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Why train when you can optimize?

justinmeiners.github.io

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Re: Why train when you can optimize?

#61

Post by steppi »

PheonixPharts wrote: post #58
steppi wrote: post #57

Earlier quoted context omitted.

It's a bit of a shame that neural networks are weak in this area because it would be incredible to have a good tool to approximate inverse functions in general. The fact that we almost never see neural networks being used as a tool for this type of work is evidence of this limitation. It's funny you say. I haven't actually used NNs much in my research but my background is in math and in my spare time I'm a maintainer…

> I might take up your challenge and write a blog post about it or something if I get any success. Success or failure, I would really enjoy seeing that write up! I would be even more excited to be proven wrong. The promise of "universal function approximator" is very temping. My personal dream would be to have it so one could essentially run scipy in reverse and learn the entire library with a NN. Even in the case I…

What a coincidence. Pyro has basically become my go to for Bayesian learning and I know those docs in and out. I’ve also skimmed that David Blei article before. Small world. I’m not very confident of success but it seems like an interesting path to explore.

Re: Why train when you can optimize?

#62

Post by Der_Einzige »

PheonixPharts wrote: post #55
steppi wrote: post #4

Neural networks can approximate any function, but that doesn’t mean they do so efficiently. Depending on the function, they can require incredible amounts of neurons and training. At their worst, they devolve into a lookup table. It’s not hard to find these examples either. Just try training a neural network to compute sin(x)! This is possible! One of the cool things about neural networks is that you can try to encod…

> Just try training a neural network to compute sin(x)! This is also the classic demo case for LSTMs, I have a notebook open right now that as a LSTM learning the sine function quite well with 32 dimensional state vector. However the authors point still stands. Neural Networks are not great at computing arbitrary functions where the output is an unbounded real number. The sine function is still limited to range that…

Is it that neural networks are weak or is it that gradient descent/backprop doesn't do well for finding good local solutions for these kinds of problems?

Re: Why train when you can optimize?

#63

Post by freemint »

doubleunplussed wrote: post #26
omrjml wrote: post #25

Earlier quoted context omitted.

Periodic function like sin(x) are not a dynamical system so its previous state does not determine the current state. So it should be approximated in that way.

Periodic functions like sin(x) are the solutions to differential equations like dy/dx = -y that describe for example, oscillations of springs, to name but one of an extremely large number of dynamical systems that behave this way.

sin(x) only arises as solution in second order systems. So d^2x/dt^2 = -x

Re: Why train when you can optimize?

#64

Post by venividivini »

cweill wrote: post #7
Buttons840 wrote: post #2

I've always been interested in reinforcement learning, believing it will magically solve anything I throw at it. Unfortunately, I haven't got it to work everywhere yet. I hoped to learn a couple good RL algorithms and then never have to actually learn the concrete details of optimization, because RL can do almost as good. I don't truly believe this, but I think it is an underlying psychological reason for my love of…

The Deepmind lead behind AlphaStar, there StarCraft 2 bot that beat several world champs, once said, "the best way to solve a reinforcement learning problem is with supervised learning". That's because supervised learning is relatively extremely efficient, and just RL with more constraints. Just start learning the basics of supervised learning for classification and regression on common benchmark tasks like CIFAR and…

I've been working on imitation learning recently and can attest that reducing RL to supervised learning gives remarkable results, even when using naive algorithms (like Behavioral Cloning).

That's an excellent quote by the way, do you perhaps have any source? Sounds like a good opener slide :)

Re: Why train when you can optimize?

#65

Post by srean »

orbifold wrote: post #51
em500 wrote: post #39

Earlier quoted context omitted.

I have the creeping feeling that soon the field is going to reinvent all of Fourier analysis from scratch.

It will be called „Neural Harmonic Analysis“, it will cite one paper by a Russian and otherwise ignore any prior work which didn’t include the word neural network.

Its sad that this is not far from the truth

Re: Why train when you can optimize?

#66

Post by vidarh »

omrjml wrote: post #25
zarzavat wrote: post #18

Earlier quoted context omitted.

It’s hard to walk if you can’t feel your legs. The problem is improperly evaluating the neural network as a function of time, instead of evaluating the network as a function of previous state. When we humans approximate functions (let’s say you’re drawing it on a piece of paper, or waving your arm around) we do not simply look at a clock and feed forward that information directly into our motor neurons. Rather, we ha…

Periodic function like sin(x) are not a dynamical system so its previous state does not determine the current state. So it should be approximated in that way.

It sounds like you're trying to say something different than the comment you replied to. sin(x) for a range of x is trivial to draw by looking at earlier parts of the curve to determine what to draw next. Back in the slow 1980's home computer days, on machines without floating point and multiply/divide, we quickly got used to approximate sine waves numerically by simply typing out sequences of integers with a rough idea of the wave it'd produce. If you gave me a subset of such a sequence and asked me to complete it, I wouldn't need much of it to assume you were wanting to approximate sin.

Re: Why train when you can optimize?

#67

Post by doubleunplussed »

freemint wrote: post #63
doubleunplussed wrote: post #26

Earlier quoted context omitted.

Periodic functions like sin(x) are the solutions to differential equations like dy/dx = -y that describe for example, oscillations of springs, to name but one of an extremely large number of dynamical systems that behave this way.

sin(x) only arises as solution in second order systems. So d^2x/dt^2 = -x

Sorry, you're absolutely correct. Brain fart. The equation I wrote actually is for an exponential, whoops.

Re: Why train when you can optimize?

#68

Post by steppi »

Der_Einzige wrote: post #62
PheonixPharts wrote: post #55

Earlier quoted context omitted.

> Just try training a neural network to compute sin(x)! This is also the classic demo case for LSTMs, I have a notebook open right now that as a LSTM learning the sine function quite well with 32 dimensional state vector. However the authors point still stands. Neural Networks are not great at computing arbitrary functions where the output is an unbounded real number. The sine function is still limited to range that…

Is it that neural networks are weak or is it that gradient descent/backprop doesn't do well for finding good local solutions for these kinds of problems?

My understanding is that it's because extrapolation is difficult in general. Extrapolating the behavior of a periodic function like sine is one thing, but extrapolating the behavior of a 1d function that tends to infinity is another challenge altogether. I happen to be very familiar with the implementation of the inverse CDF of the normal distribution though. My plan is to cook a lot of prior knowledge into the NN. Even if I get it working, the end result will likely seem more like sleight of hand than something truly impressive.

Re: Why train when you can optimize?

#69

Post by deterministic »

Optimisers are perfect for solving problems where you don’t have access to a large training set. I actually recommend starting with an optimisation algorithm first and only then try NN if using an optimisation algorithm isn’t enough to solve the problem.

Re: Why train when you can optimize?

#70

Post by thomasahle »

steppi wrote: post #4

Neural networks can approximate any function, but that doesn’t mean they do so efficiently. Depending on the function, they can require incredible amounts of neurons and training. At their worst, they devolve into a lookup table. It’s not hard to find these examples either. Just try training a neural network to compute sin(x)! This is possible! One of the cool things about neural networks is that you can try to encod…

While `x + sin(x)^2` may be monotonic itself, it only takes a simple linear combination of two neurons like `x+sin(x)^2 - (x/2 + sin(x/2)^2)` before you have a completely crazy loss landscape. I have a feeling this is why such activation functions haven't become standard.
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