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Deep Learning Is Not So Mysterious or Different
- cgdl 2y agoAgreed, but PAC-Bayes or other descendants of VC theory is probably not the best explanation. The notion of algorithmic stability provides a (much) more compelling explanation. See [1] (particularly Sections 11 and 12) [1] https://arxiv.org/abs/2203.10036 https://arxiv.org/abs/2203.10036
- bigfatfrock 2y agoI'm a huge fan of HN just for replies such as this that smash the OP's post/product with something better. It's like at least half the reason I stick around here. Thanks for the great read.
- hlynurd 2y ago>smash with something better Not a fan of the aggressive rhetoric here...
- superidiot1932 2y agoI too felt threatened
- pessimizer 2y agoViolent disagreement is violence.
- hyperliner 2y ago[dead]
- singulargalaxy 2y agoYeah, and it's not "better", but actually less general, relying on optimization/GD, unlike OP.
- noney4 2y ago[dead]
- mxwsn 2y agoGood read, thanks for sharing
- esafak 2y agoStatistical mechanics is the lens that makes most sense to me, and it's well studied.
- singulargalaxy 2y agoHard disagree. Your link relies on gradient descent as an explanation, whereas OP explains why optimization is not needed to understand DL generalization. PAC-Bayes, and the other different countable hypothesis bounds in OP also are quite divergent from VC dimension. The whole point of OP seems to be that these other frameworks, unlike VC dimension, can explain generalization with an arbitrarily flexible hypothesis space.
- cgdl 2y agoYes, and that's the problem. What Zhang et al [2] showed convincingly in the Rethinking paper is that just focusing on the hypothesis space cannot be enough since the same hypothesis space fits real and random data so it's already too large. Therefore, these methods that focus on the hypothesis space have to talk about a bias in practice towards a better subspace, and that already requires studying the specific optimization algorithm in order to understand why it picks certain hypothesis over others in the space. But once you are ready to do that then algorithmic stability is enough. You don't then need to think about Bayesian ensembles, or other proxies/simplifications etc. but can focus on just the specific learning setup you have. BTW algorithmic stability is not a new idea. An early version showed up within a few years of VC theory in the 80s in order to understand why nearest neighbors generalizes (it wasn't called algorithmic stability then though). If you are interested in this, also recommend [3]. [2] https://arxiv.org/abs/1611.03530 https://arxiv.org/abs/1611.03530 [3] https://arxiv.org/abs/1902.04742 https://arxiv.org/abs/1902.04742
- singulargalaxy 2y agoBut it's not a problem, it's actually a good thing that OP's explanation is more general. One of the main points in the OP paper is that you do not in fact need proxies or simplification. You can derive generalization bounds that do explain this behavior, without needing to rely on optimization dynamics. This exactly responds to the tests set forth in Zhang et al. OP does not "rely on Bayesian ensembles, or other proxies/simplifications". That seems to be a misunderstanding of the paper. It's analyzing the solutions that neural networks actually reach, which differentiates it from a lot of other work. It also additionally shows how other simple model classes can reproduce the same behavior, and these reproductions do not depend on optimization. "and that already requires studying the specific optimization algorithm in order to understand why it picks certain hypothesis over others in the space." But the OP paper explains how even "guess and check" can generalize similarly to SGD. It's becoming more well understood that the role of the optimizer may have been historically overstated for understanding DL generalization. It seems to be more about loss landscapes. Don't get me wrong, these references you're linking are super interesting. But they don't take away from the OP paper which is adding something quite valuable to the discussion.
- gptoperator05 2y ago[dead]
- uoaei 2y ago[flagged]
- FirstTimePostin 2y agoIt's a higher quality article than half the submissions to NeuroIPS and the rest of the AI/ML conferences, because it has potential to remain relevant next year, and because of its high didactic content. I wouldn't classify it as a "hot take".
- bonoboTP 2y agoPlease formulate your critique instead of simply labeling it with negative words.
- uoaei 2y agoSure. "Preprint" implies prior to printing, which means that there's a reasonable expectation for this paper to be submitted, accepted, and printed in a scholarly journal. What we have here is little more than a tongue-in-cheek submission which carries an aesthetic of "hot-take" throughout the paper. This is unbecoming of one committed to scholarly pursuits and all but guarantees rejection from journals committed to professionalism. Furthermore, what's really interesting is how this comment section has developed. It really is the blind leading the blind here. I will not subject myself further to the consequences of Brandolini's law except to implore the reader to consider the signal-to-noise ratio resulting from being too tolerant of posts like this.
