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Empiricism and the limits of gradient descent

togelius.blogspot.com

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Re: Empiricism and the limits of gradient descent

#31

Post by irishsultan »

maxander wrote: post #8
perl4ever wrote: post #3

Earlier quoted context omitted.

I don't understand how E=mc^2 can not be in the data. If it's a universal law, isn't it in more (all) data than any pattern that isn't universal?

The article is making a simpler point than that. If I show you the table: A B C 1 4 3 20 45 15 8 15 7 And so on for some arbitrary number of rows, you can look at the table all you want but you will not perceive "A+C=B". It's just not written there. To get A+C=B you have to generate something else in addition to the table, namely a hypothesis- but this is a creative act, not an empirical one.

Well, that hypotesis would be wrong in this particular case (check the middle row).

Which doesn't make your point wrong of course, and this is for a simple function.

Re: Empiricism and the limits of gradient descent

#32

Post by 2sk21 »

_0w8t wrote: post #29
simonster wrote: post #14

There are a couple of factual errors here. First, the difference between backprop and evolution is smaller than the author indicates. The error signal used in modern backprop training is stochastic because it is computed on a minibatch (which is why it's called stochastic gradient descent). This stochasticity seems important to achieving good results. And the most popular evolutionary algorithm in the deep learning w…

Recently I was involved in calibrating a thermal infrared camera at work. A colleague out of curiosity tried to use machine learning and ended up with model containing hundreds of parameters (weights). Yet it was not better than a trivial model using a Planck integral (based on simple assumption about how things worked) and a linear regression (to account for systematic errors), 2 parameters in total. And the simple…

ML is a blunt instrument in such situations. I think your example illustrates the point of the original article very nicely.

Re: Empiricism and the limits of gradient descent

#33

Post by AstralStorm »

perl4ever wrote: post #18
maxander wrote: post #8

Earlier quoted context omitted.

The article is making a simpler point than that. If I show you the table: A B C 1 4 3 20 45 15 8 15 7 And so on for some arbitrary number of rows, you can look at the table all you want but you will not perceive "A+C=B". It's just not written there. To get A+C=B you have to generate something else in addition to the table, namely a hypothesis- but this is a creative act, not an empirical one.

It seems to me that A+C=B and E=mc^2 are both written in, or consistent with, that table. But widening the context produces something different in each from a probabilistic perspective. A+C=B is 100% certain with narrow context, but falsified with a little more context, while E=mc^2 is less certain with narrow context, but increasingly certain with wider context.* *Like, this table is on a computer connected to a glo…

Yes, but this is just total energy. Try kinetic energy instead. (Even Newton's Ek=0.5 * mv^2 much less Lorentz special relativity or general relativity.)

Now the model with kinetic energy plus rest energy. A network unaware of time will be unable to figure it out. Especially the differential in velocity.

What you need to actually devise such laws is generalizing conflict-driven clause learning with some good rule to pick models, name them and enumerate them. E.g. defining minimum generalizing set of logic clauses with support for undecidable and uncomputable functions. (Which means deciding when to give up.) This is essentially the inverse of a MAX-SAT solver. Minimax logic representation so to speak.

Re: Empiricism and the limits of gradient descent

#34

Post by AstralStorm »

tlb wrote: post #11
petermcneeley wrote: post #7

Earlier quoted context omitted.

Speed of light has been experimentally determined long before the 40s. The discovery of the speed of light being constant lead to the special relativity (aka before GR which is the E=mcc). http://www.speed-light.info/measure/speed_of_light_history.h...

The speed of light is easy to measure. What's hard is measuring the change in mass when something gains or loses energy. A large nuclear reactor running for a year only loses a few grams of mass-energy -- you can't measure it accurately enough or be sure that the mass didn't go somewhere else like into the cooling water.

Technically with billions of events you can. This is how LHC and other particle accelerator data is analysed.

The interesting part is detecting systematic errors. (Human equivalent is "are my senses lying right now".)

Re: Empiricism and the limits of gradient descent

#35

Post by nabla9 »

simonster wrote: post #14

There are a couple of factual errors here. First, the difference between backprop and evolution is smaller than the author indicates. The error signal used in modern backprop training is stochastic because it is computed on a minibatch (which is why it's called stochastic gradient descent). This stochasticity seems important to achieving good results. And the most popular evolutionary algorithm in the deep learning w…

Also. Neural networks commonly use dropout regularization. In dropout your train only fraction (typically 50%) of randomly selected neurons. Effectively creating essembles.

