Venue: NeurIPS 2022 Conference

Reviews:

final_score: rating: 5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.
review_content: summary: Transfer learning is ubiquitous in deep learning methods, and gradient-based transfer learning is usually dominant in these areas where a pre-trained network in fine-tuned for a task. The issue with this approach is that after fine-tuning the network becomes better at the current task at hand but might 'forget' the previous task. To alleviate this issue the authors (along with others) suggest taking the 'average' of the two networks (or more networks if other fine-tuned networks are available). This approach combines the strengths of multiple models such that they retain their performance on their respective individual tasks. The authors extend this approach by considering the weighted mean of the different models (at an individual parameter level) and guide the weighing of the parameters using their respective information matrices.
strengths_and_weaknesses: Strengths
- The paper tackles an interesting and relevant problem.
- The paper presents significant empirical evidence.

Weaknesses
- The idea presented is straightforward and the main contribution of the paper is empirical results corroborating the proposed framework, and thus, lacks theoretical arguments.
- Some intuitions and sentences in the paper are not obvious.
- The arguments made in the paper are a bit difficult to follow.
questions: Can the following two sentences be clarified a bit more?

- "Since the Fisher information is a local property of a single parameter value, we limit our focus to models that were trained from the same initialization." Do you refer to "same pre-trained model" being fine-tuned multiple times? Why is this relevant if the parameter spaces are exactly the same?

- "a small Fisher value ultimately means that the parameter is relatively unimportant to the model’s behavior." I will guess that a small information will imply that the parameter cannot be estimated reliably from the data, and thus, can be removed from the "averaging". Is this a suitable interpretation?

Can Figure 3 be elaborated a bit more:

- Can you show the transition of regularization values (perhaps using different transparency).
- What are the values that simultaneously

Figure 4 shows that isotropic merging and Fisher merging perform similar to each other on an average, and standard fine-tuning can outperform these approaches on some occasions. Can
the authors provide some guidelines on when one of these three approaches should be considered?
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limitations: Some limitation of the method, e.g., numerical issues have been addressed in the paper. It will be great to address situations where Fisher merging performs better than isotropic merging and vice versa.
review_title: null

final_score: rating: 5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.
review_content: summary: This paper proposes a method for casting the problem of averaging parameters from multiple models with shared architecture as seeking a MAP estimate of the joint posterior with Laplace approximation for individual trained models.
Empirical experiments on natural language processing datasets are presented, showing its effectiveness on model ensembling, fine-tuning, and domain adaptation tasks.
strengths_and_weaknesses: 
#### Strengths
- The method proposed in this work is conceptually simple and intuitive. The paper is generally well-written and easy to follow.
- The empirical evaluation covers a wide range of tasks and metrics, including both task-specific performance and computational efficiency.

#### Weaknesses
- While I understand the point that the authors aim to propose an alternative to the plain parameter averaging approach, the introduced method is still seeking a point estimation for the joint posterior which is based on the Laplace approximation. Thus the issues of the Laplace approximation would also exist in the proposed approach, and it is hard to tell how the uncertainty in the final estimation is addressed given the results included.
- Quite a few experimental results are presented, however, only on natural language datasets and tasks. As a general parameter averaging approach, it would be beneficial to consider other data modalities as well.
- As discussed in the first point about the limitations of the Laplace approximation, for efficient estimation of the Fisher matrix, diagonal approximation is made which leaves the structure of the task ignored.
questions: - For neural networks with batch normalization, and spectral normalization, how would the parameters be averaged in the proposed method?
- How would the parameter uncertainty be addressed in the proposed method? 
limitations: Yes.
review_title: null

final_score: rating: 7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.
review_content: summary: The paper proposes a novel method for merging (pre-trained) models with the same architecture and initialisation set up. The merging strategy for obtaining the new model based on the previous ones is based on the Laplace approximation, and particularly, on the Fisher information matrix. In the manuscript, the advantages of merging via Fisher information matrix is illustrated within simpler strategies based on isotropic Gaussian approximations or just output ensembles. Experimental results using (very) large models -- i.e. BERT, show a significant performance while at the same time being simple and x5-x6 cheaper than other approaches.
strengths_and_weaknesses: **Strengths.**

The idea of merging models to transfer capabilities and knowledge to new models without the need of exhaustive re-training from the same data is sound and novel. The paper positively illustrates the problem considered and related work is well reviewed in my opinion. While the methodology section could be slightly improved (see weaknesses), the experimental section is strong, mainly due to the consideration of big models or other neural network (NN) based architectures in the results. While being simple, performance seems promising. In general, I had not seen results on merging such large models like BERT or relative ones. Also details on FLOPs or computational cost saved from merging is a good point for the community.

