An overview of the theory of overparameterized machine learning
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Re: An overview of the theory of overparameterized machine learning
#2A quick summary/translation for those of us who don't speak ML.
We keep hearing about these giant models like GPT3 with 1.5 billion paramaters. Parameters are the things that change when we train a model, you can think about them as degrees of freedom. If you have a lot of parameters, theory made us believe that the model would just "overfit" the training data, e.g. memorize it. That's bad, because when new data comes in in production we'd expect the model to not be able to "generalize" to it, e.g. make accurate predictions on data it hasn't seen before, because it's just memorized training data instead of uncovering the "guiding principles" of the data so to speak.
In practice, these huge models are, in laymans terms, fucking awesome and work really well e.g. they generalize and work in production. No one understands why.
This paper is a survey or overview of what "too many paramaters" are, and all the research into why these models work even though they shouldn't.
Re: An overview of the theory of overparameterized machine learning
#3A quick summary/translation for those of us who don't speak ML. We keep hearing about these giant models like GPT3 with 1.5 billion paramaters. Parameters are the things that change when we train a model, you can think about them as degrees of freedom. If you have a lot of parameters, theory made us believe that the model would just "overfit" the training data, e.g. memorize it. That's bad, because when new data come…
Thanks for the summary!
Re: An overview of the theory of overparameterized machine learning
#4A quick summary/translation for those of us who don't speak ML. We keep hearing about these giant models like GPT3 with 1.5 billion paramaters. Parameters are the things that change when we train a model, you can think about them as degrees of freedom. If you have a lot of parameters, theory made us believe that the model would just "overfit" the training data, e.g. memorize it. That's bad, because when new data come…
To add to this, there's a misleading phenomenon that first occurs where the performance actually gets worse with too much data/parameters/epochs, but oddly improves again if you throw even more at the model.
Re: An overview of the theory of overparameterized machine learning
#5Briefly skimmed the paper and I'm not a ML or math dude but familiar with the double descent problem.
I wonder if there's a good way to measure information content in models and how it scales with model parameters, if there are any invariants, scaling law's that arise etc. Reminds me of renormalization group methods which could be applied to a space of models, etc...
Again, I'm no expert in any of this stuff, just arm-chairing away.
Re: An overview of the theory of overparameterized machine learning
#6I'm not sure if it's related, but I've seen discussions of modern ML methods (in particular those trained using stochastic algorithms...maybe also models with low float precision...?) approximating Bayesian methods. The way I've imagined it is that the training path, by virtue of its stochasticity, resembles MCMC sampling and therefore tends to end up in regions of high posterior volume (the "typical set"), rather than high posterior density. I could see this resulting in a fit with parameters closer to their conditional expectations (in the Bayesian sense), which should be more generalizable to new data, hence fewer issues with overfitting.
A consequence of this would be that if somehow a method were able to successfully find the _global_ loss-function minimum on the training data, it would perform worse on the the test set. Fortunately, our optimization methods _don't_ find the global minimum at all.
Can anybody point me to literature on this idea? I don't know if my uninformed interpretation is actually close to what experts are thinking.
Re: An overview of the theory of overparameterized machine learning
#7I'm not sure if it's related, but I've seen discussions of modern ML methods (in particular those trained using stochastic algorithms...maybe also models with low float precision...?) approximating Bayesian methods. The way I've imagined it is that the training path, by virtue of its stochasticity, resembles MCMC sampling and therefore tends to end up in regions of high posterior volume (the "typical set"), rather th…
Oh, and I enjoyed reading this primer on the Double Descent Phenomenon for anybody, like me, who hadn't heard of it before: https://openai.com/blog/deep-double-descent/
Re: An overview of the theory of overparameterized machine learning
#8A quick summary/translation for those of us who don't speak ML. We keep hearing about these giant models like GPT3 with 1.5 billion paramaters. Parameters are the things that change when we train a model, you can think about them as degrees of freedom. If you have a lot of parameters, theory made us believe that the model would just "overfit" the training data, e.g. memorize it. That's bad, because when new data come…
To add to this, there's a misleading phenomenon that first occurs where the performance actually gets worse with too much data/parameters/epochs, but oddly improves again if you throw even more at the model.
Is this the ML equivalent of Dunning–Kruger effect? A model with a bit of data is too afraid of being wrong to be overconfident. A model with a bit more data is overconfident in itself and gets things wrong. Finally, a model with tons and tons of data understands the complexity of the problem set and once again becomes too afraid of being wrong.
Re: An overview of the theory of overparameterized machine learning
#9A quick summary/translation for those of us who don't speak ML. We keep hearing about these giant models like GPT3 with 1.5 billion paramaters. Parameters are the things that change when we train a model, you can think about them as degrees of freedom. If you have a lot of parameters, theory made us believe that the model would just "overfit" the training data, e.g. memorize it. That's bad, because when new data come…
My big beef with a lot of the 'leading edge' ML research is that it tends to be waaaaay too focused on classification problems, and ImageNet in particular. And, last I checked, you /do/ still fight with overfitting in classification models, by cleverly choosing learning rate schedules and using early stopping schemes, 'double descent' be damned.
You can solve classification with a hash function: Hash the image, and then just memorize which label goes with which hash. You can try to dodge this obviously dodgy solution by adding augmentation to the dataset. Then you instead learn to find a representation invariant under the set of augmentations, and learn the hash of that representation. It turns out these augmentation-invariant representations are actually pretty good, so we can solve the classification problem in what looks like a general way.
However, there are many other classes of problems where the hash problem doesn't exist, because the information density of the outputs is too high to memorize in the same way. Specifically, generative models, and the sorts of predictive/infill problems used for self-supervision. In these spaces, the problems are more like: "Given this pile of augmented input, generate half a megabyte of coherent output." These kinds of problems simply don't overfit: Train a speech separation model on a big dataset, and the train+eval quality metrics will just asymptote their way up and to the right until you run out of training budget.
Re: An overview of the theory of overparameterized machine learning
#10A quick summary/translation for those of us who don't speak ML. We keep hearing about these giant models like GPT3 with 1.5 billion paramaters. Parameters are the things that change when we train a model, you can think about them as degrees of freedom. If you have a lot of parameters, theory made us believe that the model would just "overfit" the training data, e.g. memorize it. That's bad, because when new data come…
My take as a 90s math grad (out of touch with modern teaching): Theory is useful to show human society is stagnant.
There’s an infinite number of sentences but our ML models are having tons of “success” as society relies on finite set in daily life; those that instigate commerce.
Like religion relied on an acceptable finite set of sentences, so too does our society. We’re a bunch of weird little missionaries living in one geometric world, still believing in bigger purpose.
ML isn’t really outputting novelty, it’s spewing our own inanity at us, and helping correct some bad math in engineering cases.
We’re easily mesmerized apes.