest as ablations.

====== Variant A – Multi-task (prompts → weights + δ) ======
* Condition encoder EEE: et=E(Pt)e_t = E(P_t)et=E(Pt) where PtP_tPt is a batch of prompts from dataset ttt.
* Hyper-decoder GGG: ΔW^t=G(et)\hat{\Delta W}_t = G(e_t)ΔW^t=G(et)
* δ-head HHH: - Option A1 (cheaper): learn a small network HHH so that δ^t=H(ΔW^t)\hat{\delta}_t = H(\hat{\Delta W}_t)δ^t=H(ΔW^t). - Option A2 (more accurate): compute δ^t\hat{\delta}_tδ^t by actually running base+ ΔW^t\hat{\Delta W}_tΔW^t on the probe set.

Loss:

Ltotal=λw∥ΔW^t−ΔWt∥2⏟DnD weight MSE+λδ∥δ^t−δt∥2⏟Delta auxiliary loss\mathcal{L}_\text{total} =
\lambda_\text{w} \underbrace{\|\hat{\Delta W}_t - \Delta W_t\|^2}_{\text{DnD weight MSE}}
+ \lambda_\delta \underbrace{\|\hat{\delta}_t - \delta_t\|^2}_{\text{Delta auxiliary loss}}Ltotal=λwDnD weight MSE∥ΔW^t−ΔWt∥2+λδDelta auxiliary loss∥δ^t−δt∥2
This keeps the original DnD objective but adds δ as an extra constraint.

====== Variant B – Two-stage with δ bottleneck ======

Stage 1: prompts → δ

Train a task encoder:

δ^t=Eψ(Pt)\hat{\delta}_t = E_\psi(P_t)δ^t=Eψ(Pt)
with loss:

Lδ-reg=∥δ^t−δt∥2\mathcal{L}_\text{δ-reg} = \|\hat{\delta}_t - \delta_t\|^2Lδ-reg=∥δ^t−δt∥2
Now δ becomes an explicit task embedding space that you learn.

Stage 2: δ → LoRA

Train a separate generator:

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

Lstage2=∥ΔW^t−ΔWt∥2+λδ-cons∥Delta(ΔW^t)−δt∥2\mathcal{L}_\text{stage2} =
\|\hat{\Delta W}_t - \Delta W_t\|^2
+ \lambda_\text{δ-cons} \|\text{Delta}(\hat{\Delta W}_t) - \delta_t\|^2Lstage2=∥ΔW^t−ΔWt∥2+λδ-cons∥Delta(ΔW^t)−δt∥2
At inference on a new dataset:
* Pnew→δ^new=Eψ(Pnew)P_\text{new} \to \hat{\delta}_\text{new} = E_\psi(P_\text{new})Pnew→δ^new=Eψ(Pnew)
* ΔW^new=Gθ(δ^new)\hat{\Delta W}_\text{new} = G_\theta(\hat{\delta}_\text{new})ΔW^new=Gθ(δ^new).

This cleanly factorizes:
* “understand the dataset” (prompts → δ),
* “instantiate a LoRA for a desired δ” (δ → weights).

====== Variant C – Behavior-first: δ + output distillation ======

To reduce reliance on raw weight MSE:
# Generate ΔW^t\hat{\Delta W}_tΔW^t from prompts.
# Compute: - δ-consistency: ∥Delta(ΔW^t)−δt∥2\|\text{Delta}(\hat{\Delta W}_t) - \delta_t\|^2∥Delta(ΔW^t)−δt∥2, - output distillation: on a small set of task prompts QtQ_tQt, minimize KL between base+ΔW^t\hat{\Delta W}_tΔW^t and base+ΔWt\Delta W_tΔWt.

Total loss:

Lbeh=λδ∥Delta(ΔW^t)−δt∥2+λdistillEq∈QtKL(pbase+ΔW^t(⋅∣q) ∥ pbase+ΔWt(⋅∣q))+λw∥ΔW^t−ΔWt∥2\mathcal{L}_\text{beh} =
\lambda_\delta \|\text{Delta}(\hat{\Delta W}_t) - \delta_t\|^2
+ \lambda_\text{distill} \mathbb{E}_{q \in Q_t} \text{KL}\big(
p_{\text{base}+\hat{\Delta W}_t}(\cdot|q) \,\|\, p_{\text{base}+\Delta W_t}(\cdot|q)
\big)
+ \lambda_\text{w} \|\hat{\Delta W}_t - \Delta W_t\|^2Lbeh=λδ∥Delta(ΔW^t)−δt∥2+λdistillEq∈QtKL(pbase+ΔW^t(⋅∣q)∥pbase+ΔWt(⋅∣q))+λw∥ΔW^t−ΔWt∥2
Here the core supervision is behavioral (δ + distillation), with weight MSE as a regularizer.

