woopwoop

Do you hate anyone who doesn't recycle? If so, I think you should set a higher bar for the sins necessary to earn your hatred.

Most people don't think hard or carefully about politics, and their political views are a very tiny fraction of what they give to the world (this is true even for most people who do think hard and carefully about politics, by the way). Their vote is never pivotal, and their views do not shape any major institutions.

I don't agree with your first sentence, but I agree with the rest of this post.

In what sense is "Attention is all you need" a pun?

Clickbait titles are something of a tradition in this field by now. Some important paper titles include "One weird trick for parallelizing convolutional neural networks", "Attention is all you need", and "A picture is worth 16x16 words". Personally I still find it kind of irritating, but to each their own I guess.

Totally unrelated, but this reminds me of my favorite title of a math article: "How often should you beat your kids?" (it's about a certain simple combinatorial game)

https://people.mpim-bonn.mpg.de/zagier/files/math-mag/63-2/f...

(My favorite line: "Levasseur analyzes the game and shows that on average you will have a score of n + (sqrt(pn) - 1)/2 + O(1/sqrt(n)) while the kid will have exactly n. We maintain, however, that only the most degenerate parent would play against a two-year-old for money, so the question should be not by how much you expect to win, but with what probability you will win at all.")

My grandfather was a (non-professional) left wing agitator who was brought in front of HUAC when he joined the NIH, and also won the Lasker-Debakey award for his contributions to the development of combination chemotherapy.

> They want me to do their work for them. During the Covid lockdown, faculty bent over backwards in every way we knew how to accommodate students during an unprecedented (in our lifetimes) health crisis. Now students expect that as a matter of routine. I am frequently asked for my PowerPoint slides, which basically function for me as lecture notes. It is unimaginable to me that I would have ever asked one of my professors for their own lecture notes. No, you can’t have my slides. Get the notes from a classmate. Read the book. Come to office hours for a conversation if you are still confused after the preceding steps. Last week I had an email from a student who essentially asked me to recap an entire week’s worth of lecture material for him prior to yesterday’s midterm. No, I’m not doing that. I’m not writing you a 3000-word email. Try coming to class.

I dunno man. Not writing a 3000 word email is one thing, but if you make a power point an then don't share it electronically, it smells like you are cajoling students to attend your lectures in order to stroke your ego. These people are paying a lot of money to attend your course; if they feel that they would get more value out of looking at your power point without attending your lectures that is not something that should be sneered away. Both as an undergraduate student and a graduate TA I was always very put off by this kind of high-handed bullying instructors would engage in to juice attendance of their courses. Just teach well and evaluate accurately. That's what they're paying you for. They're not paying for you to harass them into being at some inconvenient place at a particular time every Monday, Wednesday, and Friday.

Agree, but I would point out that the errors that I make are selected on the fact that I don't notice I'm making them, which tips the scale toward LLM errors being not as bad.

Those are not necessary to reproduce benign overfitting

A decade ago the paper "Understanding deep learning requires rethinking generalization" [0] was published. The submission is a response to that paper and subsequent literature.

Deep neural nets are notable for their strong generalization performance: despite being highly overparametrized they do not seem to overfit the training data. They still perform well on hold-out data and very often on out of distribution data "in the wild". The paper [0] noted a particularly odd feature of neural net training: one can train neural nets on standard datasets to fit random labels. There does not seem to be an inductive bias strong enough to rule out bad overfitting. It is in principle possible to train a model which performs perfectly on the training data but gives nonsense on the test data. But this doesn't seem to happen in practice.

The submission argues that this is unsurprising, and fits within standard theoretical frameworks for machine learning. In section 4 it is claimed that this kind of thing ("benign overfitting") is common to any learning algorithm with "a flexible hypothesis space, combined with a loss function that demands we fit the data, and a simplicity bias: amongst solutions that are consistent with the data (i.e., fit the data perfectly), the simpler ones are preferred".

The fact that the third of these conditions is satisfied, however, is non-trivial, and in my opinion is still not well understood. The results of [0] are reproducible with a wide variety of architectures, with or without any form of explicit regularization. If there is an inductive bias toward "simpler solutions" in fitting deep neural nets it has to come either from SGD itself or from some bias which is very generic in architecture. It's not something like "CNNs generalize well on image data because of an inductive bias toward translation invariant features." While there is some work on implicit smoothing by SGD, for example, in my opinion this is not sufficient to explain the phenomena observed in [0]. What I would find satisfying is a reproducible ablation study of neural net training that removed benign overfitting (+), so that it was clear what exactly are the necessary and sufficient conditions for this behavior in the context of neural nets. As far as I know this still has never been done, because it is not known what this would even entail.

(+) To be clear, I think this would not look like "the fit model still generalizes, but we can no longer fit random labels" but rather "the fit model now gives nonsense on holdout data".

[0] https://arxiv.org/abs/1611.03530

Yeah, it's straightforward to reproduce the results of the paper whose conclusion they criticize, "Understanding deep learning requires rethinking generalization", without any (explicit) regularization or anything else that can be easily described as a "soft preference for simpler solutions".

