[HN Gopher] Are deep neural networks dramatically overfitted? (2...
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Are deep neural networks dramatically overfitted? (2019)
Author : troyappel
Score : 201 points
Date : 2021-04-05 06:40 UTC (16 hours ago)
(HTM) web link (lilianweng.github.io)
(TXT) w3m dump (lilianweng.github.io)
| skywhopper wrote:
| What I don't see clearly addressed here is whether the test data
| that these networks are validated against are part of the larger
| data set that was used for the initial training. I'm guessing the
| validation data is usually from the same data set, in which case
| it's not really a surprise that a massively overfitted network
| would work pretty well against. Whereas some alternative data set
| produced by different people under even slightly different
| conditions will introduce many new unexpected variables that the
| network won't be equipped to handle, and that's when the
| "overfitting" to the original data set would be more obvious. But
| I'm going to guess that in practice, useful datasets vary so much
| that it's impractical to do this sort of cross checking (and in
| reality it wouldn't happen because you don't want to publish a
| negative result).
| sfink wrote:
| I'm not in the field (nor an academic, nor particularly smart),
| but my impression is that this is implicit in nearly everything
| people are doing. Almost all of the papers will be talking
| about interpolation, not extrapolation. More specifically,
| training data and test data are assumed to be partitioning an
| existing data set into test and training portions.
| "Generalization" is measured only by success at fitting the
| test data.
|
| Of course, most actual applications immediately break out of
| that model by running live against previously unobserved data
| coming from different populations, different times (just think:
| post-2020 vs pre-2020!), often different purposes. And probably
| much of the error because you're now extrapolating gets
| regarded as an engineering problem?
| charleshmartin wrote:
| You can check for some signatures of over-fitting using the
| weightwatcher tool
|
| https://calculatedcontent.com/2021/04/04/are-your-models-ove...
|
| The tool identifies weight matrices that display atypical
| behavior, where the correlation is concentrated about unusually
| large matrix elements.
|
| The idea comes from statistical mechanics of generalization,
| where it is known that neural networks that are over-fit are
| atypical and are in the spin glass phase of the learning phase
| space.
| YeGoblynQueenne wrote:
| >> If you are like me, entering into the field of deep learning
| with experience in traditional machine learning, you may often
| ponder over this question: Since a typical deep neural network
| has so many parameters and training error can easily be perfect,
| it should surely suffer from substantial overfitting. How could
| it be ever generalized to out-of-sample data points?
|
| Shouldn't this article start with presenting the evidence that
| deep neural nets _can_ generlaise to out-of-sample data? It is a
| bit frustrating having to read a discusion of the _why_ without a
| discussion of the _what_.
|
| A small introductory paragraph would suffice. For example, quote
| so-and-so on studies showing that deep neural nets can generalise
| to out-of-sample data. Ideally, quote studies that show _how
| well_ deep neural nets generalise to out-of-sample data.
|
| As the article is now, it seems to be giving many explanations
| for a phenomenon a reader won't even know exists in the first
| place.
| YetAnotherNick wrote:
| Look at imagenet results. Test set accuracy(top 1) for imagenet
| is 85% with deep net, and 50% with best of all other approaches
| and decades of CV work.
| notemaker wrote:
| Let's remember though that Imagenet is not a good
| representation of reality.
|
| See e.g. performance on OjectNet, https://objectnet.dev/,
| when trained on Imagenet. For the same classes, we see
| _dramatic_ drops in accuracy.
| YeGoblynQueenne wrote:
| Also see:
|
| _Do ImageNet Classifiers Generalize to ImageNet?_
|
| _We build new test sets for the CIFAR-10 and ImageNet
| datasets. Both benchmarks have been the focus of intense
| research for almost a decade, raising the danger of
| overfitting to excessively re-used test sets. By closely
| following the original dataset creation processes, we test
| to what extent current classification models generalize to
| new data. We evaluate a broad range of models and find
| accuracy drops of 3% - 15% on CIFAR-10 and 11% - 14% on
| ImageNet. However, accuracy gains on the original test sets
| translate to larger gains on the new test sets. Our results
| suggest that the accuracy drops are not caused by
| adaptivity, but by the models ' inability to generalize to
| slightly "harder" images than those found in the original
| test sets._
|
| https://arxiv.org/abs/1902.10811
| t_serpico wrote:
| nice. glad to see this exists.
