# The Overlooked Scaling-up Number

In recent years, there has been a constant pursuit to build larger and larger models, since researchers observed that scaling up models brought significant improvement in language understanding [1]. The following figure (credit to this blog) shows that model size scales up exponentially every year. Large companies are in a hot arms race to win the title of "largest model to date".
It is often overlooked, however, that the number of public available models also scales up exponentially. The HuggingFace Models is a famous hub for hosting pre-trained models. From the upload history of every model, I calculate the number of new models every year, and plot the trend in the following figure. The figure clearly shows an exponentially increasing trend for the number of available pre-trained models.

# The Popular But Under-exploited Model Hub

It is true that HuggingFace Models is very popular. Nevertheless, I find that the whole model hub is under-exploited, in terms of the number of models being used. The following figure is taken from my JMLR paper [2]. It analyzes the download count per month for all the pre-trained models in the HuggingFace Models. There are some obvious observations:
• Pre-trained models (PTMs) have become a cornerstone of deep learning. A single model hub has over 150 million downloads in just one month.
• The distribution of download count is extremely skewed. BERT contributes over a half. The top 10 models (except BERT) contribute less than a quarter. The top 1000 models (except the top 10) contribute less than a quarter.
In its current state, the model hub looks like a large UGC community with abundant user-generated content. Due to the lack of a recommendation system for pre-trained models, however, practitioners just pick the most popular model and nobody cares about the rest models, resulting the dilemma that the model hub is popular but under-exploited.

# A New Paradigm For Exploiting Model Hubs

The key to sufficiently exploiting model hubs is to take advantage of those under-exploited models. A good recommendation system should recommend content according to the user's preference, and so should a good paradigm for exploiting model hubs. In the last year, I worked hard on this problem and I want to share some of my thoughts here.
So far, I have made several analogies between recommendation systems and model hubs. It is intuitive for readers to understand the main idea, but technical details are different. To be specific, recommendation systems deal with "real users" and their goal is to predict user behavior, while model hubs deal with tasks and their goal is to solve a task with the help of pre-trained models.
The paradigm I propose in the paper [2] is to treat model hub as a service: a user comes with a task in the form of a dataset $\left\{\left({x}_{i},{y}_{i}\right){\right\}}_{i=1}^{n}$$\left\{\left({x}_{i},{y}_{i}\right){\right\}}_{i=1}^{n}${(x_(i),y_(i))}_(i=1)^(n)\{(x_i, y_i)\}_{i=1}^n; we should automatically rank all possible models according to their transferability to the task, and tune the models according to the requirement of the user:
• If the user has no preference for the model's architecture, just fine-tune the best-ranked model directly.
• If the user desires a specific model but it is not the best (e.g. a small model for fast inference): transfer top-K ranked models to the target model.
The paradigm is summarized in the following figure, and next I will elaborate on each step.

## Ranking Pre-trained Models

The first thing is to predict the performance of a pre-trained model $\varphi$$\varphi$phi\phi on a target task without requiring the user to actually fine-tune the model, which is called the transferability estimation problem. Researchers have explored a dozen of methods in recent years, including the class relationship [3], Bayesian evidence [4], PAC-Bayesian Metrics [5], Bhattacharyya Class Separability [6], and so on. Among these methods, the LogME method [4] is a classic one to measure the transferability by the compatability between features and labels. Researchers expect to develop good metrics that correlate well with fine-tuned performance, so that model ranking by the metric is similar to the ranking of fine-tuned performance but no fine-tuning is required, as shown in the figure below.

## Selecting Pre-trained Models

With a transferability ranking, a straightforward action is to use the best ranked model. This is true for most academic researchers as they are not constrained by the inference cost of deployed models. However, in a practical usage scenario, there are often constraints on the network architecture, parameter count, or FLOPs of computation. Therefore, the pre-trained model $\varphi$$\varphi$phi\phi satisfying these constraints is probably not the best ranked. The current state of the art is that practitioners can only fine-tune $\varphi$$\varphi$phi\phi, and the overall knowledge of the model hub cannot be exploited. With all models ranked by their transferability, we show that it is possible to transfer knowledge from several teachers (top-ranked models) to the target pre-trained model $\varphi$$\varphi$phi\phi during fine-tuning. This way, we only need to select the number of teachers for tuning.

## Tuning Pre-trained Models

The difficulty of transferring knowledge from top-K models $\left\{{\varphi }_{k}{\right\}}_{k=1}^{K}$$\left\{{\varphi }_{k}{\right\}}_{k=1}^{K}${phi_(k)}_(k=1)^(K)\{\phi_{k}\}_{k=1}^K to the target model ${\varphi }_{t}$${\varphi }_{t}$phi _(t)\phi_t lies in their heterogeneity. Our paper [2] proposed B-Tuning to project their features into a common class space so that feature distillation is possible. I will not dive into details as the method requires heavy math, but the implementation is pretty easy, and code is available.
To confirm the effectiveness of the proposed "ranking and tuning" paradigm, we conduct experiments on some popular tasks like fine-grained Aircraft classification and bird classification. The red-dashed line is the accuracy of picking the most popular pre-trained model, which is shown to be sub-optimal. By first ranking and then tuning top-K models, we can improve the accuracy by 3%~5%, thanks to the diversity of the model hub.

# Concluding remarks

Pre-trained models are universally acknowledged as a foundation of deep learning. Researchers have explored many ways to create and exploit pre-trained models, but little is done for exploiting model hubs. Our paper [2] takes the first step to show the value of exploiting all models in the model hub. The paradigm can be attractive for practitioners.
To take a step further, the scope of pre-trained model hub is not limited to large models: AI companies usually re-train models every once in a while, and all the models trained in the past can be treated as a model hub. It is a reckless waste to just discard those models. These models can be exploited to improve performance, or at least accelerate training of new models using the proposed "ranking and tuning" paradigm.
Trained models are assets, and how to activate their potential is an important problem. I believe the paper [2] is just a starting point and there is still a long way to fully addrss the problem.

# References

[1] Kaplan et al., Scaling Laws for Neural Language Models, Arxiv 2020
[2] You et al., Ranking and Tuning Pre-trained Models: A New Paradigm for Exploiting Model Hubs, JMLR 2022
[3] Nguyen et al., LEEP: A New Measure to Evaluate Transferability of Learned Representations, ICML 2020
[4] You et al., LogME: Practical Assessment of Pre-trained Models for Transfer Learning, ICML 2021
[5] Ding et al., PACTran: PAC-Bayesian Metrics for Estimating the Transferability of Pretrained Models to Classification Tasks, ECCV 2022
[6] Pandy et al., Transferability Estimation using Bhattacharyya Class Separability, CVPR 2022

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