Comment by YeGoblynQueenne | Hacker News Reader

Comment by YeGoblynQueenne | Hacker News Reader

YeGoblynQueenne

>> Our work has connections to existing work not only in deep learning, but also to various other fields

Perhaps I'm, er, biased, but the most obvious similarity that immediately jumped out to me when I started reading this article is with Inductive Programming, the broader field of machine learning algorithms that learn programs, that includes Inductive Functional Programming and Inductive Logic Programming (which I study; hence, "biased").

In fact, I'd go as far as to say that this is a new kind of Inductive Programming. Perhaps it should be called Inductive Continuous Programming or Inductive Neural Progamming or some such. But what's exceedingly clear to me is that what the article describes is a search for a program that is composed of continuous functions, guided by a strong structural bias.

The hallmarks of Inductive Progamming include an explicit encoding of strong structural biases, including by the use of a library of primitives from which the learned model is composed; a strong Occamist bias; learned models that are programs. This work ticks all the boxes. The authors might benefit from looking up the relevan bibliography.

A couple of starting pointers:

Magic Haskeller, an Inductive Functional Programming system.

http://nautilus.cs.miyazaki-u.ac.jp/%7Eskata/MagicHaskeller....

Metagol, an Inductive Logic Programming system:

https://github.com/metagol/metagol

ILASP, a system for the Inductive Learning of Answer Set Programs:

http://ilasp.com/

> In fact, I'd go as far as to say that this is a new kind of Inductive Programming.

I wouldn't. Traditional NNs are widely called funciton approximators, or function induction. That's because they're not Turing-complete, and in this case don't even have memory. This makes them decidedly not programs, just functions.

Of course, they could be modified with recurrence (a suggestion of future work), or even more complete memory systems (e.g. equipping a neural controller with a tape), making it Turing-complete.

Keep in mind the functional approximation power isn't increased by architecture search alone (there's no restriction from doing weight training). What seems novel here is how significant architecture alone is (I wouldn't guess it being this powerful), and this possibly has implications on the connection with the human brain -- in which my vague impression is that connections themselves are much more tuned than weights; also possibly giving greater emphasis on architecture training.

>> I wouldn't. Traditional NNs are widely called funciton approximators, or function induction. That's because they're not Turing-complete, and in this case don't even have memory. This makes them decidedly not programs, just functions.

But what the article describes is not function approximation anymore. Their system doesn't optimise a set of parameters. The search for an optimal set of parameters has been replaced entirely with a search for an optimal architecture with a single, shared parameter.

Note also that you don't need something to be Turing-complete for it to be a program. For instance, a regular automaton is a program, but it's not Turing complete. Turing completeness makes something, well, a Universal Turing Machine, which can compute any program. But a program is just a set of instructions.

> Note also that you don't need something to be Turing-complete for it to be a program. For instance, a regular automaton is a program, but it's not Turing complete. Turing completeness makes something, well, a Universal Turing Machine, which can compute any program. But a program is just a set of instructions.

A regular automaton is a program (and a function is a program), but all programs cannot be expressed as finite (regular) automatons (FAs). So FAs are a subset of programs. If we equate programs with mathematical algorithms, in general they really need the unlimited memory aspect (or at least the capability of abstracting memory, which in practice is always finite of course).

To make things clear, an example: a fixed function (or FA) cannot sort a list of numbers of variable size. You can train your function to sort any K numbers, which are the input variables. But because it has no memory, you cannot input variables sequentially (in the FA case you cannot input arbitrarily many variables). You've essentially created a sorting network[1].

Not only that, but for each input growth you need to re-train your architecture. The nice thing about program inference is that it hopefully captures the fundamental algorithm behind a program, which generalizes to arbitrary sizes. It's not that arbitrary sizes are necessary in practice (again computers are always bounded), it's that this abstraction/generalization is extremely useful, saving data and allowing large (arbitrary) variation in input.

[1] https://en.wikipedia.org/wiki/Sorting_network

> a Universal Turing Machine, which can compute any program

I feel there's a bit of confusion here. Turing Machines themselves can compute any program (i.e. you can represent any program as a TM) -- that follows essentially from the definition of algorithm (a set of well defined steps given unlimited paper); again languages accepted by FAs are a restricted subset of TMs (the former accepts a regular language while the latter recursively enumerable languages). There are special Turing Machines that simulate arbitrary Turing Machines -- those are called Universal Turing machines. It's a desirable characteristic of any computer, of course (the ability to input arbitrary programs).

