today is the day i stopped reading opinion pieces from the technologyreview. not for presenting an opinion i don’t agree with, but for mistaking word soup for an argument.
ah I see what you mean, sorry it took me a while. Yes, you're right, the two are dual: "fix complexity budget then optimize data error", and "fix data error budget then optimize cx".
I'm struggling to put a finger on it, but it feels that the approach in the blog post has the property that it finds the _minimum_ complexity solution, akin to driving the regularization strength in conventional ml higher and higher during training, and returning the solution at the highest such regularization that does not materially degrade the error (epislon in their paper). information theory plays the role of a measuring device that allows them to measure the error term and model complexity on a common scale, so as to trade them off against each other in training.
I haven't thought about it much but i've seen papers speculating that what happens in double-descent is finding lower complexity solutions.
Right, but see how the complexity budget is prescribed ahead of time: we first set the regularization strength or whatever, and then optimize the model. The result is the best model with complexity no greater than the budget. In this standard approach, we're not minimizing complexity, we're constraining it.
I agree with your observation about the exact noise-free nature of the problem. It allows them to formulate the problem as "minimize complexity such that you memorize the X-y relationship exactly". This would need to be generalized to the noisy case: instead of demanding exact memorization, you'd need to prescribe an error budget. But then this error budget seems like an effective complexity metaparameter, doesn't it, and we're back to square zero of cross-validation.
I'm trying to distill the essence of their approach, which imho is concealed behind inessential and particular details such as the choice of this or that compression scheme or prior distributions.
It seems like the central innovation is the construction of a "model" which can be optimized with gradient descent, and whose optimum is the "simplest" model that memorizes the input-output relationships. In their setup, "simplest" has the concrete meaning of "which can be efficiently compressed" but more generally it probably means something like "whose model complexity is lowest possible".
This is in stark contrast to what happens in standard ML: typically, we start by prescribing a complexity budget (e.g. by choosing the model architecture and all complexity parameters), and only then train on data to find a good solution that memorizes input-output relationship.
The new method is ML on its head: we optimize the model so that we reduce its complexity as much as possible while still memorizing the input-output pairs. That this is able to generalize from 2 training examples is truly remarkable and imho hints that this is absolutely the right way of "going about" generalization.
Information theory happened to be the angle from which the authors arrived at this construction, but I'm not sure that is the essential bit. Rather, the essential bit seems to be the realization that rather than finding the best model for a fixed pre-determined complexity budget, we can find models with minimal possible complexity.
1. The futile attempt by Microsoft to equip their search engine with artificial intelligence. See also: Bing (Microsoft search engine), Try (v.).
2. An attitude of confidence and contempt characteristic of large language models assumed particularly when expressing false opinions or facts. See also: Bigotry (n.).
Here's GPT's own explanation what the purpose of that while loop is:
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This code uses JavaScript's `eval` function to obfuscate the code by looping over an array of strings and passing them as arguments to `eval` to create a variable. It also uses an anonymous function to obfuscate the code. The code is deobfuscated by replacing the `eval` function and the anonymous function with their respective strings.
I wonder how a modern language model would fare here -- use something like GPT-3 to evaluate the log likelihood gain of stitching together each of all N^2 possible pairs, then merge greedily best matches until none are left. Totally within reach, I bet it could get at least _some_ of the order right.
I still don't understand why this ME feature has been created to begin with. Assuming that breaking it is a matter of time (someone clever enough thinking about it for long enough), it seems like a serious security vulnerability, worse still because an attack is undetectable.
Why create it in the first place? Are the enterprise uses the article mentions worth the risk?