| YeGoblynQueenne wrote:
| The passage I quote above speaks of "out-of-sample"
| generalisation, not "test-set" generalisation. These are not
| the same.
|
| Unfortunately such terminological confusion is common but
| "out-of-sample" should really be reserved for data that was
| not available during development of a system, either as a
| training, evaluation or testing partition. That, because "out
| of sample" suggests that the data was drawn from a different
| distribution than the, well, training sample (where the
| training sample is then subdivided to training, evaluation
| and testing partitions), i.e. the true distribution, so the
| real world.
|
| I guess the OP is instead using "out-of-sample" to mean "test
| set" (which is not uncommon), but in that case we don't need
| to look all the way to learning theory to figure it out:
| published results are well known to select for successful
| experiments, in machine learning as in many areas of
| research, unfortunately.
| rademacher wrote:
| I haven't read this paper yet so I can't speak to it's quality
| but it appears to be addressing the same questions in this post.
| Bengio is a coauthor so maybe that's a good sign . Here's the
| abstract.
|
| This paper provides theoretical insights into why and how deep
| learning can generalize well, despite its large capacity,
| complexity, possible algorithmic instability, nonrobustness, and
| sharp minima, responding to an open question in the literature.
| We also discuss approaches to provide non-vacuous generalization
| guarantees for deep learning. Based on theoretical observations,
| we propose new open problems and discuss the limitations of our
| results.
|
| https://arxiv.org/abs/1710.05468
| zibzab wrote:
| This is an interesting subject and I would love to read more on
| it!
|
| Can anyone point me to other publications on the same issue?
| Preferably something with some real-world examples?
| disgruntledphd2 wrote:
| So, the thing that I think is most important about the article
| (which was wonderful, btw) is the double descent loss curve.
| Originally demonstrated for boosting in 1989, it seems to have
| made a comeback since 2016.
|
| That being said, this kind of stuff is gonna mostly be in the
| papers, so I suggest following the interesting references from
| the article, and repeating until you feel you understand :)
| GregarianChild wrote:
| Have you got a reference for the 1989 discovery of double
| descent? I brief Googling didn't unearth it. I'm not _"
| citation needed"_-ing you. I think a lot of decision-tree and
| boosting work is being rediscovered by the DL community. I
| would love to see the original discovery.
| disgruntledphd2 wrote:
| There you go: https://projecteuclid.org/journals/annals-of-
| statistics/volu...
|
| Rather like the 1957 development of cross-validation (which
| I remember reading, but definitely don't have a cite for),
| the double descent thing is part of the paper that is used
| on the way to something else.
| cosmic_ape wrote:
| Do you mean the boosting graphs in Fig. 1, 4 of that
| paper?
|
| It looks though that they have a double descent on the
| train set too, so it might not be the same phenomenon.
|
| Nevertheless, good to know, thanks for sharing! I knew
| both papers but never thought giving much attention to
| such details of the figures of the 1998 one. Is the
| connection between the papers well known, i.e. something
| people talk about?
| ta988 wrote:
| This is pretty common in many fields. Researchers don't have
| time to read they say. I see people that complain when they
| have to read one paper a week... This is disastrous in some
| labs where their only work is to rediscover things and add
| make-up so it looks new once they realize it is not.
| disgruntledphd2 wrote:
| _I_ read more papers than that a week, and I 'm not even an
| academic :)
| qPM9l3XJrF wrote:
| The intrinsic dimension idea seemed interesting, but I didn't
| follow this bit:
|
| >By searching through the value of d=1,2,...,D, the corresponding
| d when the solution emerges is defined as the intrinsic
| dimension.
