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Deep Learning’s Impact on Image Processing, Mathematics, and Humanity

213 points by alfaiate 9y ago

gaius 9y ago
But this is true of neural nets as well, so I'm not sure why the author was trying to contrast them. Essentially it is a question of do you want a system that works well but that no-one understands or one that works not so well but is understandable? But if you meta it, it's the same.
- backpropaganda 9y ago
  I don't think even this dichotomy is real. Deep learning methods are both performant and elegant.
  - baq 9y ago
    They're elegant only if the sentence 'consider a model with a billion features' doesn't make you feel disgusted, I'm afraid.
    - backpropaganda 9y ago
      I sure hope you're not similarly disgusted by "consider a computer with a billion transistors". Computer Science is full of abstraction and complexity. Denying it to machine learning seems conservative and naive at best.
    - trevyn 9y ago
      elegant, adjective: (of a scientific theory or solution to a problem) pleasingly ingenious and simple. One easily-described approach that is state-of-the-art in a massive number of domains? That's pretty f'ing elegant.
hnarayanan 9y ago
I echo the feelings of the author of this piece, and I'm very wary of a world where predictive power always trumps deeper understanding. (Edit: I knew I'd expressed this feeling before: https://twitter.com/copingbear/status/825098385548009472 https://twitter.com/copingbear/status/825098385548009472)
backpropaganda 9y ago
I question this meme that deep learning has less mathematical elegance or interpretability than other machine learning model. It's simply not true. At this point, it reads like a mindless copypasta with the possible political intention to reduce AI funding and use, such as the EU regulation which requires all algorithms to "explain" their reasoning. Either that, or the author is just more comfortable with familiar old-school methods which makes them think that those methods are more elegant. This push towards elegance is unscientific and counterproductive, much like the mistaken push Einstein and co. made for deterministic interpretations of quantum mechanics. We can now understand that its motivation was simply due to a biased notion of elegance due to familiarity with classical mechanics. Examples of elegance in deep learning: The gating mechanisms of LSTMs (also adds to interpretability); structure of convolutions, i.e. weight sharing, translation invariance; the policy gradient theorem (Sutton 1999); dropout, its relationship to biology and variational inference; Generative Adversarial Networks, and connections to game theory, split-brain; the reparametrization trick; the log-derivative trick; connectionist temporal classification. These examples are only the surface. Depending on your specialization inside deep learning, you'd find many more. Examples of interpretability: Nguyen et al.'s Synthesizing preferred inputs to hidden neurons, Zeiler et al. convnet visualization, Guillaume Alain's linear probes of hidden layers, attention readouts in attentional models for machine translation or speech synthesis, and many more. Ultimately, deep learning methods are probabilistic, and decent deep learning engineers would be able to tell you why a model is doing what it's doing by printing probabilities and activation statistics, much like any other probabilistic machine learning model.
- trevyn 9y ago
  I'm starting to think that human resistance to change is a form of regularization.
- shas3 9y ago
  Elad's pretty clear in laying out how pre-deep learning denoising research is differently elegant compared to CNN, etc. You should also consider the context, SIAM- the applied math community, which has seen a lot of work in deep mathematical connections between PDEs, denoising, etc. The math is certainly more advanced than required for understanding deep learning and applying it to achieve better results.
leoc 9y ago
> To put it bluntly, your grandchild is likely to have a robot spouse. I'll take the other side of that bet.
- johanneskanybal 9y ago
  I was already on the fence about the article being standard deep learning click bait when I saw that :)
- taneq 9y ago
  That your grandchild is likely to be a robot spouse? ;)
- gavinpc 9y ago
  You don't think that follows easily, then?
ganfortran 9y ago
> deep learning-based solutions lack mathematical elegance and offer very little interpretability of the found solution or understanding of the underlying phenomena I disagree. Elegance and interpretability comes with one big flaw: assumption, lots of them. While deep learning based methods assume few or not. If they are so elegant why would them underperform? Probably it is because the problem we are trying to solve doesn't follow the assumptions, like convexity, etc. In that sense, one can say deep learning methods are even more elegant, because they can work end-2-end. In that sense, NN can be a blessing, because now we got the answer, we don't need to assume anything, but just to DECODE it.
- backpropaganda 9y ago
  > because they can work end-2-end Agree. Not just end-2-end, but the same model can be applied to many different tasks. DeepMind's recent papers make progress in image generation, audio generation, language modeling & machine translation using the same basic construct of a masked dilated shifted convolutions.
- hatmatrix 9y ago
  Well here's an argument for interpretability: how do you know when your model will fail? One tradeoff might be that with deep learning, it's unlikely to fail, but you won't know when it will. With conventional methods, you may not get as good of a performance in comparison, but have a better sense of the domain of applicability because you have a better understanding of the feature space (for instance, you can determine similarity of new data in this feature space when it arrives to determine whether it is similar to past data your model has been trained on).
  - throw_away_777 9y ago
    You can do the same with deep learning, your model will fail when the train data and test data are systematically different. This isn't about understanding the model, it is about understanding the data. Understanding the data is much more important than interpreting the model. Systematic uncertainty is a problem for all models.
ngcc_hk 9y ago
You can do regression Exam score= cat_a + cont_b + err but how do you say something like cf male female has 10 score advantage and family income impact is ... Can Galileo invent physics by doing nn