**Weaknesses.**
In my opinion, there are two small points of weakness:

- *Section 2:* The methodology described in Sec. 2 for the isotropic + Fisher merging could be improved, or at least connect better with probabilistic modelling. For me, was not difficult to follow and key details are included, but perhaps some intermediate details or equations are missing. For instance, equation in L102 introduces densities $p(\theta|\theta_i, I)$, not being 100% clear enough where they come from. Similarly, in L129-L132, Fisher matrix is introduced within data $x,y$ which are not previously defined. 

- *Laplace Approximation:* There is a recent interest in the community on Laplace approximation and Hessian-based methods, mainly due to their utility for providing alternatives to Bayesian NNs (approximating posterior on the parameters). Even being a different goal, I find the paper somehow connected, and some references could be perhaps included (Laplace Redux, + previous and follow-up approaches). Additionally, I am a bit surprised about the lack of difficulties for computing the Fisher information matrix (even being diagonalised) in such enormous architectures.. I would appreciate if authors could elaborate a bit more on this and the computational cost.
questions: Some additional questions that I would appreciate to be answered.

- *Q1.* If I understand correctly, once each $m$-th model is trained, we are able to compute the Fished matrix in a *posthoc* manner. Once F
 Is computed/approximated, we can use it for training the new model merging. Does this last merging re-visit old data? Or F is assumed to be fixed and known without the need of re-accessing $x$ or $y$?

- *Q2.* This is just a curiosity, but as far as I know, BERT models use self-attention layers in their architecture. Do these type of layers/operations introduce unmergeable parameters? In other recent Laplace papers, some type of layers could not be considered due to the difficulties for computing Hessians.

- *Q3.* How many models are being merged in the experiments? And how large is the space of parameters? Could the authors provide some numbers on the validation set accuracy of the individual pre-trained models? 

- *Q4.* Are convolutional layers considered also as parameters to be merged?

limitations: Yes
review_title: null

final_score: rating: 6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
review_content: summary: The paper studies the problem of how to effectively average existing deep learning models, which has broad application background in transfer learning. The authors proposed to derive a **geometric centroid** of the given models based on information geometry. Based on certain simplifications (such as diagonal Fisher information matrix, FIM), the resulting model is in closed form based on the FIM in eq.(4). On real-world transfer learning experiments, the authors showed that the proposed method is better than empirical averaging.
strengths_and_weaknesses: Pros:

- The proposed method is efficient based on a diagonal approximation of the Fisher matrix (as in Adam).
- Strong experimental results with extensive study in modern deep learning models.

Cons:

- The paper can be regarded as an application of information geometry into deep learning. The theoretical depth can be improved to explain why it works well.
- Some historical literature on model selection and information geometry can be more carefully investigated.
questions: Sec. 2. related expressions regarding the posterior can be better formulated and clearly written. For example, why $\theta^{\star}=\sum_{i}\log{}p(\theta|\theta_i,I)$? and why $p(\theta|\theta_i,I)$ is the posterior? What is the associated prior? These formulations can be improved.

The presented work is a simple application of Fisher information into modern machines. Most of the cited papers are from recent deep learning communities. The idea of using information geometry for model averaging is not new. Related literature where similar ideas were known and used should be better acknowledged.  For example, see  [1][2][3].

[1] "Specification Uncertainty and Model Averaging", Larry M. Bartels, 1997.

[2] "Sided and Symmetrized Bregman Centroids", Nielsen & Nock, 2009.

[3] "Model Selection and Model Averaging in Phylogenetics: Advantages of Akaike Information Criterion and Bayesian Approaches Over Likelihood Ratio Tests", David Posada, Thomas R. Buckley, 2004.