==== 4. Experimental Plan ====

===== 4.1 Datasets and tasks =====

Use a setup that’s as close as possible to existing works (for easy comparison):
* Base model: a mid-size LLaMA/Gemma/Qwen.
* Task domains: reuse the 5 tasks from Delta Activations (LEGAL, MATH, MEDICAL, COMMONSENSE, CODING) and ideally some from DnD’s benchmarks.
* For each domain: - Train a reference LoRA (or reuse existing checkpoints if available). - Build prompt batches PtP_tPt for training the generator.

===== 4.2 Baselines =====
# DnD baseline – prompts → LoRA, trained only with weight MSE, same architecture.
# LoRA retrieval baseline – maybe a simple “find closest existing LoRA via bag-of-words or prompt embedding” to show that your method indeed does more than retrieval.

===== 4.3 Metrics =====
* Task performance (main metric): accuracy / exact match / BLEU / etc., depending on domain, on: - in-domain test sets, - unseen test datasets (cross-drag).
* Adapter reconstruction quality: - Parameter MSE (for sanity), - Functional distance: average KL divergence between outputs of base+generated vs base+true LoRA on a held-out set.
* Embedding behavior: - Distance between δ^t\hat{\delta}_tδ^t and δt\delta_tδt, - Cluster quality (silhouette score) in δ space for generated vs true LoRAs, as in the Delta paper. 2509.04442v1
* Generalization to new tasks: - Train generator on a subset of domains and evaluate on held-out domains/datasets (e.g., train on MATH+LEGAL+CODING, test on MEDICAL or new dataset). Compare DnD vs δ-augmented variants.

===== 4.4 Ablation studies =====
* Remove δ loss (back to vanilla DnD) to measure gain.
* Vary: - ∣Dprobe∣|D_\text{probe}|∣Dprobe∣ (1, 5, 20 prompts), - λ weights (λδ,λdistill\lambda_\delta, \lambda_\text{distill}λδ,λdistill), - A1 vs A2 for δ computation (predicted vs exact).
* Train with fewer prompt–checkpoint pairs and see whether δ helps under low-data regime.
* Randomize δ (shuffle across tasks) as a negative control to show that improvements vanish.

===== 4.5 Compositional experiments (optional but cool) =====

Leverage the additive properties of Delta Activations:
* Take δ_math, δ_code, δ_medical from existing LoRAs.
* Form combined codes: - δ_math+code = δ_math + δ_code - δ_math+medical = δ_math + δ_medical
* Decode via GGG to LoRAs and test on mixed benchmarks (e.g., math problems with code, math problems referencing medical scenarios).

Compare:
* δ-addition + decode vs
* naive LoRA addition/merging vs
* DnD directly trained on mixed-task data (if available).

This probes whether δ truly captures compositional structure over tasks and whether your generator can realize that composition in weights.

==== 5. Expected Contributions ====
* Method: A data-to-LoRA generator augmented with Delta Activations as auxiliary behavioral supervision, showing improved training stability and/or generalization versus a pure weight-MSE baseline.
* Analysis: Empirical evidence about: - how much behavioral information δ actually carries for reconstructing adapters, - whether δ-based supervision is particularly helpful in low-data or OOD settings.
* Practical takeaway: A better recipe for training DnD-like systems: “always add a δ-head/δ-loss; it costs little and improves robustness.”
* Optional: Insights into compositionality in δ-space (task mixing, factorization), connecting the “generator-side structure” story in the compositional paper to task/adapter-level behavior.

==== 6. Risks / Weaknesses (the honest part) ====
* δ is inherently lossy. Even with a good probe set, different LoRAs can share similar Delta Activations. So δ can’t fully disambiguate adapters; improvements might be modest rather than dramatic.
* Probe bias. Fixed generic probes might underspecify behavior for narrow domains (e.g., some specialized coding style), and δ could mislead the generator.
* Compute overhead. Computing exact δ for generated LoRAs inside the training loop doubles forward passes for probe prompts. You’ll probably need an approximate δ-head HHH, which adds its own approximation error.
* Still no theory. Unlike the compositional generator-identifiability work, there is no clean theorem saying “this δ-regularized generator must produce the right LoRA.” This will be an empirical improvement story, not a theory paper.

But as an incremental, concrete improvement to data-to-LoRA, this is very defensible: it piggybacks on two existing ideas (DnD + Delta Activations), adds a new, plausible type of supervision, and gives lots of measurable knobs to experiment with.

If you want, next step we can narrow down to one main variant (probably multi-task A or two-stage B), and I can help you turn this into a 1–2 page “mini-proposal” with more formal notation and maybe pseudo-code.