- deleted 9y ago
  [deleted]
arximboldi 9y ago
This is an interesting article. It made me think of the socio-political consequences of the move towards neural networks. Many of us, children of the personal computer revolution, were attracted to computers for its empowering and democratizing effects. Just with a computer you could build anything! You are as powerful as any of "them"! The proprietary software model was developed to monetize end consumers by enchaining them, but the free software model and the fertile communities of the early Internet showed that the model of personal computation could not simply be displaced by legalese. But if we take the author's position on the impact of deep networks, the model of computation is changing again. If teaching deep networks is the new way to write useful programs, our brains and personal computers are not enough... they are obsolete. We now need clusters and, most importantly, massive access to data! This gives extraordinary leverage to the hoarders of data and servers of the Internet, the googles and the facebooks. I'd like to think that maybe we are just at the beginning, the early "mainframe neural networks" era. That we just have to wait until there is enough technology and new markets discovered to build the "personal neural network". That consensual, open and distributed ways of sharing data will emerge and that new massively parallel computers will become affordable by the masses. That the models of neural networks will become well divulged and simplified and kids will be able to program them with their "Neural Basic"... But at the moment the prospects don't look good. The Internet is becoming more and more centralized, personal computers harder and harder to program and there is a general "war on general computation" [1]. Even universities seem to bedisplaced by the Internet Lords in driving neural network development... Maybe it is already a good time to start thinking about what "Libre Neural Networks" look like. And how can we get there. [1] https://www.youtube.com/watch?v=HUEvRyemKSg https://www.youtube.com/watch?v=HUEvRyemKSg
linux_devil 9y ago
" The facts speak loudly for themselves; in most cases, deep learning-based solutions lack mathematical elegance and offer very little interpretability of the found solution or understanding of the underlying phenomena." I don't agree with this statement, a simple look at cs231n lecture series will show you how much math is involved. A lot of articles/people claim its a black box, but while writing a small network architecture you realise it's not. Methods like stride, padding, activations, learning rate, optimisations, drop outs etc. give you "aha" moment which is followed by a mathematical explanation. One should study the topic thoroughly before criticising it.
- matt4077 9y ago
  "Interpretability", in this case, is concerned with the problem domain, not ML itself. A hypothetical example: A trained decision tree algorithm for a medical decision may place the gender, or the age, of the patient at the root. That lends itself to a quick interpretation as to the relevance of factors for treatment, whereas with a Neural Net, you'll get millions of arbitrary floats that do not impart any meaning just by looking at them. That's not to say NNs don't sometimes give tantalising insights, as the article points out. I've seen a view visualisations of generative character models that were fascinating–such as finding individual neutrons tracking sentence length or nesting depth. Same for some interesting patterns emerging in the intermediate layers of object recognition networks: oh, I never knew ears were so important for face recognition.
- reader5000 9y ago
  There is no understanding of why NN training converges in reasonable time and does not over/underfit. (Unlike for say convex SVMs)
- gjulianm 9y ago
  Having a lot of math involved does not mean that it is mathematically elegant. As a mathematician, I ask myself several questions. First of all, what is really a neural network? Is it an approximating function? Is it a geometric separation on a space, such as SVM? Is it a manifold classificator? (see http://colah.github.io/posts/2014-03-NN-Manifolds-Topology/ http://colah.github.io/posts/2014-03-NN-Manifolds-Topology/, which is very interesting) Also, what are we approximating? Continuous functions? Non-continuous functions? Are they even functions and not probability measures? Are those functions arbitrary or do they represent something like a manifold? And the most important: how well are we approximating whatever we want to approximate? The universal approximation theorem gives uniform convergence for measurable functions, but do not specify at which rate or depending on which parameters. It is a strong theorem but not that surprising from the mathematical standpoint, where you already know that you can approximate any function by continuous, compactly supported functions. Finally, how do you mathematically define the problems that arise in neural networks? What is overfitting? How does the learning algorithm affect the results? The fact that some techniques are justified by mathematical explanations does not mean that it is mathematically elegant. For it to be mathematically elegant you should have at least clear definitions of the objects of study and the problems you want to solve. I don't think this is the case in neural networks.
projectorlochsa 9y ago
Author mentions style transfer as a product of NN research. Yet this paper [1] from 2014 works extremely well, no neural networks. Here's one from 2008 [2] that worked extremely well too, better than most early NN techniques. Although, deep learning is far from the intuitive approach that existed 10 years ago. It's clearer now how to reason about models, layers, activation functions etc. As much as there's no mathematical foundation, I do not believe it helps that much in the case of SVMs or whatever else. There still has to be experimentation, approximation and proper testing. [1]: https://dspace.mit.edu/handle/1721.1/100018 https://dspace.mit.edu/handle/1721.1/100018 [2]: http://link.springer.com/chapter/10.1007%2F978-3-540-88690-7_3?LI=true http://link.springer.com/chapter/10.1007%2F978-3-540-88690-7...
- jph00 9y ago
  To claim that those techniques are even in the same ballpark as deep learning based style transfer is just silly. They are extremely limited in their application, as you can clearly see by looking at the examples. And the entire approaches are overfit to the particular applications that they show, so they can't be readily extended. These are actually excellent examples of how deep learning has totally changed our expectations of what can be done with computer vision by using deep learning.