We refer to program description languages that can describe any Turing Machine as Turing-complete. You could make a Universal Turing machine that accepts this kind of language directly or you could in principle just build a Turing machine that executes the given algorithm (for example using a gate array/FPGA to encode the state automaton, plus some large memory for the tape).

Yes, sloppy definition of Turing completenes on my part. I apologise unrservedly.

But, I still don't understand your objection. You agree that a regular automaton is a program, and that it's not Turing complete. So a program does not need to be Turing complete.

I didn't say, nor do I think, that the algorithm described in this article is Turing complete. I think it perfoms program induction. That's as far as I went. I still don't see where Turing completeness comes into it.

[sorry- splitting this off 'cause it's getting a bit large and to make the whole thing easier to read]

>> What seems novel here is how significant architecture alone is (I wouldn't guess it being this powerful), and this possibly has implications on the connection with the human brain -- in which my vague impression is that connections themselves are much more tuned than weights; also possibly giving greater emphasis on architecture training.

You are surprised by how significant architecture is. I am not surprised at all. I think it's been very clear for a while now that the success of deep neural networks is entirely due to their architectures that are fine-tuned to specific tasks. On the one hand, it's obvious that this is the case if you look at the two major successes of deep learning: CNNs for vision and LSTMs (and variants) for sequence learning. Both are extremely precise, extremely intricate architectures with an intense focus one one kind of task, and that kind of task, alone. On the other hand, the vast majority of neural net publications are specifically about new architectures, or, rather, tweaks to existing architectures.

In fact, in my boldest moments I'd go as far as to suggest that weight training with gradient optimisation has kept deep neural nets back. Gradient optimisation gets stuck in local minima, and it will always get stuck in local minima, and therefore always be dumb as bricks. Which is evident in the way deep neural nets overfit and are incapable of extrapolating outside their training datasets.

> Gradient optimisation gets stuck in local minima, and it will always get stuck in local minima, and therefore always be dumb as bricks. Which is evident in the way deep neural nets overfit and are incapable of extrapolating outside their training datasets.

This seems extremely harsh, given the vast successes of deep neural nets calling them 'dumb as bricks' (there are too many examples of extrapolation outside datasets to count[1]). They have proven generalization capability when care is taken against over fitting (almost any model has this ability). Also there are results showing getting stuck in local minima is unlikely in highly-dimensional parameter spaces (the curvature in a large number of directions needs to coincide), and in any case rarely you're seeking the global minimum because of said over-fitting issues.

[1] It should be self-evident because they would hardly be of any use if unable to extrapolate at all. See GANs (https://www.thispersondoesnotexist.com/), AlphaGo (https://en.wikipedia.org/wiki/AlphaGo), etc.

That neural nets overfit to their training data and are incapable of extrapolation is not controversial.

For a high-level discussion, see the following article, by Francois Chollet, the maintainer of the deep learning library, Keras:

https://blog.keras.io/the-limitations-of-deep-learning.html

It is also not controversial that gradient optimisation gets stuck in local optima. A good exercise to convince yourself of this is to implement a simple gradient descent algorithm and observe its behaviour.

>> [1] It should be self-evident because they would hardly be of any use if unable to extrapolate at all.

That is why deep neural nets are trained with such vast amounts of data and computing power: it's to compensate for their inability to generalise to unseen instances.

That, too, is not controversial. It is common knowledge that the recent success of deep learning is due to the availability of larger datasets and more powerful computers than in past years. For example, see this interview with Geoff Hinton:

http://techjaw.com/2015/06/07/geoffrey-hinton-deep-learning-...

Geoffrey Hinton: I think it’s mainly because of the amount of computation and the amount of data now around but it’s also partly because there have been some technical improvements in the algorithms. Particularly in the algorithms for doing unsupervised learning where you’re not told what the right answer is but the main thing is the computation and the amount of data.

The algorithms we had in the old days would have worked perfectly well if computers had been a million times faster and datasets had been a million times bigger but if we’d said that thirty years ago people would have just laughed.

I hope this is helpful. I understand there are misconceptions about the strengths and limitations of deep neural nets that are not very easy to see with the naked eye. But it's a good idea to approach such an overhypoted technology with a skeptical mind and, e.g., ask yourself: why is all that data necessary, if they are so good at learning?

Reply on news.ycombinator.com