|
| Is the idea to increase the "intrinsic dimension" until the
| network is able to learn? I'm not sure I buy the part of the
| argument where because the network is able to learn when the
| "intrinsic dimension" is kept low, it therefore follows that the
| "intrinsic dimension" is also low even when we aren't forcing it
| to be low. It seems a bit like saying "because we can obtain 90%
| accuracy on MNIST with a 10-parameter model, it therefore follows
| that a 1000-parameter model for MNIST only has 10 'intrinsic'
| parameters". Seems like a dubious / handwavey argument to me.
| belgian_guy wrote:
| The intrinsic dimension paper indeed doesn't really show that
| big networks also search in small subspaces (and neither does
| it claim to), but this has already been shown in related papers
| like https://arxiv.org/abs/1812.04754
| yxhuvud wrote:
| Well it is not the first time the idea of dimensionality
| reduction have been used in the field. It is for example the
| idea behind latent semantic methods (LSI and LSA).
| samcodes wrote:
| this is a good explanation of intrinsic dimension
| https://eng.uber.com/intrinsic-dimension/
| rocqua wrote:
| I think it is related to the lottery ticket idea. Essentially,
| you try to find the lowest d such that you can find a 'winning
| ticket' network of size d.
| sfink wrote:
| I found this to be a great survey post on a question I've been
| wondering more and more as I hear about all of the machine
| learning going on. I'm no academic nor mathematician, and I fear
| that diving into actual papers would quickly blow out the few
| remaining neurons I have left, but this article was mostly
| understandable and brought up a lot of points that have been
| floating around in my head. Kudos to the author.
|
| The one substantive comment I want to make is that I really
| wonder about the difficult to reproduce findings. What's going on
| when attempts to reproduce them fail? It's a general question,
| but I do wonder how much of that is because other effects are
| swamping the signal, and how much is that the finding only
| applies to limited situations. (Not that those are entirely
| different.) If I don't see the double-u curve, is it because my
| problem space has an atypical shape, or because the researchers'
| did?
| mjburgess wrote:
| Compression is a necessary but not sufficient condition for
| 'comprehension'. The whole 'compression' idea here is a bit of a
| misdirection; it will be a side effect of any success.
|
| The data fed into these systems is just measurements of target
| systems (eg., of light for photographs). This data is radically
| incomplete, so no compression of it will be an accurate (eg., 3d)
| model.
|
| To reconstruct the world you need to measure the measuring device
| (ie., the body) as it interacts with the target system. In most
| cases you need, also, the hypothesis behind the action to resolve
| ambiguity in the measurement data.
|
| Eg., you need to know you moved your hand to touch the fireplace
| to properly interpret what 'finger pain' means.
|
| It is for reasons of this kind that 'comprehension' is an
| engineering problem, not a programme for a universal turing
| machine (which has no device boundaries).
|
| It is engineering in the sense that 'compression' has to occur
| under the right measurement procedures, with hypothesis-laden
| action, etc.
|
| Focusing on mathematical abstracta completely misses the problem.
|
| All deep systems do is compress their training data to form
| archetypes and compare novel input to compressed archetypes.
| Since the data itself is necessarily profoundly ambiguous there
| is only a trivial sense of 'generalisation' achievd.
| 0x008 wrote:
| Such a great comment, thank you
| wokwokwok wrote:
| > Focusing on mathematical abstracta completely misses the
| problem...
|
| I don't think it does.
|
| We've been studying these networks for a long time now, and
| "common sense" interpretations are largely "completely bs" when
| examined closely.
|
| These investigations have a tangible impact on how to prune and
| design networks.
|
| High level hand waving about measuring the measuring device may
| seem profound, but I fail to see any meaningful application.
|
| You _can_ reconstruct 3D images from a few samples; see neural
| radiance fields. The observer is irrelevant.