  - projectorlochsa 9y ago
    Deep learning based style transfer that got viral a year or two ago was worse than this 2008 result, especially worse for that hone application to portraits. The hype was nowhere near just because there's no deepness. I admit that https://arxiv.org/abs/1705.01088 https://arxiv.org/abs/1705.01088 this beats everything and is extremely powerful and simple but the hype for deep things seems a bit too strong.
- j2kun 9y ago
  It's important to note that we know the limitations of SVMs because of the theory. That's usually what a theory provides. There are also a few methods, like boosting, that are purely the result of theory.
- 9y ago
swagonomixxx 9y ago
First comment I make on HN, but I feel compelled to say something. This post reeks of the author piping on about the "good old days" of mathematical elegance. Firstly, mathematical elegance is not an objective metric by any means. Many mathematicians disagree on what results are most elegant, though there are many commonalities as well. Secondly, all of machine learning is quite elegant. I'm by no means an expert since I only took two courses in my fourth year that were surveys of many methods (quite mathematically rigorous btw) but I've taken enough math to be able to judge what is elegant or not. As the author himself says, he has slightly modified his research methods. These days you'd be a fool to ignore deep learning, whether you have a deep understanding of it or not.
- matt4077 9y ago
  I felt the article was quite fair in acknowledging the intriguing results of deep learning, and decidedly arguing against ignoring them. "Elegance" can indeed not be defined, but I believe the misunderstanding here is more about the point of view: Deep neural networks are plenty elegant when looked at from an ML POV. But, if you're an expert in, for example, image processing, using a DNN as a tool, the solution it may give you won't be "elegant" by anybody's definition. It is, after all, a repetitive formula with X million arbitrary floats. Previous ML methods usually resulted in models, or formulas, that were small enough to "grasp" intuitively. The "beauty", or "elegance" was that often, you could find connections from terms in your model to the real world.
  - ganfortran 9y ago
    > Previous ML methods usually resulted in models, or formulas, that were small enough to "grasp" intuitively. Which is not true in practice. SVM in reality is an instance based method, with thousands to 10 thousands high-dimensional vectors as its 'parameters'. Random forests, which is famous for its ease of interpretability is no easy meal either when you end up with 100s of trees with outrageous branches. Not mention that real world model are embarrassingly complex ensemble of smaller but still complex models.
c0achmcguirk 9y ago
> "But what about us scientists? What is the true objective behind the vast effort that we invested in the image denoising problem?" This is the telegraph operator lamenting all the time spent learning Morse Code when the telephone was invented. I think scientists can be motivated by looking for new ways to solve real problems. Don't weep over the time spent understanding the classic models. Rejoice that we have a much better tool to further mankind.
frankmcsherry 9y ago
There seems to be a lot of angst in the responses about how deep nets et al "are too elegant; are too interpretable!". It's important to remember that the intended product of science is not tools, it is understanding. Deep nets may produce very elegant and interpretable tools, from a very elegant and interpretable theory, but that is not what the scientists are looking for. They are generally creating and assessing theories in their subject domains, which are then evaluated by the tools they have built. Deep learning does do a great job of providing a baseline ("your theory must be this accurate to matter"), but it seems to do a much less great job at extracting new understanding.
- backpropaganda 9y ago
  Machine learning has departed from the venture of understanding-based science much before deep learning [1][2]. Thus, singling out deep learning reeks of motivated reasoning or just lack of awareness of the history of machine learning. Having said that, there still exists the lunatic fringe (it's a compliment) inside deep learning who continue to work on the task of generative modeling in the hope of "understanding the world" rather than "solving a task". Yoshua Bengio and Yann LeCun don't miss an opportunity to impress on the world how important unsupervised learning is. Physics too has abandoned understanding for predictive power. If you take philosophy of science seriously, you either have to pick "science is whatever the elite society believes in (Kuhn)" or "science gives us tools for prediction (Post-Kuhn)". Claiming that science helps in finding truth or understanding, is going to put you in a very indefensible slippery slope. "Understanding" is a subjective human concept, and not worth pursuing. Humans evolved to run from tigers, and struggle with harder tasks like understanding quantum mechanics or understanding the brain. The directionality of scientific progress as evidenced by QM is not "understanding", but tooling and predictive power. I hope Deep Learning is going to follow the path of predictive power, rather than regress into the pseudoscientific mess of elegance and understanding. [1]: http://www2.math.uu.se/~thulin/mm/breiman.pdf http://www2.math.uu.se/~thulin/mm/breiman.pdf [2]: http://norvig.com/chomsky.html http://norvig.com/chomsky.html
  - bamboozled 9y ago
    "Understanding" is a subjective human concept, and not worth pursuing." Isn't human understanding of how our environment works precisely how you're able to sit in your chair and write comments on HN for others to read?
hprotagonist 9y ago
Deep learning is a perfectly useful engineering solution. As a tool for basic research, particularly in the biomedical realm, it's awful. You get a system that performs pretty well most of the time, but tells you nothing of interest. That's fine, as far as it goes, but "performs pretty well" is so much more useful in industry than "we know how X biological system works" that entire fields that are interested in the mechanics of how perceptual biological systems work and may be fixed are getting eaten alive. To our collective detriment, I think.
NumberSix 9y ago