There should be more discussion on why it works better than the empirical averaging approach. Instead, the authors introduced the method "as is" without sufficient theoretical arguments or motivation.
limitations: The paper is theoretical and does not have a negative societal impact as far as I can tell.
review_title: null

final_score: rating: 7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.
review_content: summary: This paper explore "merging" models, i.e. combining the parameters of two or more models into a single model. It advances an increasing popular research direction in averaging parameters of models that share the same architecture and initialization. Their main contribution is to go beyond the way parameters are typically averaged, by having individual weights for each of the parameters. For such, the authors advocate for finding a model with the most likely set of parameters, considering the posteriors of all models being averaged. Their method is based on approximating each model's posterior as a Gaussian distribution whose precision matrix corresponds to its Fisher information. This then leads to a closed-form solution for which weights to use for each parameter when averaging multiple models. Authors additionally have global hyper-parameters which can be tuned to control the importance of each model when averaging. The authors present a series of experiments in both natural language processing and computer vision, contrasting their Fisher-weighted averaging with previous work where simple averaging is used (i.e., without any parameter-specific weights). The authors also explore new settings for combining models, in addition to existing ways like robust fine-tuning or model soups. Code  for replicating the experiments will be publicly released.
Overall, this paper presents a solid advance in our understanding and methods for combining models. Considering that pre-training is becoming increasingly expensive and intractable to repeat, this line of work is very timely. I believe this paper would be of interest to many in the community, and I recommend its acceptance. 
strengths_and_weaknesses: **Strengths**

1) The research direction this paper explores is timely, and I believe would be of interest to many.

2) The ideas presented in this work are novel, and it departs significantly from previous work.

3) The experiments presented are comprehensive and solid. Compared to standard (isotropic) merging, Fisher merging provides improvements in most cases, sometimes by large amounts. Moreover, their method does not incur in any extra compute at inference time compared to the models being merged. Finally, the fact that the the authors conduct experiments both in natural language processing and computer vision showcases the generality of their findings.

4) I found the experiments presented in Section 3.1 to be particularly interesting, since authors combine models with external checkpoints, created independently by multiple people. Considering model zoos like the Hugging Face model hub are growingly rapidly, this experiment is a great proof of concept of a future were we take better advantage of such resources.

5) The paper provides a great review of related work, and contextualizes itself and its contributions well with respect to recent literature.

**Weaknesses**

1) In some cases, the improvements gained via Fisher merging (compared to Isotropic merging, which has been previously explored) are small or even inexistent. Better understanding *when* Fisher merging provides larger gains compared to Isotropic merging would greatly strengthen the paper.

2) Compared to Isotropic merging, Fisher merging can require extra compute. In section 3.3, the authors claim that merging is more computationally efficient than fine-tuning, but this only holds true when assuming that all checkpoints being merged are already available. While this can be true for many datasets, there are scenarios where it does not hold, for instance, for recently released, less popular or private tasks. Moreover, the proposed procedure might be infeasible in some cases: for instance, consider fine-tuning a CLIP model on ImageNet, as in Sec. 3.2. CLIP models are public, but their training data is not. Given that the authors advocate for using data from the dataset used to train the model for computing the Fisher matrix (L. 141), how can this be done if it is not public? If other datasets can be used for computing the Fisher matrix, which ones to chose? Does the choice matter? Further exploring and discussing this would strengthen the paper.

questions: Have the authors explored larger language models? I believe this line of work is most attractive when pre-training is prohibitively expensive (if pre-training is cheap, why not just combine the datasets and pre-train again?). It would also be interesting to show that this can work with parameter-efficient fine-tuning methods like adapters.
limitations: The authors discuss some limitations of their method and how to address them (for instance, numerical issues and unmergeable parameters). As previously mentioned in the Strengths and Weaknesses section, I believe better understanding of when Fisher merging provides large improvements over Isotropic merging would greatly strengthen the paper.
review_title: null

Meta-review: metareview: Most reviewers agree that the paper proposes some interesting novel ideas and  that its
strengths overcome some of its weaknesses (eg lack on theoretical guarantees). As such, we are
think that the paper is worth publishing and expect  the authors to improve the manuscript
in accordance with some of the reviewers comment. 

confidence: Certain
Decision: Accept