[HN Gopher] Deep Learning Is Not So Mysterious or Different
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       Deep Learning Is Not So Mysterious or Different
        
       Author : wuubuu
       Score  : 233 points
       Date   : 2025-03-17 16:47 UTC (6 hours ago)
        
 (HTM) web link (arxiv.org)
 (TXT) w3m dump (arxiv.org)
        
       | cgdl wrote:
       | Agreed, 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
        
         | bigfatfrock wrote:
         | I'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 wrote:
           | >smash with something better
           | 
           | Not a fan of the aggressive rhetoric here...
        
             | superidiot1932 wrote:
             | I too felt threatened
        
               | pessimizer wrote:
               | Violent disagreement is violence.
        
         | mxwsn wrote:
         | Good read, thanks for sharing
        
         | esafak wrote:
         | Statistical mechanics is the lens that makes most sense to me,
         | and it's well studied.
        
       | TechDebtDevin wrote:
       | Anyone 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-i...
        
         | kaptainscarlet wrote:
         | Double Bam
        
         | ajitid wrote:
         | Also would like to add that he has a YouTube channel as well
         | https://youtube.com/@statquest
        
         | Lerc wrote:
         | I 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
         | 
         | 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 wrote:
       | > 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 wrote:
         | I'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 wrote:
         | 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".
        
         | whiteandnerdy wrote:
         | You'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
        
           | levocardia wrote:
           | Dropout is roughly equivalent to layer-specific L2
           | regularization, and it's easy to see why: asymptotically,
           | dropping out random neurons will achieve something similar to
           | shrinking weights towards zero proportional to their
           | (squared) magnitude.
           | 
           | Trevor Hastie's Elements of Statistical Learning has a nice
           | proof that (for linear models) L2 regularization is also
           | semi-equivalent to dimensionality reduction, which you could
           | use to motivate a "simplicity prior" idea in deep learning.
           | 
           | Yet another way of thinking about it, in the context of ReLU
           | units, is that a layer of ReLUs forms a truncated hyper-plane
           | basis (like splines but in higher dimensions) in feature
           | space, and regularization induces smoothness in this
           | N-dimensional basis by shrinking that basis towards being a
           | flat hyper-plane
        
         | jonathanhuml wrote:
         | The solution to the L1 regularization problem is actually a
         | specific form of the classical ReLU nonlinearity used in deep
         | learning. I'm not sure if similar results hold for other
         | nonlinearities, but this gave me good intuition for what
         | thresholding is doing mathematically!
        
         | chriskanan wrote:
         | Here is an example for data-efficient vision transformers:
         | https://arxiv.org/abs/2401.12511
         | 
         | Vision transformers have a more flexible hypothesis space, but
         | they tend to have worse sample complexity than convolutional
         | networks which have a strong architectural inductive bias. A
         | "soft inductive bias" would be something like what this paper
         | does where they have a special scheme for initializing vision
         | transformers. So schemes like initialization that encourage the
         | model to find the right solution without excessively
         | constraining it would be a soft preference for simpler
         | solutions.
        
       | inciampati wrote:
       | An 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
        
       | YesBox wrote:
       | I 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 wrote:
         | this 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 wrote:
         | Pretty 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.
        
         | docfort wrote:
         | There 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 [1]:
         | https://arxiv.org/abs/2410.04265v1
        
         | montebicyclelo wrote:
         | > How close would this be to GPT 2
         | 
         | Here's a post from 2015 doing something a bit like this [1]
         | 
         | [1] https://nbviewer.org/gist/yoavg/d76121dfde2618422139
        
         | nickysielicki wrote:
         | Markov chains are very very far off from gpt2.
        
         | janalsncm wrote:
         | The problem is that for any reasonable value of N (>100) you
         | will need prohibitive amounts of storage. And it will be
         | extremely sparse. And you won't capture any interactions
         | between N-99 and N-98.
         | 
         | Transformers do that fairly well and are pretty efficient in
         | training.
        
         | 0cf8612b2e1e wrote:
         | The scaling is brutal. If you have a 20k word vocabulary and
         | want to do 3 grams, you need a 20000^3 matrix of elements (8
         | trillion). Most of which is going to be empty.
         | 
         | GPT and friends cheat by not modeling each word separately, but
         | a large dimensional "embedding" (just a vector if you also find
         | new vocabulary silly). The embedding represents similar words
         | near each other in this space. The famous king-man-queen
         | example. So even if your training set has never seen "The Queen
         | ordered the traitor <blank>", it might have previously seen,
         | "The King ordered the traitor beheaded". The vector
         | representation lets the model use words that represent similar
         | concepts without concrete examples.
        