Deep learning/neural networks -- as well as a number of other "machine learning" methods -- is fitting a mathematical model with a huge number of fitted (tunable) parameters and component functions to data. It has been known for a long time -- arguably back to the discovery of the Taylor series expansion in the early days of calculus -- that any function can be approximated arbitrarily well by the composition of an arbitrarily large composition of other functions. If the task is interpolation between the data points this can be highly accurate. It the task is extrapolation such as prediction or designing a truly new machine or system in an engineering application, the approximation will often fail. The about one percent error rate in predictions of planetary motions from epicycles is one of the earliest cases of this problem. The simple example is approximating data with a polynomial with an arbitrary number of terms such as in the Taylor series expansion. With enough terms a polynomial model can always approximate any data set arbitrarily well. Polynomial models can interpolate very well unless the data has some generally unusual behavior -- changing unpredictably at successively finer scales for example. However, finite polynomial models almost always extrapolate grossly incorrectly. As you move away from the data set in the space of independent variables such as X, the largest power N in X^N dominates and the polynomial approximation function blows up to either plus or minus infinity which is rarely physical. What we think of as "understanding" corresponds conceptually in part to the ability to make accurate predictions. "Understanding" or "explanation" corresponds mathematically not to some arbitrary super-complex function with large numbers of arbitrary parameters but rather to a mathematical object such as as system of differential equations (e.g. Maxwell's Equations for Electromagnetism or the General Theory of Relativity) that express interrelationships among the variables and data points.
- ppod 9y ago
  Machine learning researchers are well aware of the problem of out-of-sample predictions, in fact most of the work goes into making systems appropriately generalizable by making architectures robust through dropout or regularization. The resulting systems might not correspond to our intuitive definition of "understanding", but they look more similar to what we know about the human brain than an elegant function with a small number of interpretable parameters.
deepnotderp 9y ago
In my opinion, this push towards "mathematical elegance " and "interpretability" is hurting us and is unscientific. About interpretability, I'll quote Yann LeCun here, you don't really care too much about whether or not your taxi driver is interpretible, he's a black box. Not only that, but there are a variety of new methods such as attention mechanisms, gradient masks and auxiliary explainer networks that give really good interpretability. And it's funny how this criticism never comes up for SVMs... I also think it's unscientific to expect mathematical elegance from everything. Math is ultimately a logical descriptor tool for AI, a means, not an end in itself. Besides, there's actually a host of involved mathematics underlying the seemingly simple SGD of deep nets. For example, tropical geometry has been used to analyze the loss surfaces of ReLU networks and random matrix theory has been employed to analyze the loss surfaces with respect to the quality of local minima. Tl;dr: deep nets are far more interpretible than they've been given credit for and they're also more mathematical than some (such as this author ) would have you believe.
deleted 9y ago
[deleted]
return0 9y ago
I have no doubt that some day (soon?) neural networks will be able to explain themselves (using language). But the explanation they give will be less than satisfactory to our aesthetic criteria. Occam's razor is a great aesthetic rule, but it doesn't guarantee beauty. We will most likely find out that the computational vision of the past had managed to find some rules covering some cases, but it missed many more, most of which will be higher-order and not that elegant. And it may turn out denoising was a rather messy problem, as was probably speech recognition. Drugs work but we don't know how a surprisingly large number of them work. Yet chemists don't complain about them. Theoreticians should not complain either. Deep nets give them a huge subject matter that probably hides many interesting insights in it. I mean, don't convolutional layers look like gabor filters? The question of what can be understood from them can go deep, to the limits of the ability of language/math to express ideas.
- nske 9y ago
  I don't see a problem in splitting all these domains to an "applied" school, that focuses research into evolving solutions that currently seem effective in approximating answers for certain engineering problems, and a more theoretical school that has the potential to carve new revolutionary paths while pursuing some (abstract?) ideal such as mathematical elegance. One shouldn't exclude the other and apparently there are enough scientists around that are attracted to either one of the two approaches.
crb002 9y ago
Good Computerphile episode on understanding what is going inside a neural net, https://www.youtube.com/watch?v=BFdMrDOx_CM https://www.youtube.com/watch?v=BFdMrDOx_CM . Looking at high information neurons to see what they pick up can yield a lot of insight into the problem.
mwytock 9y ago
Many methods in machine learning and statistics benefit from two types of theory: 1) Optimization theory - which says, if I repeat this iterative method N times I will find a (nearly) globally optimal solution 2) Statistical theory - which says, if I observe this process N times I can accurately estimate a population quantity with high probability Deep learning does not benefit from the same theoretical guarantees. For the most part the response from the community is "but it works really well!" which is a fair and valid response especially since what most practitioners care about is predictive accuracy. Personally, I find applying neural networks extremely annoying at times due to the amount of twiddling of hyperparameters, slow convergence, etc.
pinouchon 9y ago
> In its feed-forward architecture, layers of perceptrons—also referred to as neurons—first perform weighted averaging of their inputs, followed by nonlinearities such as a sigmoid or rectified-linear curves. I have a really hard time keeping reading after this passage.