- bonoboTP 2y agoThis is still just name calling. You are just using negatively charged adjectives without quoting or arguing the substance or even the style. Is your crique only about the presentation or the substance of the ideas too? What makes it unprofessional? To me it looks much better than a substantial chunk of my review stacks at ML conferences and journals. Are you an ML researcher? Maybe you're used to a different research community that's more "uptight"?
- TechDebtDevin 2y agoAnyone who wants to demystify ML should read: The StatQuest Illustrated Guide to Machine Learning [0] By Josh Starmer. To this day I haven't found a teacher who could express complex ideas as clearly and concisely as Starmer does. It's written in an almost children's book like format that is very easy to read and understand. He also just published a book on NN that is just as good. Highly recommend even if you are already an expert as it will give you great ways to teach and communicate complex ideas in ML. [0]: https://www.goodreads.com/book/show/75622146-the-statquest-illustrated-guide-to-machine-learning https://www.goodreads.com/book/show/75622146-the-statquest-i...
- kaptainscarlet 2y agoDouble Bam
- ajitid 2y agoAlso would like to add that he has a YouTube channel as well https://youtube.com/@statquest https://youtube.com/@statquest
- Lerc 2y agoI have followed a fair few StatQuest and other videos (treadmills with Youtube are great for fitness and learning in one) I find that no single source seems to cover things in a way that I easily understand, but cumulatively they fill in the blanks of each other. Serrano Academy has been a good source for me as well. https://www.youtube.com/@SerranoAcademy/videos https://www.youtube.com/@SerranoAcademy/videos The best tutorials give you a clear sense that the teacher has a clear understanding of the underlying principles and how/why they are applied. I have seen a fair few things that are effectively. 'To do X, you {math thing}' While also creating the impression that they don't understand why {math thing} is the right thing to do, just that {math thing} has a name and it produces the result. Meticulously explaining the minutiae of {math thing} substitutes for a understanding of what it is doing. It really stood out to me when looking at UMAP and seeing a bunch of things where they got into the weeds in the math without explaining why these were the particular weeds to be looking in. Then I found a talk by Leland McInnes that had the format. {math thing} is a tool to do {objective}. It works, there is a proof, you don't need to understand it to use the tool but the info for that is over there if you want to tale a look. These are our objectives, let's use these tools to achieve them. The tools are neither magical black boxes, nor confused with the actual goal. It really showed the power of fully understanding the topic.
- getnormality 2y ago> rather than restricting the hypothesis space to avoid overfitting, embrace a flexible hypothesis space, with a soft preference for simpler solutions that are consistent with the data. This principle can be encoded in many model classes, and thus deep learning is not as mysterious or different from other model classes as it might seem. How does deep learning do this? The last time I was deeply involved in machine learning, we used a penalized likelihood approach. To find a good model for data, you would optimize a cost function over model space, and the cost function was the sum of two terms: one quantifying the difference between model predictions and data, and the other quantifying the model's complexity. This framework encodes exactly a "soft preference for simpler solutions that are consistent with the data", but is that how deep learning works? I had the impression that the way complexity is penalized in deep learning was more complex, less straightforward.
- bornfreddy 2y agoI'm not a guru myself, but I'm sure someone will correct me if I'm wrong. :-) The usual approach to supervised ML is to "invent" the model (layers, their parameters) or more often copy one from known good reference, then define the cost function and feed it data. "Deep" learning just means that instead of a few layers you use a big number of them. What you describe sounds like an automated way of tweaking the architecture, IIUC? Never done that, usually the cost of a run was too high to let an algorithm do that for me. But I'm curious if this approach is being used?
- woopwoop 2y agoYeah, 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".
- deleted 2y ago[deleted]
- whiteandnerdy 2y agoYou're correct, and the term you're looking for is "regularisation". There are two common ways of doing this: * L1 or L2 regularisation: penalises models whose weight matrices are complex (in the sense of having lots of large elements) * Dropout: train on random subsets of the neurons to force the model to rely on simple representations that are distributed robustly across its weights
- inciampati 2y agoAn example, which is interesting, in which "deep" networks are necessary, is discussed in this fascinating and popular recent paper on RNNs [1]. Despite the fact that the minGRU and minLSTM models they propose don't explicitly model ordered state dependency, they can learn them as long as they are deep enough (deep >= 3): > Instead of explicitly modelling dependencies on previous states to capture long-range dependencies, these kinds of recurrent models can learn them by stacking multiple layers. [1] https://arxiv.org/abs/2410.01201 https://arxiv.org/abs/2410.01201
- YesBox 2y agoI wish I had the time to try this: 1.) Grab many GBs of text (books, etc). 2.) For each word, for each next $N words, store distance from current word, and increment count for word pair/distance. 3.) For each word, store most frequent word for each $N distance. [a] 4.) Create a prediction algorithm that determines the next word (or set of words) to output from any user input. Basically this would compare word pairs/distance and find most probable next set of word(s) How close would this be to GPT 2? [a] You could go one step further and store multiple words for each distance, ordered by frequency
- currymj 2y agothis is pretty close to how language models worked in the 90s-2000s. deep language models -- even GPT 2 -- are much much better. on the other hand, the n-gram language models are "surprisingly good" even for small n.