           | andrewla wrote:
           | Importantly, though, LLMs do not take the embeddings as input
           | during training; they take the tokens and learn the
           | embeddings as part of the training.
           | 
           | Specifically all Transformer-based models; older models used
           | things like word2vec or elmo, but all current LLMs train
           | their embeddings from scratch.
        
             | naasking wrote:
             | And tokens are now going down to the byte level:
             | 
             | https://ai.meta.com/research/publications/byte-latent-
             | transf...
        
         | fsndz wrote:
         | I actually tried sth like that with the Bible back in 2021.
         | scaling is bitch. very difficult to train these types of
         | models.
        
       | EncomLab wrote:
       | The 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 wrote:
         | You'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 wrote:
           | It'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 wrote:
             | Okay, 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.
        
         | 01HNNWZ0MV43FF wrote:
         | But the weights trained from machine learning are a black box,
         | in the sense that no human designed e.g. the image processing
         | kernels that those weights represent.
         | 
         | That is one reason people are skeptical of them, not only is
         | training a large model at home expensive, not only is the data
         | too big to trivially store, but the weights are not trivial to
         | debug either
        
         | xmprt wrote:
         | The mystery was never in the "how do computers calculate the
         | probabilities of next tokens" but rather in the "why is it able
         | to work so well" and "what does this individual neuron
         | contribute to the whole model"
        
       | rottc0dd wrote:
       | If anyone wants to delve into machine learning, one of the superb
       | resources I have found is, Stanfords "Probability for computer sc
       | ientists"(https://www.youtube.com/watch?v=2MuDZIAzBMY&list=PLoROM
       | vodv4...).
       | 
       | 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=PLZHQObOWTQ...).
        
         | rottc0dd wrote:
         | Caltech's learning from data was really good too, if someone is
         | looking for theoretical understanding of ML topics.
         | 
         | https://work.caltech.edu/telecourse
        
         | randomtoast wrote:
         | Apparently the word "delve" is the biggest indicator of the use
         | of ChatGPT according to Paul Graham.
        
           | wincy wrote:
           | I'd love to see an article delve into why that is.
        
             | treyd wrote:
             | Because it's common in Nigerian English, which is where
             | they outsourced a lot of the RLHF conditioning work to.
        
               | Hugsun wrote:
               | Really!? Do you have a source for this? This would be
               | really interesting if true.
        
             | sva_ wrote:
             | https://pshapira.net/2024/03/31/delving-into-delve/
        
           | EGreg wrote:
           | Saying that kind of stuff is the biggest indicator of Paul
           | Graham (pg) himself
        
           | tasty_freeze wrote:
           | That seems utterly bizarre to me. I don't use "delve"
           | frequently myself, but it is common enough that it doesn't
           | jump out as an unusual word. Perhaps it is overused or used
           | in a not-exactly-usual context that tips one off that it is
           | LLM-generated, but by itself it signifies nothing to me.
        
             | godelski wrote:
             | It is a very common word used in Nigerian style English
             | which was a very common place they were outsourcing RLHF
             | tasks to. A sibling comment has a link but it is also easy
             | to google.
        
         | chamomeal wrote:
         | I watched the 3b1b series on neural nets years ago, and it
         | still accounts for 95% of my understanding of AI in general.
         | 
         | I'm not an ML person, but still. That guy has a serious gift
         | for explaining stuff.
         | 
         | His video on the uncertainty principle explained stuff to me
         | that my entire undergrad education failed to!
        
         | bogeholm wrote:
         | Looks nice - are there written versions?
        
         | vcdimension wrote:
         | and if anyone is interested in delving more deeply into the
         | statistical concepts & results referenced in the paper of this
         | post (e.g. VC-dimension, PAC-learning, etc), I can recommend
         | this book: https://amzn.eu/d/7Zwe6jw
        
       | buffalobuffalo wrote:
       | When 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 wrote:
       | Correct 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 wrote:
         | MLPs 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 wrote:
         | This 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.
        
         | andrewla wrote:
         | In 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 wrote:
       | So where is the line that something becomes 'AI' and is
       | regulated?
        
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