213 points by alfaiate 9y ago

But this is true of neural nets as well, so I'm not sure why the author was trying to contrast them. Essentially it is a question of do you want a system that works well but that no-one understands or one that works not so well but is understandable? But if you meta it, it's the same.

backpropaganda 9y ago
I don't think even this dichotomy is real. Deep learning methods are both performant and elegant.
- baq 9y ago
  They're elegant only if the sentence 'consider a model with a billion features' doesn't make you feel disgusted, I'm afraid.
  - backpropaganda 9y ago
    I sure hope you're not similarly disgusted by "consider a computer with a billion transistors". Computer Science is full of abstraction and complexity. Denying it to machine learning seems conservative and naive at best.
  - trevyn 9y ago
    elegant, adjective: (of a scientific theory or solution to a problem) pleasingly ingenious and simple. One easily-described approach that is state-of-the-art in a massive number of domains? That's pretty f'ing elegant.

hnarayanan 9y ago

I echo the feelings of the author of this piece, and I'm very wary of a world where predictive power always trumps deeper understanding. (Edit: I knew I'd expressed this feeling before: https://twitter.com/copingbear/status/825098385548009472 https://twitter.com/copingbear/status/825098385548009472)

backpropaganda 9y ago

I question this meme that deep learning has less mathematical elegance or interpretability than other machine learning model. It's simply not true. At this point, it reads like a mindless copypasta with the possible political intention to reduce AI funding and use, such as the EU regulation which requires all algorithms to "explain" their reasoning. Either that, or the author is just more comfortable with familiar old-school methods which makes them think that those methods are more elegant. This push towards elegance is unscientific and counterproductive, much like the mistaken push Einstein and co. made for deterministic interpretations of quantum mechanics. We can now understand that its motivation was simply due to a biased notion of elegance due to familiarity with classical mechanics. Examples of elegance in deep learning: The gating mechanisms of LSTMs (also adds to interpretability); structure of convolutions, i.e. weight sharing, translation invariance; the policy gradient theorem (Sutton 1999); dropout, its relationship to biology and variational inference; Generative Adversarial Networks, and connections to game theory, split-brain; the reparametrization trick; the log-derivative trick; connectionist temporal classification. These examples are only the surface. Depending on your specialization inside deep learning, you'd find many more. Examples of interpretability: Nguyen et al.'s Synthesizing preferred inputs to hidden neurons, Zeiler et al. convnet visualization, Guillaume Alain's linear probes of hidden layers, attention readouts in attentional models for machine translation or speech synthesis, and many more. Ultimately, deep learning methods are probabilistic, and decent deep learning engineers would be able to tell you why a model is doing what it's doing by printing probabilities and activation statistics, much like any other probabilistic machine learning model.

trevyn 9y ago
I'm starting to think that human resistance to change is a form of regularization.
shas3 9y ago
Elad's pretty clear in laying out how pre-deep learning denoising research is differently elegant compared to CNN, etc. You should also consider the context, SIAM- the applied math community, which has seen a lot of work in deep mathematical connections between PDEs, denoising, etc. The math is certainly more advanced than required for understanding deep learning and applying it to achieve better results.

leoc 9y ago

> To put it bluntly, your grandchild is likely to have a robot spouse. I'll take the other side of that bet.

johanneskanybal 9y ago
I was already on the fence about the article being standard deep learning click bait when I saw that :)
taneq 9y ago
That your grandchild is likely to be a robot spouse? ;)
gavinpc 9y ago
You don't think that follows easily, then?

ganfortran 9y ago

> deep learning-based solutions lack mathematical elegance and offer very little interpretability of the found solution or understanding of the underlying phenomena I disagree. Elegance and interpretability comes with one big flaw: assumption, lots of them. While deep learning based methods assume few or not. If they are so elegant why would them underperform? Probably it is because the problem we are trying to solve doesn't follow the assumptions, like convexity, etc. In that sense, one can say deep learning methods are even more elegant, because they can work end-2-end. In that sense, NN can be a blessing, because now we got the answer, we don't need to assume anything, but just to DECODE it.

backpropaganda 9y ago
> because they can work end-2-end Agree. Not just end-2-end, but the same model can be applied to many different tasks. DeepMind's recent papers make progress in image generation, audio generation, language modeling & machine translation using the same basic construct of a masked dilated shifted convolutions.
hatmatrix 9y ago
Well here's an argument for interpretability: how do you know when your model will fail? One tradeoff might be that with deep learning, it's unlikely to fail, but you won't know when it will. With conventional methods, you may not get as good of a performance in comparison, but have a better sense of the domain of applicability because you have a better understanding of the feature space (for instance, you can determine similarity of new data in this feature space when it arrives to determine whether it is similar to past data your model has been trained on).
- throw_away_777 9y ago
  You can do the same with deep learning, your model will fail when the train data and test data are systematically different. This isn't about understanding the model, it is about understanding the data. Understanding the data is much more important than interpreting the model. Systematic uncertainty is a problem for all models.

