Dynamic Weight Generation (MeG)

Updated 23 December 2025

Dynamic Weight Generation (MeG) is a methodology that uses conditional diffusion models to dynamically generate neural weights based on contextual signals.
It enables zero-shot generalization and scalable knowledge editing in applications such as environment-adaptive prediction and large-scale LLM modifications.
MeG leverages advanced techniques like graph-structured VAEs and dynamic neuron insertion to overcome limitations of static models, ensuring high performance and adaptability.

Dynamic Weight Generation (MeG) refers to a class of methodologies that dynamically generate neural network weights, often via conditional generative models such as diffusion models, to enable highly adaptive, context- or query-dependent model behaviors. Prominent applications include zero-shot generalization in dynamical systems across varying environments and large-scale knowledge editing in LLMs, where MeG achieves both high effectiveness and scalability by circumventing the limitations of static parameter updates and capacity-constrained editing mechanisms (Li et al., 20 May 2025, Wan et al., 16 Dec 2025).

1. Motivations and Problem Formulations

Dynamic Weight Generation arises from the need to efficiently adapt neural predictors to novel tasks or scenarios for which retraining, fine-tuning, or permanent weight modification are impractical or insufficient. In the environment-adaptive prediction of dynamical systems, static predictors $f_{\theta,e}$ trained in a specific environment $e$ exhibit poor transferability to new environments $e^*$ . Similarly, standard knowledge-editing for LLMs (e.g., ROME, MEMIT, T-Patcher, SCEN) faces limited capacity and escalating interference as the number of edit targets grows. MeG addresses these limitations via models that generate, at inference, weights or neuron parameters as a direct function of contextual signals such as environment descriptors or queries, thus enabling genuine zero-shot adaptation or large-scale, interference-free knowledge editing (Li et al., 20 May 2025, Wan et al., 16 Dec 2025).

2. Methodological Foundations

Two principal instantiations define state-of-the-art MeG paradigms:

EnvAd-Diff for scientific machine learning: Predicts environment-conditional weights $\theta^*$ $θ^{*}$ for lightweight neural operator "experts" (FNO, UNO, WNO). The method first constructs a "model zoo" of expert networks, each tuned to an environment $e_i$ $e_{i}$ , then trains a graph-structured VAE over weight graphs, followed by a conditional diffusion model in latent space $Z$ $Z$ . The generative pipeline is:
1. Encode weight graphs into latent vectors via a VAE.
2. Train a T-step diffusion model $p_\theta$ to sample $Z_0 \sim p(Z|e)$ .
3. Decode to obtain functional weights $\tilde{W}$ for new environments $e^*$ or surrogate labels $c^*$ .
MeG for Massive LLM Editing: Deploys a single dynamic neuron within a chosen LLM FFN layer. For each query $x$ , a diffusion model generates input–output weights $z(x)$ conditioned on the text-encoded representation $c=f_{TE}(x)$ . The dynamic neuron is introduced at inference time and does not alter the base model or accumulate interference from prior edits. The process leverages a contrastive InfoNCE loss for paraphrase generalization and a Familiarity Network for irrelevant-query filtering (Wan et al., 16 Dec 2025).

3. Model Architectures and Generative Mechanisms

MeG systems are characterized by generative mechanisms centered on diffusion processes and auxiliary encoders:

Diffusion-based Generation: For both tasks, the generative process comprises:
- Forward (noising): Gaussian noise is incrementally added to latent variables or neuron weights.
- Reverse (denoising): A neural network (Transformer or DiT) conditioned on context reconstructs clean weights via a series of denoising transitions, parameterized as $p_\theta(w_{t-1}|w_t, c)$ or $p_\theta(Z_{t-1}|Z_t, e)$ , with conditioning vector $c$ (text-embedding) or $e$ (environment).
- Sampling acceleration: DDIM or similar techniques reduce inference steps (e.g., 50 vs. 1000).
Graph-structured and Neuronal Representations: For environment-adaptive prediction, weight graphs are constructed where each node aggregates all weights (and biases) into feature vectors, enabling node-wise normalization and scalable heterogeneity handling. In MeG for LLMs, the dynamic neuron is defined by a concatenation of its input/output weight vectors, with layer-specific dimensionality.