| mjburgess wrote:
| My comment here wasnt aimed at the problem of understanding
| and improving DNNs; rather, of generalisation and
| 'comprehension' proper.
|
| 3d image reconstruction is trivially possible, with the right
| data and with the right assumptions encoded into the right
| algorithm.
|
| My target of attack here is the equivocation that
| 'compression is comprehension'.
|
| In my view comprehension isnt about 'generalization via
| compressed archetypes' as in ordinary NNs.
|
| And it isnt about 3d reconstruction given the relevant
| modification to data and approach.
|
| Rather generalization is abduction. It is the ability to, via
| a single instance, form law-like provisional universalising
| models which explain your environment. This process will lead
| to a 'compressed', 'representation', but nothing like the
| sense in which compression is here used.
|
| It is this that intuitively is naively assumed of these
| systems. They do not, and cannot, abduct. Abduction isnt a
| statistical process; involving at the very least,
| counterfactual reasoning and hypothetical action.
|
| This is the problem that such equivocations miss (ie. that c
| = c).
|
| And in my view this is an engineering challenge; not
| something to be specified for a universal computer.
|
| The relevant capacities missing arent better means of
| compression.
| wokwokwok wrote:
| > In my view comprehension isnt about 'generalization via
| compressed archetypes' as in ordinary NNs...
|
| How is this helpful?
|
| Be specific.
|
| The point being made is that inductions can be made by a
| compressed representation of the data.
|
| No one is claiming this is a key insight to AGI; you're
| just taking the word "comprehension" and arbitrarily
| assigning it some personal meaning.
|
| This is _why_ mathematicial descriptions are useful; you're
| personal view of what "comprehension" means isn't relevant
| here.
|
| The article doesn't discuss comprehension.
|
| That is something you've, as far as I can tell,
| meaninglessly brought into this discussion.
|
| How are your insights helpful for improving DNNs?
|
| Be specific.
| trap_chateau wrote:
| Sorry but I have to chime in here. His thoughts seem
| insightful and relevant to discussion. You are calling
| his contributions 'meaningless' and condescendingly
| telling him twice to 'be specific'. That's not how things
| are meant to be discussed around here and not how you get
| an answer out of someone.
| mscharrer wrote:
| Isn't the observer model explicitly built into NeRF
| architectures?
| mjburgess wrote:
| It is; ive just skim read a paper.
|
| Though, One trivial way to do it, with NNs in any case, is
| just to project forward from a range of observer models and
| guess the observer parameters from them.
|
| This is still the wrong sense of generalisation. What cant
| be guessed is why a person took consecutive pictures at
| given angles/etc.
|
| Such information is necessary to resolve deep ambiguities
| in cases where your observer model will fail.
|
| Eg., yesterday i looked out my window and thought i saw two
| people; it was actually one with a shadow+bag.
|
| I moved my eyes/head/body in such away so as to fit a
| variety of models and i was able to 'read the scene' in the
| end.
|
| _That_ is comprehension.
| jmmcd wrote:
| And there's no reason we couldn't have a deep learning
| system where the input data (images) included time-stamps
| and movement vectors, and it could be good both at easy
| image classification, and at choosing particular "head
| movements" like those you performed, to help resolve
| ambiguous cases.
|
| Further food for thought: these ambiguous cases seem (do
| you agree?) to be very rare.
| Erlich_Bachman wrote:
| > long time
|
| 4 decades is not a long time. It is a minuscule amount of
| time in the grand scheme of things.
| p1esk wrote:
| It might be the case, like with quantum mechanics, that NN
| theory is just fundamentally weird (e.g. because the space
| is so multidimensional), and it's hard for us to understand
| it no matter how long we study it.
| sfink wrote:
| > Focusing on mathematical abstracta completely misses the
| problem.
|
| That rather depends on what you think the problem is or ought
| to be. I'm not sure that the author or many readers agree with
| you. It seemed fairly clear to me that they are interested in
| how well they can generate outputs corresponding to novel
| inputs that do well on some utility function. And for that, the
| "mathematical abstracta" is rather important and useful.
