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Double Descent in Human Learning
- esafak 3y agoGradient descent finds the minimum L2 norm solution of the least squares? So adding a L2 regularization term should do nothing if the objective is convex, right? Is this common knowledge? I must have missed the memo, or be getting rusty.
- canjobear 3y agoThe formal claim is in Appendix A here: https://arxiv.org/pdf/2303.14151.pdf https://arxiv.org/pdf/2303.14151.pdf
- svantana 3y agoIt finds the minimum with regards to the training data. The double descent phenomenon is about error on unseen data.
- jwilber 3y agoThere’s definitely more to the picture than that - it’s really about how models in the interpolation region behave (see https://mlu-explain.github.io/double-descent/ https://mlu-explain.github.io/double-descent/ or https://mlu-explain.github.io/double-descent2/ https://mlu-explain.github.io/double-descent2/)
- deleted 3y ago[deleted]
- macleginn 3y agoIt depends on the inputs. E.g., if two elements of the input are highly correlated, the network can assign an arbitrarily high positive weight to one element and then correct this by assigning an arbitrarily high negative weight to the other, with the total contribution of the two elements being reasonable. However, if these input elements are not as tightly correlated in the test data, the results may be bad. L2 regularisation ensures that this does not happen. (In practice, the effect will be mitigated by the activation function, but weights do blow up in training, leading to "saturated" models, which exhibit weird behaviours.)
- elcomet 3y agoThe objective is usually not convex in deep learning.
- elcomet 3y agoYou don't necessarily want the optimal solution, L2 regularization can give you a slightly worse solution on the training set but that will be better at generalization on unseen data.
- valine 3y agoI’ve heard the argument made that LLMs are simply models overfit on the entirety of the internet. Double decent is a good counter point to that claim, it suggests something more interesting than simple overfitting is happening with large parameter counts.
- hackernewds 3y agoHow is double descent a good counterpoint to the claim?
- qumpis 3y agoThat novel reasoning is due to the model transitioning to a generalization regime, not merely parroting training data?
- malux85 3y agoOverfitting is lack of genralisation, LLMs can produce novel output by using abstraction composition, which you cannot do without generalisation. Other signs of non-overfitting: Abstraction laddering, task decomposition, novel (i.e. unseen) joke explanation
- version_five 3y agoI'd be interested to know if anyone has studied how overfitting translates into the domain of llm output: it's easy to understand when you're fitting a line though data, or building a classifier, you overfit and your test set loss is higher than your training set loss, and this directly relates to worse performance of the model. For an llm picking probably next words, what's the analogy, and does overfitting make it "worse" even if a test set loss is higher?
- bheadmaster 3y agoI find it hard to believe that every single problem has a solution on the internet, which is what "overfitting" would imply. I was playing Fallout: New Vegas on Wine, and for some reason, the music on my pipboy wasn't playing. I searched the internet for the Wine errors from the terminal to no avail, and as a last resort asked ChatGPT. It gave me step-by-step instructions on how to fix it, and it worked. If that doesn't demonstrate that LLMs have some kind of internal model of the world and understanding of it, then I don't know what will.
- jwilber 3y agoIn case you need a refresher, I made a very visual introduction to Double Descent here: https://mlu-explain.github.io/double-descent/ https://mlu-explain.github.io/double-descent/ (There’s a math-ier follow up linked as wel).
- dir_balak 3y agoFantastic material. Big thanks!
- version_five 3y agoIntuition of double descent: when you have the about the same number of parameters as data points, a fit curve looks like one of those shitty "polynomial fits" in excel, where away from the data points it over and under shoots the curve wildly. Lots more parameters and this calms down to give smooth interpolation between the curves. I can imagine some tasks where people have the same problem. You're overfit to a very specific task, but outside it "when you have a hammer everything looks like a nail" and you end up doing something dumb.
- contravariant 3y agoThe linear regression is somewhat interesting, but also points out that the double descent might have a somewhat strange cause. What technically happens is that as you have more parameters you not only optimize for the model fit, but also for the size of the parameters. If you force the model to fit your training data perfectly then it is no wonder that you can only start to optimize the size of your parameters after you have enough leeway to easily fit the entire training set. However another way to achieve the same effect is to make the assumption that the parameters should be small(ish) explicit. Fitting the whole training set is nice but ultimately pointless if you're just fitting noise. If the actual data is a simple polynomial + random noise then fitting all the noise will give a worse estimate.
- gnramires 3y agoI think you're right, cross-validation should enable you to detect overfitting. When you see severe overfitting, you can try a different model (say a statistical model including noise), or add regularization hyperparameters, which you can tune via cross validation (or simply re-run the fit a number of times, because information contained in hyperparameters alone tends to be very low, hence not run risk of overfitting in the hyperparameter tuning process).
- topaz0 3y agoI would have thought the "few parameter" high-error region corresponds more naturally to the part of language learning where the learner overgeneralizes and thinks everything is regular, and the "many parameter" high-error region corresponds to knowing the irregular forms for each word that you've encountered. But this blog seems to think of it in the other way around. Maybe I'm missing something.
- arthur2e5 3y agoIt can be argued that the human case correlates better with the "data double descent" model, assuming the brain network size does not change. The thing is... it does! It goes up and down as connections grow and get pruned. Biology is messy. Biological analogies can never be perfectly clean, especially for a system as giant as a human.
- clbrmbr 3y agoIn the polynomial fit case: it’s pretty clear to me that if the number of parameters is higher than the degrees of freedom in the data, then the model can simply memorize the input. That doesn’t explain why it generalizes well, though.
- occamrazor 3y agoIt”s only mentioned at the end. If you use some regularization, you have many ways to fit the data (almost) perfectly, and you choose the one with the smallest coefficients, which is often one that generalizes well. And even without explicit regularization, some training methods implicitly apply sone form of regularization, when the number of parameters exceeds the number of data points.
- johndough 3y agoHas anyone been able to reproduce double descent without trying to invert a seriously ill-posed linear system? Showing that a solver has numerical issues which go away when enough parameters are introduced does not really prove anything. This looks much more like regularization though floating point rounding. By the way, the linked Colab notebook is missing a "self." in front of the "lamb" in the unused regularization branch of the fit function.
- sebzim4500 3y agoOpenAI paper on double descent: https://arxiv.org/pdf/1912.02292.pdf https://arxiv.org/pdf/1912.02292.pdf They show it happens across a variety of architectures and real world datasets