4. Conditioning and Surrogate Labeling

Effective dynamic weight generation depends crucially on the conditioning signals:

Environmental Variables and Surrogates (Li et al., 20 May 2025):
- Where explicit environment variables are unavailable, function-based distances $D_{ij}$ (expected output differences) are computed across expert models, and a principal component (PCA) projection yields a low-dimensional surrogate scalar $c_i$ per environment.
- A Prompter (SVR) maps sequence initial states $x_0$ to $c^*$ for unseen environments at test time.
Query Embeddings and Familiarity (Wan et al., 16 Dec 2025):
- In LLM editing, the context vector $c$ is obtained by passing the input query $x$ through a text encoder $f_{TE}(\cdot)$ , trained with InfoNCE loss for improved paraphrase coverage.
- A familiarity classifier $f_p$ identifies whether a query requires editing (entropy $H < \epsilon$ ), ensuring weight injection only for relevant requests and minimizing locality degradation.

5. Experimental Results and Key Findings

Empirical evaluations establish Dynamic Weight Generation as highly effective across domains:

Task	Baseline Model(s)	Scale $N$	Score (MeG)	Score (Best Baseline)	Locality (MeG)	Locality (Baseline)
ZsRE (Phi-2, AG/TF)	ROME/MEMIT, etc.	10,000	82.80	45.64	91.14/95.84	18.22/80.78
COUNTERFACT (GPT-J)	ROME/MEMIT, etc.	10,000	71.19	5.65	61.50/65.52	1.22/8.60
Cylinder Flow RMSE	FNO (500M)	—	0.065	0.083	—	—

Key findings include:

Substantial performance gains: EnvAd-Diff generated 1M-parameter neural operator models outperform 500M-parameter foundation models for both in-domain and out-of-domain generalization (e.g., out-domain RMSE 0.065 vs. 0.083 in cylinder flow) (Li et al., 20 May 2025).
High scalability: MeG maintains Reliability and Locality at $N=10,000$ edits, with harmonic mean scores far surpassing baselines (Score +~37 points for ZsRE, +~65 points for COUNTERFACT) (Wan et al., 16 Dec 2025).
Ablation analyses: Removal of functionally-informed losses or initializations leads to 20–30% error increase in environment adaptation. In editing, discarding the familiarity network reduces Locality by ~35 points; non-contrastive encoders degrade Generality by ~30 points.

6. Limitations and Current Challenges

Observed limitations include:

Model Zoo Dependence: EnvAd-Diff requires extensive domain pretraining and per-environment fine-tuning to build a diverse, high-quality model zoo. Data efficiency and active environment selection remain open areas (Li et al., 20 May 2025).
Dimensionality of Surrogate Labels: The present approach uses a 1D surrogate (PCA); scaling to richer or unobserved environments may benefit from learned encoders or multi-dimensional embeddings.
Inference Overhead: MeG for LLMs incurs approximately 5–6% extra inference cost for edited queries due to diffusion sampling, though irrelevant queries are handled at zero overhead (Wan et al., 16 Dec 2025).
Pre-collect Phase: MeG requires pre-computing fine-tuned neuron weights for each edit, then training the diffusion model on these pairs.

7. Extensions and Prospects

Dynamic Weight Generation opens several new directions:

Generalizability: The MeG paradigm can be extended beyond PDE/ODE prediction and LLM editing, to any context where model function varies with unsupervised or latent variables (robotics, material modeling, acoustics) (Li et al., 20 May 2025).
End-to-End Training: Joint optimization of prompters and diffusion networks could further improve adaptation fidelity.
Learnable Environment Embeddings: Moving from PCA-based surrogates to encoder-derived environment templates may address complex, high-dimensional regimes.
On-the-fly Model Surgery: MeG demonstrates feasibility of per-query generation and insertion of weights, suggesting new paradigms for dynamic modularity and functional expandability in deep learning architectures (Wan et al., 16 Dec 2025).

Dynamic Weight Generation, through conditional diffusion models and context-driven embedding strategies, defines a new class of generative-by-weight neural adaptation. It supports scalable, interference-free, high-fidelity edits and transfers across a range of tasks, with implications for both scientific machine learning and LLM systems (Li et al., 20 May 2025, Wan et al., 16 Dec 2025).