| "Comprehension" might also be important and useful, but is
| itself neither necessary nor sufficient.
|
| A self-driving car will hopefully try to avoid running over a
| two-headed person crossing a road, without needing to worry
| about whether a two-headed person is mythical vs a
| miscomprehension of a woman carrying a child.
|
| Besides, the layer at which comprehension occurs is not fixed.
| Our measuring devices themselves take in ambiguous inputs and
| process them. Do you stop at the surface of the skin? The nerve
| impulses? Various layers within the brain and nervous system?
|
| Your complaint is reasonable, yet is not really that different
| from saying that computers are pointless without any I/O
| capabilities -- it doesn't matter what they compute if it is
| unobservable and has no effect on the world. That is true, yet
| doesn't mean that the whole of computer science is "a bit of a
| misdirection".
| logicchains wrote:
| >Compression is a necessary but not sufficient condition for
| 'comprehension'.
|
| Actually, algorithmic information theory shows that maximum
| compression necessarily entails maximum comprehension, because
| the only way to maximally compress something is to exactly
| understand the process producing it.
| visarga wrote:
| Compression is applied to data collected in the past while
| comprehension or intelligence also require adapting well to
| the future. Thus a pure compressor would optimize for a
| static distribution while an intelligent agent will probably
| be sub-optimal because it also needs to learn and adapt to
| the future.
| fractionalhare wrote:
| The parent commenter is not disagreeing with information
| theory (and what you're saying is shown in the article
| anyway).
|
| They're making a practical distinction that you generally
| don't have access to the actual thing in an empirical format
| for which compression will achieve true learning. Instead you
| have access to training data which represents, let's say, a
| projection of the actual thing in a smaller space with fewer
| dimensions.
|
| Like trying to learn from images instead of the 3d world.
| Humans learn to distinguish between objects in a
| 3-dimensional space using sight _and_ interaction. This
| learning generalizably transfers to recognition in 2
| dimensions. We don 't generally equip models with robotic
| interfaces to train in 3d before benchmarking them on
| ImageNet.
| reader_mode wrote:
| > We don't generally equip models with robotic interfaces
| to train in 3d before benchmarking them on ImageNet.
|
| Don't they train models using 3D rendering and simulations
| ? We have relatively realistic simulations for various
| scenarios - having a learned model that could make
| inferences based on those complex simulations sounds like a
| win.
| logicchains wrote:
| >Like trying to learn from images instead of the 3d world.
| Humans learn to distinguish between objects in a
| 3-dimensional space using sight and interaction. This
| learning generalizably transfers to recognition in 2
| dimensions.
|
| If we use human "comprehension" as a reference point, then
| the relevant point of comparison should be the
| understanding a human can develop given the same inputs.
| fractionalhare wrote:
| Sure. But again, _practically_ speaking, that isn 't the
| reality of how we learn. The commenter wasn't refuting
| Kolmogorov complexity. They're just saying it's an
| extremely limited way of viewing the problem. Useful
| sure, but insufficient.
| wongarsu wrote:
| Sure, but how do you measure that? How do we figure out
| how much understanding a human can develop from only ever
| seeing 2d pictures, without any movement or interaction
| with a 3d world?
|
| Most ML problems are things humans are quite good at and
| have a lot of context to draw from.
| gbrown wrote:
| But what if we drop the word comprehension, and we just go
| with "functional approximation X -> Y, computed from a finite
| dataset, which minimizes a predictive risk "?
|
| It's unclear why compression is necessary there, except as a
| practical benefit.
| funkisjazz wrote:
| Yeap, it gets into a philosophical debate of what
| comprehension.
|
| One could argue it's not about compression in bits but
| compression to primitives that makes sense to the human mind.
| But then the definition becomes to fuzzy because it naturally
| invites the question "Who's mind?"
| mjburgess wrote:
| Relative to a device to perform the understanding.