- WheatMillington 2y agoPretty sure this wouldn't produce anything useful. Pretty sure this would generate incoherent gibberish that looks and sounds like English but makes no sense. This ignores perhaps the most important element of LLM's, the attention mechanism.
- bob1029 2y agoAnd, the attention mechanism scales quadratically with context length. This is where all of the insane memory bandwidth requirements come from.
- docfort 2y agoThere is some recent work [0] that explores this idea, scaling up n-gram models substantially while using word2vec vectors to understand similarity. Used to compute something the authors call the Creativity Index [1]. [0]: https://infini-gram.io https://infini-gram.io [1]: https://arxiv.org/abs/2410.04265v1 https://arxiv.org/abs/2410.04265v1
- montebicyclelo 2y ago
- EncomLab 2y agoThe implication that any software is "mysterious" is problematic - there is no "woo" here - the exact state of the machine running the software may be determined at every cycle. The exact instruction and the data it executed with may be precisely determined, as can the next instruction. The entire mythos of any software being a "black box" is just so much advertising jargon, perpetuated by tech bros who want to believe they are part of some Mr. Robot self-styled priestly class.
- margalabargala 2y agoYou're misunderstanding. A level of abstraction is necessary for operation of modern systems. There is no human alive who, given an intermediate step in the middle of some running learning algorithm, is able to understand and mentally model the full system at full man-made resolution, that is, down to the transistor level, on a modern CPU. Someone wishing to understand a piece of software in 2025 is forced to, at some point, accept that something somewhere "does what it says on the tin" and model it thusly rather than having a full understanding.
- EncomLab 2y agoIt's not misunderstanding at all - but your response is certainly an attempt to obfuscate the point being made. The moment you represent anything in code, you are abstracting a real thing into it's digital representation. That digital representation if fully formed at every cycle of the digital system processing it, and the state of the system - all the way down to the transistor level may be precisely determined. To say otherwise is to make the same error as those who claim that consciousness or understanding are indefinable "extra-ordinary" things that we have to just accept exist without any justification or evidence.
- margalabargala 2y agoOkay, then, you're just using your own personal definition of "black box" instead of the one everyone else uses. Something that's a black box is unknown to the speaker. It's not understood to be unknowable to anyone.
- rottc0dd 2y agoIf anyone wants to delve into machine learning, one of the superb resources I have found is, Stanfords "Probability for computer scientists"(https://www.youtube.com/watch?v=2MuDZIAzBMY&list=PLoROMvodv4rOpr_A7B9SriE_iZmkanvUg https://www.youtube.com/watch?v=2MuDZIAzBMY&list=PLoROMvodv4...). It delves into theoretical underpinnings of probability theory and ML, IMO better than any other course I have seen. (Yeah, Andrew Ng is legendary, but his course demands some mathematical familarity with linear algebra topics) And of course, for deep learning, 3b1b is great for getting some visual introduction (https://www.youtube.com/watch?v=aircAruvnKk&list=PLZHQObOWTQDNU6R1_67000Dx_ZCJB-3pi https://www.youtube.com/watch?v=aircAruvnKk&list=PLZHQObOWTQ...).
- rottc0dd 2y agoCaltech's learning from data was really good too, if someone is looking for theoretical understanding of ML topics. https://work.caltech.edu/telecourse https://work.caltech.edu/telecourse
- abhgh 2y agoI highly recommend the course you've mentioned (by Yaser Abu-Mostafa). In fact I still recommend it for picking up the basics; very good mix of math and intuition, Abu-Mostafa himself is a terrific teacher, and he is considerate and thoughtful in responding to questions at the end of his presentations. The last part is important if you're a beginner: it builds confidence in you that its probably ok to ask what you might consider a simple question - it still deserves a good answer. The series is a bit dated now in terms of what it covers, but still solid as a foundational course.