ngcc_hk 9y ago

You can do regression Exam score= cat_a + cont_b + err but how do you say something like cf male female has 10 score advantage and family income impact is ... Can Galileo invent physics by doing nn

deleted 9y ago
[deleted]

arximboldi 9y ago

This is an interesting article. It made me think of the socio-political consequences of the move towards neural networks. Many of us, children of the personal computer revolution, were attracted to computers for its empowering and democratizing effects. Just with a computer you could build anything! You are as powerful as any of "them"! The proprietary software model was developed to monetize end consumers by enchaining them, but the free software model and the fertile communities of the early Internet showed that the model of personal computation could not simply be displaced by legalese. But if we take the author's position on the impact of deep networks, the model of computation is changing again. If teaching deep networks is the new way to write useful programs, our brains and personal computers are not enough... they are obsolete. We now need clusters and, most importantly, massive access to data! This gives extraordinary leverage to the hoarders of data and servers of the Internet, the googles and the facebooks. I'd like to think that maybe we are just at the beginning, the early "mainframe neural networks" era. That we just have to wait until there is enough technology and new markets discovered to build the "personal neural network". That consensual, open and distributed ways of sharing data will emerge and that new massively parallel computers will become affordable by the masses. That the models of neural networks will become well divulged and simplified and kids will be able to program them with their "Neural Basic"... But at the moment the prospects don't look good. The Internet is becoming more and more centralized, personal computers harder and harder to program and there is a general "war on general computation" [1]. Even universities seem to bedisplaced by the Internet Lords in driving neural network development... Maybe it is already a good time to start thinking about what "Libre Neural Networks" look like. And how can we get there. [1] https://www.youtube.com/watch?v=HUEvRyemKSg https://www.youtube.com/watch?v=HUEvRyemKSg

linux_devil 9y ago

" The facts speak loudly for themselves; in most cases, deep learning-based solutions lack mathematical elegance and offer very little interpretability of the found solution or understanding of the underlying phenomena." I don't agree with this statement, a simple look at cs231n lecture series will show you how much math is involved. A lot of articles/people claim its a black box, but while writing a small network architecture you realise it's not. Methods like stride, padding, activations, learning rate, optimisations, drop outs etc. give you "aha" moment which is followed by a mathematical explanation. One should study the topic thoroughly before criticising it.

matt4077 9y ago
"Interpretability", in this case, is concerned with the problem domain, not ML itself. A hypothetical example: A trained decision tree algorithm for a medical decision may place the gender, or the age, of the patient at the root. That lends itself to a quick interpretation as to the relevance of factors for treatment, whereas with a Neural Net, you'll get millions of arbitrary floats that do not impart any meaning just by looking at them. That's not to say NNs don't sometimes give tantalising insights, as the article points out. I've seen a view visualisations of generative character models that were fascinating–such as finding individual neutrons tracking sentence length or nesting depth. Same for some interesting patterns emerging in the intermediate layers of object recognition networks: oh, I never knew ears were so important for face recognition.
reader5000 9y ago
There is no understanding of why NN training converges in reasonable time and does not over/underfit. (Unlike for say convex SVMs)
gjulianm 9y ago
Having a lot of math involved does not mean that it is mathematically elegant. As a mathematician, I ask myself several questions. First of all, what is really a neural network? Is it an approximating function? Is it a geometric separation on a space, such as SVM? Is it a manifold classificator? (see http://colah.github.io/posts/2014-03-NN-Manifolds-Topology/ http://colah.github.io/posts/2014-03-NN-Manifolds-Topology/, which is very interesting) Also, what are we approximating? Continuous functions? Non-continuous functions? Are they even functions and not probability measures? Are those functions arbitrary or do they represent something like a manifold? And the most important: how well are we approximating whatever we want to approximate? The universal approximation theorem gives uniform convergence for measurable functions, but do not specify at which rate or depending on which parameters. It is a strong theorem but not that surprising from the mathematical standpoint, where you already know that you can approximate any function by continuous, compactly supported functions. Finally, how do you mathematically define the problems that arise in neural networks? What is overfitting? How does the learning algorithm affect the results? The fact that some techniques are justified by mathematical explanations does not mean that it is mathematically elegant. For it to be mathematically elegant you should have at least clear definitions of the objects of study and the problems you want to solve. I don't think this is the case in neural networks.

projectorlochsa 9y ago

Author mentions style transfer as a product of NN research. Yet this paper [1] from 2014 works extremely well, no neural networks. Here's one from 2008 [2] that worked extremely well too, better than most early NN techniques. Although, deep learning is far from the intuitive approach that existed 10 years ago. It's clearer now how to reason about models, layers, activation functions etc. As much as there's no mathematical foundation, I do not believe it helps that much in the case of SVMs or whatever else. There still has to be experimentation, approximation and proper testing. [1]: https://dspace.mit.edu/handle/1721.1/100018 https://dspace.mit.edu/handle/1721.1/100018 [2]: http://link.springer.com/chapter/10.1007%2F978-3-540-88690-7_3?LI=true http://link.springer.com/chapter/10.1007%2F978-3-540-88690-7...

