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Comment by quantombone | Hacker News Reader

Back in around 2008, SVMs were all the rage in computer vision. We would use hand designed visual features and then a linear SVM on top. That was how object detectors were built (remember DPM?)

Funny how SVMs are just max-margin loss functions and we just took for granted that you needed domain expertise to craft features like HOG/SIFT by hand.

By 2018, we use ConvNets to learn BOTH the features and the classifier. In fact, it’s hard to separate where the features end and the classifier begins (in a modern CNN).

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So the pitch is that you don't have to do feature engineering... but then instead it seems people do network structure engineering with featurish things like convolutions.

The performance is still better in most cases but I often have to wonder, are people just doing feature engineering once removed and is the better performance just the result of having WAY more parameters in the model?

I guess one upshot to the SVM approach is that there's math for quantifying how well a given model will generalize, subject to some assumptions.

Is there anything like that in the ANN world?

In short, no. Not for practically large models used in common tasks like image classification or speech to text.

are people just doing feature engineering once removed and is the better performance just the result of having WAY more parameters in the model?

Not really, or sort of, depending on how you think.

A deep neural network does work - at least to some extent - because of the large number of parameters. However, it is practical because it can be trained in a reasonable amount of time.

Things like ResNets are useful because they allow us to train deeper networks.

You can create a SVM with the same number of parameters[1], and in theory it could be as accurate (this is basically the no free lunch theorem[2]). But you won't be able to train it to the same accuracy.

[1] Of course there are practical concerns about what you do for features, since hand created features just aren't as good as neural network ones. One thing people do now is use the lower layers of a deep neural network as a feature extractor and then put a SVM on top of them as the classifier. This works quite well, and is reasonably fast to train.

[2] https://en.wikipedia.org/wiki/No_free_lunch_theorem

But you won't be able to train it to the same accuracy.

I'm not sure I agree with this bit in theory. A Neural Network is a stack of basis functions; and this stack can also be seen as a bunch of basis functions. And basis functions are what kernels represent. Trivially, you could then "copy" the weights that a ANN would learn into a kernel and obtain the same accuracy.

The reason this doesn't work in practice is, in SVMs, you tend not to learn kernels from scratch but use (possibly a combination of) standard parameterized kernels - [1]. The learning step in the SVM adapts this standard kernel to your dataset as much as the parameters allow, but this would be sub-optimal compared to learning a kernel (or the corresponding basis functions) from scratch that's built just for your data. With a well trained ANN the latter is what you get.

[1] there has been a fair amount of work on learning kernels too, but its not as mainstream as using standard kernels.

Trivially, you could then "copy" the weights that a ANN would learn into a kernel and obtain the same accuracy.

Sure.

I'm not sure I agree with this bit in theory.

No one really agrees with it in theory - I'm not aware of a good theoretical explanation as to why some deep networks are easier to train. And yet there is a growing body of real, generalized practical hints which work pretty reliably.

This is pretty exciting! There is undiscovered ideas here. But it is unsatisfactory from the theoretical sense at the moment.

If you use the right sort of kernel for an SVM it becomes a neural network with automatic architecture derivation.

See slide 7:

http://www.cs.rpi.edu/~magdon/courses/LFD-Slides/SlidesLect2...

Significantly, it becomes a simple, 2-layer neural network. The power of the advances of neural networks in the past decade have largely relied on "deep" architectures with many layers. Very deep networks effectively learn the features from the data, rather than learn a decision surface over a set of hand-crafted features, as in learning with SVMs or shallow neural networks.

I thought it had been proven that a two layer neural network has the same power as a deep one (obviously with a much greater width). It's just that deep neural networks are a lot more practical to train in practice. So I'm not sure how important that distinction is.

This is something of an academic factoid that has nothing to do with the practice of training and using neural networks, or with the merits of deep networks that I was describing above.

Shallow feed-forward networks are "universal function approximators" [0] when the number of hidden neurons is finite but unbounded. Of course, the width of that layer grows exponentially in the depth of the deep network that you might wish to approximate [1].

The statement that "[i]t's just that deep neural networks are a lot more practical to train" (emphasis mine) sounds somewhat reductive; it's not only that depth is a nice trick or hack for training speed, but that depth makes the success of deep networks in the past decade at all possible. We live in a world with bounded computing resources and bounded training data. You cannot subsume all deep networks into shallow networks, and shallow networks into SVMs in the real world. So I am pretty sure of how important that distinction is.

And what's more, depth extracts a hierarchy of interpret-able features at multiple scales[2], and a decision surface embedded within that feature space, rather than a brittle decision surface in an extremely high dimensional space with little semantic meaning. One of these approaches generalizes better than the other to unseen data.

[0] https://en.wikipedia.org/wiki/Universal_approximation_theore... [1] https://pdfs.semanticscholar.org/f594/f693903e1507c33670b896... [2] https://distill.pub/2017/feature-visualization/

An important addition to this is priors: deep networks allow to express the prior that hierarchical representation, i.e. composing into multiple layers of abstractions make sense (see e.g. conv nets).

If an SVM kernel can replicate a 2 layer NN, why couldn't there be a kernel for a X layer NN, and then autoderive the architecture just like SVMs can autoderive the correct number of neurons? Then there'd also be a more robust theoretical understanding of what's happening.

See my other point, there might be, in fact there definitely is for any working NN, but as of now (2019, happy new year) we probably can't find it

An infinitely sized 2 layer NN is universal in the same way a Turing machine is universal — sure you can write any program; God help you if you try.

If i remember my Goodfellow correctly (and quickly checking, wikipedia, I did https://en.wikipedia.org/wiki/Universal_approximation_theore... ), there is a nuance here which is almost always missed: you can represent any function with a sufficiently wide 2 layer neural network, it doesn't say anything about being able tune the network until you find a correct setting (i.e. learnability).

This is important. Flippantly said,discarding learnability and speed of convergence, you can get the power of any neural network by the following algorithm:

1. Randomly generates a sufficiently wide bit pattern 2. Interprets it as a program and run it on the test set 3. discard results until the desired accuracy is reached

Fwiw the "deep learning" advances in NLP have typically still been from shallow networks, almost always less than 10 layers and usually more like 2.

Could you say a little more about this?

I ask because when we're training human to understand things, there are a variety of benefits to separate feature-understanding from the classifiers. In particular, you get gains in flexibility, extendability, and debuggability.

I get why people are happy to take the ConvNet gains and run with them for now. But have you seen any interesting work to get the benefits of separation in the new paradigm? (Or, alternately, is there a reason why those concerns are outmoded?)

That's actually closer to how deep learning started. Initially, deep learning mostly consisted of unsupervised (task independent) features with a linear classifier on top. We had to fit an unsupervised model (e.g. autoencoder) layer by layer before using the feature layers in a supervised task.

This was because we didn't understand how to train a deep model end-to-end until later. When we learned how to make that end-to-end training work it tended to perform better because the learned features were task specific.

You can still learn general features in a bunch of ways, in addition to the older method using autoencoders. For one example, multiple supervised heads with auxiliary losses can learn more generalize features.

To be fair there is a lot of domain knowledge embedded in the use of a convolutional architecture. There is a fascinating paper where the authors don't even train the weights of the convolutional layers and are still able to achieve good performance.

https://arxiv.org/pdf/1606.04801v2.pdf

It’s also hard to separate the design of the neural architecture from the definition of the feature extractor.

I feel like we pushed features into the architecture and called it a day.

Otherwise, why we would we need a gazillion architectures for different problems (or even the same exact problem)?

You still may want to replace softmax layer with support vector machine for classification sometimes.

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