Gradient descent and evolutionary algorithms (and many other search algorithms) advance in the hypothesis space with incremental (stochastic) steps and both algorithms are path dependent. How they generate and update their hypothesis, how big steps they take, how they represent their state, and how they apply randomness creates unique learning bias but there is nothing fundamentally different.

Re: Empiricism and the limits of gradient descent

#36

Post by goatlover »

simonster wrote: post #14

There are a couple of factual errors here. First, the difference between backprop and evolution is smaller than the author indicates. The error signal used in modern backprop training is stochastic because it is computed on a minibatch (which is why it's called stochastic gradient descent). This stochasticity seems important to achieving good results. And the most popular evolutionary algorithm in the deep learning w…

> Given sufficient training data, a neural network can probably learn to model physics.

Maybe basic Newtonian physics, but I seriously doubt any ANN we've built to date could come up with QM or Relativity no matter how wonderfully massive and accurate the data was.

Looks to me like those required sophisticated conceptual understanding of the world in addition to leaps of the imagination and creative thought experiments.

Re: Empiricism and the limits of gradient descent

#37

Post by goatlover »

tlb wrote: post #12
maxander wrote: post #8

Earlier quoted context omitted.

The article is making a simpler point than that. If I show you the table: A B C 1 4 3 20 45 15 8 15 7 And so on for some arbitrary number of rows, you can look at the table all you want but you will not perceive "A+C=B". It's just not written there. To get A+C=B you have to generate something else in addition to the table, namely a hypothesis- but this is a creative act, not an empirical one.

If you connect A and B as the input to a linear neural net, and train against C, it'll very quickly arrive at weights of [-1, +1] and be able to correctly predict C given A and B. Whether or not it represents it in notation humans are familiar with, it has learned it for the practical purpose of being able to compute the function.

But how would a neural network know to connect data for mass with data for the measured speed of light? Why would a neural network be looking for an equation for energy conversion in the first place? If you just provide tons of raw data from instruments, what does that mean? What do yo do with it?

Sure, a human can clean the data and put it into a format that gives meaningful results. But if we're just talking about an AI learning from raw data with no supervision, where does it even start?

Re: Empiricism and the limits of gradient descent

#38

Post by mannykannot »

goatlover wrote: post #37
tlb wrote: post #12

Earlier quoted context omitted.

If you connect A and B as the input to a linear neural net, and train against C, it'll very quickly arrive at weights of [-1, +1] and be able to correctly predict C given A and B. Whether or not it represents it in notation humans are familiar with, it has learned it for the practical purpose of being able to compute the function.

But how would a neural network know to connect data for mass with data for the measured speed of light? Why would a neural network be looking for an equation for energy conversion in the first place? If you just provide tons of raw data from instruments, what does that mean? What do yo do with it? Sure, a human can clean the data and put it into a format that gives meaningful results. But if we're just talking about…

As someone who finds this interesting but does not know enough to take a position, I think a bigger question would be how does it come up with the abstract concept of energy?

I am aware that Alpha Go Zero came up with various strategic abstractions of the game that are recognized by competent players, and some novel ones, but I do not know where this program and its self-play training stands in the dichotomy of this debate.

Re: Empiricism and the limits of gradient descent

#39

Post by togelius »

simonster wrote: post #14

There are a couple of factual errors here. First, the difference between backprop and evolution is smaller than the author indicates. The error signal used in modern backprop training is stochastic because it is computed on a minibatch (which is why it's called stochastic gradient descent). This stochasticity seems important to achieving good results. And the most popular evolutionary algorithm in the deep learning w…

I had to make a few simplifications to spell out the differences clearly and avoid making the text infinitely long. It's true that most current gradient descent algorithms are stochastic because they are computed in batch mode, and that sophisticated evolution strategies approximate the gradient. I still think the differences are significant, in that evolution updates less often and the direction of the update is much less (if at all) dependent on the feedback.

Now, your point about to what extent this is really about neural networks is a good one. Could a network learn F=ma, even if we could not interpret it? Maybe. With the right data, represented the right way.

Re: Empiricism and the limits of gradient descent

#40

Post by vinn124 »

hmartiros wrote: post #9

In my experience if you have even a little smoothness in your problem's cost manifold, taking advantage of gradients is invaluable to sample efficiency. Many losses which don't seem differentiable can be reformulated as such - you can look around and see a wide array of algorithms being put into end-to-end learned frameworks. If the dimensionality is small, second-order methods (or approximations thereof) can do dram…

> Many losses which don't seem differentiable can be reformulated as such...

agreed, especially with policy gradients.

> If the dimensionality is small, second-order methods (or approximations thereof) can do dramatically better yet.

i have not seen second order derivatives in practice, presumably due to memory limitations. can you point me to examples?

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