In short: we have compiled information about the date of development and trainable parameter counts of n=139 machine learning systems between 1952 and 2021. This is, as far as we know, the biggest public dataset of its kind. You can access our dataset here, and the code to produce an interactive visualization is available here.
We chose to focus on parameter count because previous work indicates that it is an important variable for model performance , because it helps as a proxy of model complexity and because it is information usually readily available or easily estimable from descriptions of model architecture.
We hope our work will help AI researchers and forecasters understand one way in which models have become more complex over time, and ground their predictions of how the field will progress in the future. In particular, we hope this will help us tease apart how much of the progress in Machine Learning has been due to algorithmic improvements versus increases in model complexity.
It is hard to draw firm conclusions from our biased and noisy dataset. Nevertheless, our work seems to give weak support to two hypotheses:
The structure of this article is as follows. We first describe our dataset. We point out some weaknesses of our dataset. We expand on these and other insights. We raise some open questions. We finally discuss some next steps and invite collaboration.
This article was written by Jaime Sevilla, Pablo Villalobos and Juan Felipe Cerón. Jaime’s work is supported by a Marie Curie grant of the NL4XAI Horizon 2020 program.
We thank Girish Sastry for advising us on the beginning of the project, the Spanish Effective Altruism community for creating a space to incubate projects such as this one, and Haydn Belfield, Pablo Moreno and Ehud Reiter for discussion and system submissions.
I think the story for the discontinuity is basically "around 2018 industry labs realized that language models would be the next big thing" (based on Attention is all you need, GPT-2, and/or BERT), and then they switched their largest experiments to be on language (as opposed to the previous contender, games).
Similarly for games, if you take DQN to be the event causing people to realize "large games models will be the next big thing", it does kinda look like there's a discontinuity there (though there are way fewer points so it's harder to tell, also I'm inclined to ignore things like CURL which came out of an academic lab with a limited compute budget).
This story doesn't hold up for vision though (taking AlexNet as the event); I'm not sure why that is. One theory is that vision is tied to a fixed dataset -- ImageNet -- and that effectively puts a max size on how big your neural nets can be.
You might also think that model size underwent a discontinuity around 2018, independent of which domain it's in -- I think that's because the biggest experiments moved from vision (2012-15) to games (2015-19) to language (2019-now), with the compute trend staying continuous. However, in games the model-size-to-compute ratio is way lower (since it involves RL, while vision and language involve SL). For example, AlphaZero had fewer parameters than AlexNet, despite taking almost 5 orders of magnitude more compute. So you see max model size stalling a bit in 2015-19, and then bursting upwards around 2019.
Aside: I hadn't realized AlphaZero took 5 orders of magnitude more compute per parameter than AlexNet -- the horizon length concept would have predicted ~2 orders (since a full Go game is a couple hundred moves). I wonder what gets the extra 3 orders. Probably at least part of it comes from the difference between using a differentiable vs. non-differentiable objective function.
I think that in a forward pass, AlexNet uses about 10-15 flops per parameter (assuming 4 bytes per parameter and using this table), because it puts most of its parameters in the small convolutions and FC layers. But I think AlphaZero has most of its parameters in 19x19 convolutions, which involve 722 flops per parameter (19 x 19 x 2). If that's right, it accounts for a factor of 50; combined with game length that's 4 orders of magnitude explained.
I'm not sure what's up with the last order of magnitude. I think that's a normal amount of noise / variation across different tasks, though I would have expected AlexNet to be somewhat overtrained given the context. I also think the comparison is kind of complicated because of MCTS and distillation (e.g. AlphaZero uses much more than 1 forward pass per turn, and you can potentially learn from much shorter effective horizons when imitating the distilled targets).
I also looked into number of training points very briefly, Googling suggests AlexNet used 90 epochs on ImageNet's 1.3 million train images, while AlphaZero played 44 million games for chess (I didn't quickly find a number for Go), suggesting that the number of images was roughly similar to the number of games.
So I think probably the remaining orders of magnitude are coming from the tree search part of MCTS (which causes there to be > 200 forward passes per game).
One reason it might not be fitting as well for vision, is that vision has much more weight-tying / weight-reuse in convolutional filters. If the underlying variable that mattered was compute, then image processing neural networks would show up more prominently in compute (rather than parameters).
Could it be inefficient scaling? Most work not explicitly using scaling laws to plan it seems to generally overestimate in compute per parameter, using too-small models. Anyone want to try to apply Jones 2021 to see if AlphaZero was scaled wrong?
Planned summary for the Alignment Newsletter:
This post presents a dataset of the parameter counts of 139 ML models from 1952 to 2021. The resulting graph is fairly noisy and hard to interpret, but suggests that:1. There was no discontinuity in model size in 2012 (the year that AlexNet was published, generally acknowledged as the start of the deep learning revolution).2. There was a discontinuity in model size for language in particular some time between 2016-18.
This post presents a dataset of the parameter counts of 139 ML models from 1952 to 2021. The resulting graph is fairly noisy and hard to interpret, but suggests that:
1. There was no discontinuity in model size in 2012 (the year that AlexNet was published, generally acknowledged as the start of the deep learning revolution).2. There was a discontinuity in model size for language in particular some time between 2016-18.
You can see my thoughts on the trends in model size in [this comment](https://www.alignmentforum.org/posts/GzoWcYibWYwJva8aL/parameter-counts-in-machine-learning?commentId=sFFBeva2fDgsoynDC).
Thank you for collecting this dataset! What's the difference between the squares, triangles, and plus-sign datapoints? If you say it somewhere I haven't been able to find it I'm afraid.
Thank you! The shapes mean the same as the color (ie domain) - they were meant to make the graph more clear. Ideally both shape and color would be reflected in the legend. But whenever I tried adding shapes to the legend instead a new legend was created, which was more confusing.
If somebody reading this knows how to make the code produce a correct legend I'd be very keen on hearing it!EDIT: Now fixed