Learning on LoRAs: GL-Equivariant Processing of Low-Rank Weight Spaces for Large Finetuned Models

We thank the reviewer for taking their time to review our paper. Here we address comments by the reviewer, please let us know if you have any further questions:

I don't really understand why this is at all useful…

We agree that we could have been clearer in our explanation of the usefulness of LoL models. See our general comment for why we believe LoL models are useful. We specifically address your two specific usefulness-related questions below:

The model allows you to predict the accuracy of the model if a set of LoRA weights is applied; how is this useful? Why not just apply the LoRA weights and actually measure the accuracy?

As we write in our paper (Section 5.3) “This could be useful in evaluations of finetuned models, as standard evaluations of language models can require a lot of time and resources, whereas our LoL models can evaluate these models with one quick forward pass.“

Quantitatively, for the experiments in the paper, computing CLIP score with our LoL models are up to 53,700 times faster than with standard evaluation, and evaluating an LLM on ARC-C can be 730,000 times faster. More specifically:

• Evaluating CLIP score of one diffusion model takes 36 ± 2 seconds (660 forward passes, on 33 fixed prompts) when doing a standard evaluation. But it only takes .0133 of a second with one GL-Net forward pass (and .00067 seconds per model at batch size 250).
• Evaluating ARC-C test accuracy of a Qwen2 1.5B finetune requires 220 seconds (over 1,100 data points) with standard evaluation. But it only takes .0075 of a second with our GL-Net at batch size 1 (and .00003 seconds per model at batch size 250).

Moreover, this trade-off can be even more in the favor of LoL models in different scenarios. For instance, some researchers use thousands of times more prompts to compute CLIP score (Saharia et al. 2022), or 10x larger multiple-choice datasets like MMLU to measure LLM performance. Instead of taking over 30 minutes to evaluate models on these benchmarks, we can use LoL models to evaluate them in a fraction of a second.

We will add these quantitative measurements to our paper.

(Saharia et al. 2022) "Photorealistic text-to-image diffusion models with deep language understanding." NeurIPS 35 (2022). https://arxiv.org/abs/2205.11487.

Why is it useful to predict how many data points the model was fine tuned on... If I have a set of LoRA adapters, I'll try every single one and the set of LoRA weights that does best is the one I'll use (regardless of how many data points it was trained on...).

As we cite in our paper, the task of predicting dataset size from LoRA weights was considered in prior work https://arxiv.org/abs/2406.19395. They dedicate their whole paper to this task, and they write extensive motivation for the task. In our paper, we also already described the utility of this task (Section 5.2.2): “The success of this task implies a privacy leak, since model developers may sometimes wish to keep the size of their finetuning dataset private. Moreover, the dataset size is a useful quantity to know for data membership inference attacks and model inversion attacks, so accurately predicting dataset size could improve effectiveness of these attacks too“. Basically, model trainers sometimes want to keep properties of their finetuning datasets private; this task explores the extent to which data properties can be inferred from released LoRA weights.

We thank the reviewer for appreciating our new LoL architectures, novel datasets, and experiments across different types of finetuned models. Here we address some comments of the review:

1. … the number of parameters and the training costs associated with different model structures and methods, is not sufficiently clear. … How many GPU hours during the collection of these LoRA models?

Good point. We will add the number of parameters for the LoL models of the experiments in the Appendix. Here is the table for your reference:

Also, we add GPU-hour estimates for training all of the LoRAs.

2. The motivation behind the task selection for LoL models is not clearly articulated… it is not immediately clear why these tasks are important or how they contribute to advancing the field …
3. The practical usage of the LoL models is not explicitly addressed. Are there any potential real-world applications except the dataset size prediction?

Good point, we could have been clearer on how we explain the usefulness of LoL models and these tasks. See the general comment for an in-depth explanation of the usefulness. In short, there are useful applications of the tasks we consider (e.g. 20,000 times faster evaluation of finetuned models using LoL models for accuracy prediction), and we believe the LoL framework and models we introduced could be quite useful in future application work.

3. Other methods used for comparison in this work are not clearly defined and lacks sufficient discussion.

Could you elaborate on what you mean here? To be clear, the 5 LoL models we experiment with are proposed and implemented by us. Though, there are some similarities to existing work (e.g. we mention in Section 3.2 that our MLP+SVD is similar to the model of Salama et al. 2024, except they use a NN classifier instead of an MLP).

1. The LoRA model datasets used in this work are derived from Stable Diffusion V1.4 and Qwen2. A key question is whether the LoL model will remain effective if LoRA models are obtained from different versions, such as Stable Diffusion V2.1 or Qwen V2.5.