jph00 9y ago
To claim that those techniques are even in the same ballpark as deep learning based style transfer is just silly. They are extremely limited in their application, as you can clearly see by looking at the examples. And the entire approaches are overfit to the particular applications that they show, so they can't be readily extended. These are actually excellent examples of how deep learning has totally changed our expectations of what can be done with computer vision by using deep learning.
- projectorlochsa 9y ago
  Deep learning based style transfer that got viral a year or two ago was worse than this 2008 result, especially worse for that hone application to portraits. The hype was nowhere near just because there's no deepness. I admit that https://arxiv.org/abs/1705.01088 https://arxiv.org/abs/1705.01088 this beats everything and is extremely powerful and simple but the hype for deep things seems a bit too strong.
j2kun 9y ago
It's important to note that we know the limitations of SVMs because of the theory. That's usually what a theory provides. There are also a few methods, like boosting, that are purely the result of theory.
9y ago

swagonomixxx 9y ago

First comment I make on HN, but I feel compelled to say something. This post reeks of the author piping on about the "good old days" of mathematical elegance. Firstly, mathematical elegance is not an objective metric by any means. Many mathematicians disagree on what results are most elegant, though there are many commonalities as well. Secondly, all of machine learning is quite elegant. I'm by no means an expert since I only took two courses in my fourth year that were surveys of many methods (quite mathematically rigorous btw) but I've taken enough math to be able to judge what is elegant or not. As the author himself says, he has slightly modified his research methods. These days you'd be a fool to ignore deep learning, whether you have a deep understanding of it or not.

matt4077 9y ago
I felt the article was quite fair in acknowledging the intriguing results of deep learning, and decidedly arguing against ignoring them. "Elegance" can indeed not be defined, but I believe the misunderstanding here is more about the point of view: Deep neural networks are plenty elegant when looked at from an ML POV. But, if you're an expert in, for example, image processing, using a DNN as a tool, the solution it may give you won't be "elegant" by anybody's definition. It is, after all, a repetitive formula with X million arbitrary floats. Previous ML methods usually resulted in models, or formulas, that were small enough to "grasp" intuitively. The "beauty", or "elegance" was that often, you could find connections from terms in your model to the real world.
- ganfortran 9y ago
  > Previous ML methods usually resulted in models, or formulas, that were small enough to "grasp" intuitively. Which is not true in practice. SVM in reality is an instance based method, with thousands to 10 thousands high-dimensional vectors as its 'parameters'. Random forests, which is famous for its ease of interpretability is no easy meal either when you end up with 100s of trees with outrageous branches. Not mention that real world model are embarrassingly complex ensemble of smaller but still complex models.

c0achmcguirk 9y ago

> "But what about us scientists? What is the true objective behind the vast effort that we invested in the image denoising problem?" This is the telegraph operator lamenting all the time spent learning Morse Code when the telephone was invented. I think scientists can be motivated by looking for new ways to solve real problems. Don't weep over the time spent understanding the classic models. Rejoice that we have a much better tool to further mankind.

frankmcsherry 9y ago

There seems to be a lot of angst in the responses about how deep nets et al "are too elegant; are too interpretable!". It's important to remember that the intended product of science is not tools, it is understanding. Deep nets may produce very elegant and interpretable tools, from a very elegant and interpretable theory, but that is not what the scientists are looking for. They are generally creating and assessing theories in their subject domains, which are then evaluated by the tools they have built. Deep learning does do a great job of providing a baseline ("your theory must be this accurate to matter"), but it seems to do a much less great job at extracting new understanding.

backpropaganda 9y ago
Machine learning has departed from the venture of understanding-based science much before deep learning [1][2]. Thus, singling out deep learning reeks of motivated reasoning or just lack of awareness of the history of machine learning. Having said that, there still exists the lunatic fringe (it's a compliment) inside deep learning who continue to work on the task of generative modeling in the hope of "understanding the world" rather than "solving a task". Yoshua Bengio and Yann LeCun don't miss an opportunity to impress on the world how important unsupervised learning is. Physics too has abandoned understanding for predictive power. If you take philosophy of science seriously, you either have to pick "science is whatever the elite society believes in (Kuhn)" or "science gives us tools for prediction (Post-Kuhn)". Claiming that science helps in finding truth or understanding, is going to put you in a very indefensible slippery slope. "Understanding" is a subjective human concept, and not worth pursuing. Humans evolved to run from tigers, and struggle with harder tasks like understanding quantum mechanics or understanding the brain. The directionality of scientific progress as evidenced by QM is not "understanding", but tooling and predictive power. I hope Deep Learning is going to follow the path of predictive power, rather than regress into the pseudoscientific mess of elegance and understanding. [1]: http://www2.math.uu.se/~thulin/mm/breiman.pdf http://www2.math.uu.se/~thulin/mm/breiman.pdf [2]: http://norvig.com/chomsky.html http://norvig.com/chomsky.html
- bamboozled 9y ago
  "Understanding" is a subjective human concept, and not worth pursuing." Isn't human understanding of how our environment works precisely how you're able to sit in your chair and write comments on HN for others to read?

hprotagonist 9y ago

Deep learning is a perfectly useful engineering solution. As a tool for basic research, particularly in the biomedical realm, it's awful. You get a system that performs pretty well most of the time, but tells you nothing of interest. That's fine, as far as it goes, but "performs pretty well" is so much more useful in industry than "we know how X biological system works" that entire fields that are interested in the mechanics of how perceptual biological systems work and may be fixed are getting eaten alive. To our collective detriment, I think.