- _ce5e 2y agoFully agree! 3blue1brown is who have single-handedly thought me a majority of what I've needed to know about it. I actually started building my own neural network framework last week in C++! It's a great way to delve into the details of how they work. It currently supports only dense MLP's, but does so quite well, and work is underway for convolutional layers and pooling layers on a separate branch. https://github.com/perkele1989/prkl-ann https://github.com/perkele1989/prkl-ann
- buffalobuffalo 2y agoWhen I was first getting into Deep Learning, learning the proof of the universal approximation theorem helped a lot. Once you understand why neural networks are able to approximate functions, it makes everything built on top of them much easier to understand.
- talles 2y agoCorrect me if I'm wrong, but an artificial neuron is just good old linear regression followed by an activation function to make it non linear. Make a network out of it and cool stuff happens.
- esafak 2y agoMLPs are compositions of generalized linear models. That's not very enlightening though; the "mysterious" part is the macroscopics of the composition, which you can't really understand with the tools of statistics.
- hatthew 2y agoThis is like saying "the human brain is just some chemistry." You have the general idea correct, but there's a lot more going on that just that, and the emergent system is so much more complex that it deserves its own separate field.
- roenxi 2y agoAlthough with extra irony. "linear regression followed by an activation function to make it non linear". So it isn't good old linear regression because it is explicitly delinearised.
- andrewla 2y agoIn a sense; linear regression can be computed exactly so refers to a specific technique for producing a linear model. Most artificial neurons are trained stochastically rather than holistically, i.e. rather than looking at the entire training set and computing the gradient to minimize the squared loss or something similar, they look at each training example and compute the local gradient and make small changes in that direction. In addition, the "activation function" almost universally used now is the rectified linear unit, which is linear for positive input and zero for negative input. This is non-decreasing at least as a function, but the fact that it is not monotonic means that there is no additional loss accrued for overcorrecting in the negative direction. Given this, using the term "linear regression" to describe the model of an artificial neuron is not really a useful heuristic.
- totetsu 2y agoSo where is the line that something becomes ‘AI’ and is regulated?
- d_burfoot 2y agoDNNs do not have special generalization powers. If anything, their generalization is likely weaker than more mathematically principled techniques like the SVM. If you try to train a DNN to solve a classical ML problem like the "Wine Quality" dataset from the UCI Machine Learning repo [0], you will get abysmal results and overfitting. The "magic" of LLMs comes from the training paradigm. Because the optimization is word prediction, you effectively have a data sample size equal to the number of words in the corpus - an inconceivably vast number. Because you are training against a vast dataset, you can use a proportionally immense model (e.g. 400B parameters) without overfitting. This vast (but justified) model complexity is what creates the amazing abilities of GPT/etc. What wasn't obvious 10 years ago was the principle of "reusability" - the idea that the vastly complex model you trained using the LLM paradigm would have any practical value. Why is it useful to build an immensely sophisticated word prediction machine, who cares about predicting words? The reason is that all those concepts you learned from word-prediction can be reused for related NLP tasks. [0] https://archive.ics.uci.edu/dataset/186/wine+quality https://archive.ics.uci.edu/dataset/186/wine+quality
- gptoperator05 2y ago[dead]
- yomritoyj 2y agoYou may want to look at this. Neural network models with enough capacity to memorize random labels are still capable of generalizing well when fed actual data Zhang et al (2021) 'Understanding deep learning (still) requires rethinking generalization' https://dl.acm.org/doi/10.1145/3446776 https://dl.acm.org/doi/10.1145/3446776
- Tewboo 2y agoI've seen the same patterns in neural networks that I've seen in simpler algorithms. It's less about mystery and more about complexity.
- janpmz 2y agoYou can listen to an explanation of the paper here: https://www.pdftomp3.com/shared/67d8abf0ecf38326f8973e49 https://www.pdftomp3.com/shared/67d8abf0ecf38326f8973e49 I created this tool last year to listen to a machine learning book, now I use it for ML papers. The explanations are still a bit repetitive, its not perfect yet.
- fastball 2y agoWell it's not called Mysterious Learning or Different Learning for a reason. In fact, with how many misnomers there are in the world, I think Deep Learning is actually a pretty great name, all things considered. It properly communicates (imo) that the training data and resulting weights are complex enough that just looking at the learning/training process on its own is not sufficient to understand the resulting system (vs other "less deep" machine learning where it mostly is).
- deleted 2y ago[deleted]
- woopwoop 2y agoA 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 https://arxiv.org/abs/1611.03530
- theahura 2y agoDoesn't the simplicity bias come explicitly from regularization techniques, including drop out or l2 norm?