|
| A string X maximally compresses datsets Y iff X is a
| 'comprehending' of Y.
|
| 'OK'... but what produces and evaluates X? ie.,
| comprehension.
|
| This is the problem with defining these terms mathematically;
| you state the problem in basically useless ways.
|
| Yes, you can specify what eqn produces the mass of the higgs
| boson. Thats basically no guide to building the LHC.
|
| The production of such understanding is not abstract.
| Comprehension isnt a relation between two binary strings; it
| is an action taken in an environment with a goal.
| logicchains wrote:
| >Relative to a device to perform the understanding.
|
| It uses Kolmogorov complexity, which is defined as the
| length of a shortest computer program in a predetermined
| programming language that produces the object as output.
| Note that this measure is relative to a programming
| language, not a program, and the exact choice of language
| doesn't matter too much. Compression means creating a
| smaller program that produces the same output, and to
| produce the same output with less code necessarily requires
| more understanding.
|
| As a concrete example, imagine the output is [1,2,fizz,4,bu
| zz,fizz,7,8,fizz,buzz,11,fizz,13,14,fizzbuzz..1000). The
| longest program to output this would just hard-code it in
| the source code (much as a very inexperienced programmer
| might solve the problem, or a large neural net). Someone
| with a better understanding would write a program using
| iteration and the modulus operator, which would be shorter.
| space_rock wrote:
| I will nitpick and say that models don't compress data but
| extract useful information. Compression lossly or lossless is
| for data reconstruction. Machine learning models retain
| information that generalises
|
| https://arxiv.org/abs/1906.05849
| jhgb wrote:
| Isn't lossy compression pretty much the same thing as
| extracting some amount of useful information?
| Retric wrote:
| No, because lossy compression has the goal of preserving
| elements for replay. At the extreme you could turn a movie
| into subtitles, but not a costume from the movie alone. The
| costume might contain more information from the movie, but
| you can meaningfully recreate the movie from a single
| costume.
| jhgb wrote:
| If I derive Kepler's laws from positions of planets, I
| have preserved elements of their motion for replay as
| well.
| Retric wrote:
| The laws alone don't have enough information to replay
| their motion without each planets location, a foci, the
| orbital period, and an associated timestamp or equivalent
| information.
|
| So, include that data and it's lossy compression, exclude
| it and it's not.
| teruakohatu wrote:
| According to Wikipedia [data] compression "is the process
| of encoding information using fewer bits than the original
| representation" [1] while lossy compression is "the class
| of data encoding methods that uses inexact approximations
| and partial data discarding to represent the content" [2]
|
| There is a difference between feature extraction and
| compression. The former selects the most unique and
| important elements from a set of data, while the latter
| attempts, in the case of lossy compression, to find a
| smaller approximation of the original data set.
|
| For example imagine a data set of paintings. Feature
| extraction might simply identify what color paints were
| used in each painting. That alone might allow
| classification of paintings with respect to the painter,
| style or period. But this would not be an approximation of
| the original picture, unless you consider resizing a
| Jackson Pollock into an 8x1 pixel image to be compression.
|
| [1] https://en.wikipedia.org/wiki/Data_compression [2]
| https://en.wikipedia.org/wiki/Lossy_compression
| miltondts wrote:
| "The former selects the most unique and important
| elements from a set of data, while the latter attempts,
| in the case of lossy compression, to find a smaller
| approximation of the original data set."
|
| The compressor finds a smaller approximation of the data
| by finding the most redundant data, and as a byproduct it
| also finds the most unique. At least from the description
| you gave there is no difference between the two.
|
| "For example imagine a data set of paintings. Feature
| extraction might simply identify what color paints were
| used in each painting. That alone might allow
| classification of paintings with respect to the painter,
| style or period. But this would not be an approximation
| of the original picture, unless you consider resizing a
| Jackson Pollock into an 8x1 pixel image to be
| compression."
|
| You can and we do use compressors to do exactly that.