NumberSix 9y ago

Deep learning/neural networks -- as well as a number of other "machine learning" methods -- is fitting a mathematical model with a huge number of fitted (tunable) parameters and component functions to data. It has been known for a long time -- arguably back to the discovery of the Taylor series expansion in the early days of calculus -- that any function can be approximated arbitrarily well by the composition of an arbitrarily large composition of other functions. If the task is interpolation between the data points this can be highly accurate. It the task is extrapolation such as prediction or designing a truly new machine or system in an engineering application, the approximation will often fail. The about one percent error rate in predictions of planetary motions from epicycles is one of the earliest cases of this problem. The simple example is approximating data with a polynomial with an arbitrary number of terms such as in the Taylor series expansion. With enough terms a polynomial model can always approximate any data set arbitrarily well. Polynomial models can interpolate very well unless the data has some generally unusual behavior -- changing unpredictably at successively finer scales for example. However, finite polynomial models almost always extrapolate grossly incorrectly. As you move away from the data set in the space of independent variables such as X, the largest power N in X^N dominates and the polynomial approximation function blows up to either plus or minus infinity which is rarely physical. What we think of as "understanding" corresponds conceptually in part to the ability to make accurate predictions. "Understanding" or "explanation" corresponds mathematically not to some arbitrary super-complex function with large numbers of arbitrary parameters but rather to a mathematical object such as as system of differential equations (e.g. Maxwell's Equations for Electromagnetism or the General Theory of Relativity) that express interrelationships among the variables and data points.

ppod 9y ago
Machine learning researchers are well aware of the problem of out-of-sample predictions, in fact most of the work goes into making systems appropriately generalizable by making architectures robust through dropout or regularization. The resulting systems might not correspond to our intuitive definition of "understanding", but they look more similar to what we know about the human brain than an elegant function with a small number of interpretable parameters.

deepnotderp 9y ago

In my opinion, this push towards "mathematical elegance " and "interpretability" is hurting us and is unscientific. About interpretability, I'll quote Yann LeCun here, you don't really care too much about whether or not your taxi driver is interpretible, he's a black box. Not only that, but there are a variety of new methods such as attention mechanisms, gradient masks and auxiliary explainer networks that give really good interpretability. And it's funny how this criticism never comes up for SVMs... I also think it's unscientific to expect mathematical elegance from everything. Math is ultimately a logical descriptor tool for AI, a means, not an end in itself. Besides, there's actually a host of involved mathematics underlying the seemingly simple SGD of deep nets. For example, tropical geometry has been used to analyze the loss surfaces of ReLU networks and random matrix theory has been employed to analyze the loss surfaces with respect to the quality of local minima. Tl;dr: deep nets are far more interpretible than they've been given credit for and they're also more mathematical than some (such as this author ) would have you believe.

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return0 9y ago

I have no doubt that some day (soon?) neural networks will be able to explain themselves (using language). But the explanation they give will be less than satisfactory to our aesthetic criteria. Occam's razor is a great aesthetic rule, but it doesn't guarantee beauty. We will most likely find out that the computational vision of the past had managed to find some rules covering some cases, but it missed many more, most of which will be higher-order and not that elegant. And it may turn out denoising was a rather messy problem, as was probably speech recognition. Drugs work but we don't know how a surprisingly large number of them work. Yet chemists don't complain about them. Theoreticians should not complain either. Deep nets give them a huge subject matter that probably hides many interesting insights in it. I mean, don't convolutional layers look like gabor filters? The question of what can be understood from them can go deep, to the limits of the ability of language/math to express ideas.

nske 9y ago
I don't see a problem in splitting all these domains to an "applied" school, that focuses research into evolving solutions that currently seem effective in approximating answers for certain engineering problems, and a more theoretical school that has the potential to carve new revolutionary paths while pursuing some (abstract?) ideal such as mathematical elegance. One shouldn't exclude the other and apparently there are enough scientists around that are attracted to either one of the two approaches.

crb002 9y ago

Good Computerphile episode on understanding what is going inside a neural net, https://www.youtube.com/watch?v=BFdMrDOx_CM https://www.youtube.com/watch?v=BFdMrDOx_CM . Looking at high information neurons to see what they pick up can yield a lot of insight into the problem.

mwytock 9y ago

Many methods in machine learning and statistics benefit from two types of theory: 1) Optimization theory - which says, if I repeat this iterative method N times I will find a (nearly) globally optimal solution 2) Statistical theory - which says, if I observe this process N times I can accurately estimate a population quantity with high probability Deep learning does not benefit from the same theoretical guarantees. For the most part the response from the community is "but it works really well!" which is a fair and valid response especially since what most practitioners care about is predictive accuracy. Personally, I find applying neural networks extremely annoying at times due to the amount of twiddling of hyperparameters, slow convergence, etc.

pinouchon 9y ago

> In its feed-forward architecture, layers of perceptrons—also referred to as neurons—first perform weighted averaging of their inputs, followed by nonlinearities such as a sigmoid or rectified-linear curves. I have a really hard time keeping reading after this passage.