Good question. To answer it, we trained additional datasets (with Stable Diffusion 1.5, 2.1, and Llama 3.2 3B) and ran new experiments:

For LLMs, we create a dataset Llama-ARC-LoRA, of 2000 finetuned Llama3.2 3 billion parameters LLMs. These networks are 2x larger and have different architecture from the Qwen2-1.5B models. Nonetheless, the results are very qualitatively similar:

For Stable Diffusion, we also test OOD generalization between Stable Diffusion V1.4 and V1.5 with GLNet to show our results are not specific to Stable Diffusion V1.4.

We also see that our models perform well on SD2.1, though less well than for SDv1 versions:

2. Is there a clear rationale behind the choice of model architecture for the LoL models? Specifically, is using an MLP sufficient for the tasks at hand, or could other architectures be more effective?

Good question. We just used an MLP for our models (besides GL-Net) for simplicity, given that we already propose 5 LoL models. We think that other architectures could indeed be better in certain ways, and are worth exploring in future work. For instance, one could try using convolutional or attentional modules, where the sequence dimension is the layer index.

We thank the reviewer for appreciating our framework, theory, and extensive experiments.

1 - The paper could benefit from a more thorough introduction to concepts like GL-invariance, O-invariance, and O-Align …

Thank you for this comment. We will try to make our exposition clearer, and also add more background and references on relevant materials in the appendix.

2 - GL-net’s superior performance may be partly due to a higher number of parameters or computational requirements compared to other LoL architectures…

Actually, GL-net uses less parameters in general than the MLP-based methods, especially MLP + Dense. For instance, see this table (which we will include in the revised PDF).

Also, as we show in Section 5.5, the preprocessing and forward pass time of GL-Net doesn’t increase much as input data size increases, but the same does not hold for some of the other baselines. However, GL-Net can be slower for smaller input networks.

3 - The visuals … could benefit from clearer labeling and expanded captions to help interpret performance differences among models​. While the data is comprehensive, more explanatory notes within the figures would enhance accessibility for readers.

Fair point. We will add additional notes, including references to relevant parts of the main text in Figure 3 and Figure 2.

4 - The GL(r)-equivariant models, while theoretically sound, are complex … While this complexity is justified for theoretical exploration, a discussion on trade-offs and simplifications would make it easier for practitioners to implement the approach.

Previous work in weight-space learning, such as Navon et al. (2023), has shown simpler approaches that could be integrated as baselines to contrast model complexity and efficiency​.

Indeed, this is why we developed 4 MLP-based LoL models in addition to GL-Net. Much like Navon et al. (2023), we proposed and empirically tested a pure MLP model, as well as an MLP with alignment. We will add more to our revised PDF of practical trade-offs, so that we elaborate more on the theoretical properties listed in Table 1.

1 - Can the proposed methodologies (such as GL-equivariant architectures) be directly applied to other LoRA-based fine-tuning variants, like DoRA (Liu et al., 2024)?

We already discussed the DoRA and KronA LoRA variants in Appendix E, with a characterization of their symmetries. In the revised PDF, we will also include additional notes on how LoL models can be applied to these variants.

2 - Is the performance boost primarily due to the model’s increased number of parameters or computational requirements … how would you describe the cost/performance trade-off for GL-net in practical applications, especially in contexts where computational efficiency is prioritized?

See number of parameters in our above answer. We are not yet sure of the full trade-offs of GL-Net, but we suspect it may be more beneficial in tasks where more expressiveness is needed, whereas the simpler MLP-based methods may be fine in other tasks.

3 - GL-net shows relatively lower performance on the dataset size prediction task. Could this lower performance be attributed to overfitting? If so, would any regularization techniques be effective here, and are there any architectural adjustments that could improve generalization on this specific task?

Yes, that is possible, and there are interesting questions here. Even though GL-net and the other MLP-based methods are expressive enough to express MLP + SVD, overfitting or some other phenomena prevent this in practice. In Section D.3 we further analyze the predictions of GL-net on this task. Perhaps different loss functions may help on this task, including regularization, or data augmentation that does not affect singular values.

4 - The authors briefly mention future applications of GL-equivariant networks, such as model merging and LoRA editing (Conclusion)​. Could authors please elaborate…

Indeed, these future applications are quite interesting. In this paper we only explored invariant tasks. To do equivariant tasks, we need to remove the invariant head of the model. Further, we may need to create different equivariant modules, such as equivariant normalization layers, which may take similar form to our equivariant nonlinearities. Model merging may be done via approaches similar to previous work on aligning model weights with metanetworks (Navon et al. 2023b), and LoRA editing may be done similarly to the INR editing tasks of Zhou et al. 2024b, where a metanetwork predicts an edit direction in a way that is trained by a supervised learning task. These require different types of losses and data setups.