| Take a painting (or a set) as reference and use it to
| compress other paintings and the greater the compression
| the more similar the styles are.
|
| For an example see: https://www.sciencedirect.com/science
| /article/abs/pii/S00313...
|
| EDIT: In fact one step in a compressor is feature
| extraction (usually called modelling) and the other is
| coding.
| viraptor wrote:
| Is there a meaningful / well defined difference? One could
| say that lossy compression is extraction of useful
| information. You need to identify unnecessary information to
| know what to discard safely.
| mjburgess wrote:
| One is a subset of the other. Compression being the larger
| category.
|
| A mean is a compression of a dataset _and_ useful
| information.
|
| My issue in my comment is that 'compression' corresponds to
| a massive class of technquies and there isnt a lot of
| content in the observation that useful information is
| compressive.
|
| However there is some hypey people out there who think this
| observation has legs. Precisely the people who think
| intelligence is a mathematical problem, and not an
| engineering one -- which is my view.
|
| ie., that a body isnt incidental to intelligence, but the
| heart of it.
|
| Or: devices matter.
| typon wrote:
| I tend to think about it the same way as you. Having an
| algorithm for multiplying two numbers is qualitatively
| different than having a lossy compression of a huge
| dataset of multiplication tables. The latter is what GPT3
| has and it just doesn't scale.
| space_rock wrote:
| Consider a generative adversarial network for faces. Photos
| have let's say some unique scars
|
| A successful model could create faces with scars in them.
| But not the exact scar and face and background that they
| trained on without additional information. What you are
| looking for is mutual information between the images not
| compression
|
| Yes you could use a very well trained GAN for face
| compression. But a GAN model itself would not be able to
| reconstruct its training input without being shown the
| images again
| blackbear_ wrote:
| I get so pissed every time the double descent paper gets brought
| up, maybe because of the hubris in its abstract. No "questions
| about the mathematical foundation of machine learning" were
| raised by deep learning and a few silly experiments are far from
| showing "limits of classical analyses".
|
| All the paper shows is (1) stupid ways of counting model
| complexity and (2) that gradient descent is flawed. Nobody in
| their right mind believes that _increasing_ the number of hidden
| neurons can result in a network that is _worse_ on the test set.
| Since the bigger network contains the smaller network, it is
| perfectly capable of achieving the same performance, so the only
| reason why this does not happen is that SGD cannot find it. But
| of course "SGD cannot always find good solutions" is surprising
| to nobody, so let's just shit on decades of serious work to get
| our little paper out.
|
| Sorry for the rant.
| eugenhotaj wrote:
| > Since the bigger network contains the smaller network, it is
| perfectly capable of achieving the same performance, so the
| only reason why this does not happen is that SGD cannot find
| it.
|
| This is maybe true in the limit of infinite data, but not true
| in any practical sense, and I don't think it has anything to do
| with SGD. E.g. polynomial basis functions also have this
| property, but you can't use an arbitrarily large polynomial
| order or you'll eventually overfit. You can get a closed-form
| solution for polynomial regression problems, so no SGD
| involved.
| mjburgess wrote:
| The interesting contribution was forcing interpolation on the
| training set, right?
|
| Its one of those papers where if you had a real handle on how
| everything works, wasnt surprising. But it was more a rebuke on
| some cargo cult ideas.
|
| Lots of impactful papers have that form, eg., Gettier's paper
| on justified true belief.
| Nimitz14 wrote:
| I really do not understand your post. One doesn't train on the
| test set, so of course it's reasonable to think that increasing
| the number of parameters will cause more overfitting.
| blackbear_ wrote:
| And yet that is not what is observed in practice. See figures
| 1 and 2 of that paper [1].
|
| What I am complaining about is that the authors are confusing
| "what can be represented" by a neural network with "what can
| be easily learned" via SGD. I argued that the peak in test
| loss in those figures is observed becuse SGD struggles to
| find a solution that generalizes well, not because those
| networks are intrinsically less powerful (as the paper seems
| to imply).