Here is data from the IMF, for example, showing US and EU area GDP as a percentage of global output over time, gradually declining since 1980. The decline from 1960 to 1980 in the US was even more dramatic: in 1960 the United States GDP was about 40% of global GDP.

https://www.imf.org/external/datamapper/PPPSH@WEO/EU/CHN/USA

They aren't proofs, they're just numbers. All the questions have numerical answers. That's how they're evaluated.

If he had written "Twitter is important because a critical mass of important people use it to communicate directly with the general public" I would not have called the essay dumb. What he actually wrote is that Twitter was a new messaging protocol which was (a) obviously not true at the time and (b) a red herring.

I don't fault op for posting it. I agree that it's an interesting historical artifact, but intrinsically the essay is dumb.

I hate to be blandly negative, but this deserves (deserved?) it. This is dumb. Message boards had this property, as did blogs. There is nothing meaningful in this short essay.

Edit: if you think message boards and blogs were too specific, here are a couple of other media with this property: radio and television.

I agree that openai is somewhat sketchy about this, but they're sketchy about everything. In the past though they have admitted up front to data contamination (e.g. the original gpt-4 press release did not use big-bench as a benchmark due to data contamination). For the Putnam in particular: this is not a benchmark that they use. There is no reason to exclude it since it is not part of the "test set" in any meaningful sense.

I don't understand what their definition of a band limited function on a manifold is supposed to be.

That's funny, because to me these headlines about how deep learning is over-hyped and hitting the wall remind me of headlines from ten years ago about how... deep learning is over-hyped and hitting the wall.

I am a pure mathematician by training. I _hate_ machine learning. The entire field seems to me like a bunch of unprincipled recipes and random empirics. The fact that it works is infuriating, and genuinely seems like a tragedy to me. The bitter lesson is very bitter indeed.

But I've been hearing the refrain of this article for a decade now. I just don't believe it anymore.

My argument is not that slippery problems are unimportant or extraneous, it's that this paper does not convincingly demonstrate that these models are actually especially bad at this kind of reasoning.

Real discourse is also full of typos which accidentally invert the meaning of things, asking the wrong question for deep reasons, asking the wrong question for shallow reasons, and all of the other things that justify subtracting the below average size kiwis from the final answer.

This paper, among other things, shows that LLMs have dramatically worse performance on basic algebra questions when you add in irrelevant information. The examples are things like "John picked 43 kiwis on Monday, 24 kiwis on Tuesday. On Wednesday, 5 of the kiwis he picked were smaller than usual. Altogether, on Monday, Tuesday, and Wednesday, John picked 87 kiwis. How many kiwis did John pick on Wednesday?" In this question, the remark about some of the kiwis on Wednesday being small is irrelevant, but adding things like this reduces performance on a popular benchmark from 95% to 77% for GPT-4o, for example.

I don't find this very impressive. Forget LLMs for a second. Let's say _you_ read a question of that kind with some bit of irrelevant information. There are two possibilities you have to consider: the question may as well have excluded the irrelevant information, or the question was miswritten and the irrelevant information was meant to be relevant. The latter is a perfectly live possibility, and I don't think it's a dramatic failure to assume that this is correct. I have to confess that when I read some people's LLM gotcha questions, where they take some popular logic puzzle and invert things, I think I would get them "wrong" too. And not wrong because I don't understand the question, but wrong because with no context I'd just assume the inversion was a typo.

I'm curious about what happens with the no-op dataset if you include in the prompt that the questions may contain irrelevant information.

I've lived in cities with decent homeless populations (Austin, New York) for almost my entire life. I read about this phenomenon of homeless people defecating on the streets all the time. I've literally never seen this in real life. Neither the act itself, nor human waste on the ground. Am I just very lucky? What gives?

My PhD thesis was about the extension of smooth functions. In the 1960s, ideas in this area were studied under the umbrella of ideals of smooth functions, and had applications to catastrophe theory. So I spent some time reading about this topic. If you want a reading recommendation, the book "Differentiable Germs and Catastrophes" I remember being good, as well as "Stable Mappings and their Singularities".

I bring this up because I believe that at the time catastrophe theory was seen as a "widely-applicable science of systems". Or at least some practitioners tried to sell it as such. This point of view eventually soured to the detriment of catastrophe theory, which cleared out. I don't think this was a good thing: catastrophe theory (the study of the singularities of smooth maps and their consequences to dynamical systems) is an interesting topic with many remaining open questions. But it was seen as cringe that people were, e.g., using Whitney's classification of the generic singularities of planar maps to try to say something about predator/prey dynamics or whatever. Any claim about applications of catastrophe theory was infected with this stink, and so people lost interest in it.

When I took Dan Freed's algebraic topology course, one time he asked us if two spaces were the same. Then he looked at us for a moment and said that actually that was a "Bill Clinton question: the answer depends on what the meaning of the word is is".

My point is not merely that there exist socially competent people who advance science at the highest level, but that I reject the claim that this is an anti-correlation. I do not think that scientific genius and social grace are anti-correlated, or antithetical.

It says there is a "strong anti-correlation" between being a weird nerd and being pleasant to be around socially. This may be true, but it is not my experience that there is a strong anti-correlation between being an exceptional mathematician and being pleasant to be around socially. Despite the stereotype, in my experience the best mathematicians are not the ones who stare at their shoes when you talk to them.