|
| [1] https://arxiv.org/pdf/1812.11118.pdf
| Nimitz14 wrote:
| > And yet that is not what is observed in practice. See
| figures 1 and 2 of that paper
|
| Yeah... that's why the paper is a good contribution
| contrary to what you're saying. Not sure why you're
| repeating this information.
|
| > What I am complaining about is that the authors are
| confusing "what can be represented" by a neural network
| with "what can be easily learned" via SGD. I argued that
| the peak in test loss in those figures is observed becuse
| SGD struggles to find a solution that generalizes well, not
| because those networks are intrinsically less powerful (as
| the paper seems to imply).
|
| I mean.. those models are by definition less powerful as
| they have less parameters. The (to me) main point of the
| paper is to point out a symptom which is interesting. Their
| explanation for the symptom being (maybe) wrong doesn't
| detract from the important work of showing the symptom
| exists.
|
| A legitimate criticism would be that there have been
| earlier papers showing the same thing.
|
| Sidenote: It seems having a larger model does make it
| easier for SGD to find good solutions[1]
|
| [1] https://www.youtube.com/watch?v=kcVWAKf7UAg
| PartiallyTyped wrote:
| Let's for a second assume that we bound the weights within
| [-1,1], considering that we are using floats to represent them
| which are a subset of real numbers, by increasing the number of
| hidden neurons, you increase the class of models that you can
| select from, any single bit change in the weights means a
| different model. By increasing the class of models in your
| search space, you increase the number of models that perform
| good on training, but perform worse on test, i.e. underestimate
| true loss.
|
| Exactly because you select a single model and you have more
| models that underestimate the true (read test) error, you *may*
| be more likely to get models with worse performance on the test
| set compared to using a smaller network exactly because in the
| smaller network you are searching within a smaller
| distribution.
| unishark wrote:
| I'm not clear why you are blaming SGD. Maybe I missed the
| point. In principle SDG might well find the global optimal. The
| problem is this optimal is achieved only for training data. It
| could certainly perform worse on the test set. Maybe you are
| referring to the entire training process? The general idea is
| from the days of SVM's where the optimization method was
| convex.
|
| Though personally I do find a lot this modern "experimental"
| research quite hokey. I don't think this is something academics
| should be getting research funding to pursue. This is engineers
| building intuition about how to tune their product.
| GregarianChild wrote:
| In practise, how do you know if SDG has converged to a global
| optimum, and do you let it run long enough in practise until
| covergence?
| unishark wrote:
| You don't know. The point was even if you did get there it
| could still be an overfit model you don't want, since it's
| based on a training data set, not the true statistics of
| the distribution the samples come from.
| moultano wrote:
| The fact that over parametrized models can generalize better
| than under parameterized models, and that both are better than
| models that can just barely interpolate is a genuinely new
| insight that was not predicted by any prior theory.
| kensai wrote:
| I recently came across of a similar flaw in the EEG
| classification experiments. I think most results should be taken
| with a grain of salt until comprehensively and irrefutably
| confirmed by independent teams.
|
| https://news.ycombinator.com/item?id=26696546
| ta988 wrote:
| Great find, thanks!
| drothlis wrote:
| This contamination of test data from the training data reminds
| me of "Overly Optimistic Prediction Results on Imbalanced Data:
| a Case Study of Flaws and Benefits when Applying Over-sampling"
| [1] where almost 50% of the 24 peer-reviewed studies that use
| machine learning based on a particular publicly-available
| dataset, were claiming near-perfect accuracy at predicting the
| risk of pre-term birth for a patient, but were actually testing
| (accidentally) on training data.
|
| [1]: https://arxiv.org/abs/2001.06296
| timy2shoes wrote:
| Oversampling, then applying a train-test split? Jesus, that's
| like machine learning 101. But then again, I see a lot of
| questionable practices in the application of ML in biology.
| kvathupo wrote:
| Nothing to add, other than to say that I love her blog!
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