7 ms·

What does a neural network actually do?

151 points by zercool 12y ago

ctdavies 12y ago
They write comments on HN.
- jacquesm 12y ago
  Those are Markov-chain based text generators. (yes, I got the joke).
  - Houshalter 12y ago
    Well recently a lot of work has gone into using NNs for natural language processing. Typically it's trained to do something like predict the next word or character in a sequence. Using that you could possibly create a far better generative model than markov chains, and create more realistic sentences. Perhaps you could even combine them (NN gets the output of the markov chain to help make it's prediction.)
  - ctdavies 12y ago
    :( I wish everyone else did.
csense 12y ago
I've found that, in practice, traditional neural networks tend to be prone to overfitting and are finicky about their parameters (in particular the topology and number of nodes you choose). I use the word "traditional" to describe the NN architecture discussed in the article. Recent NN research has been promising [1], but this article strictly discusses traditional NN's. I don't really have much experience with the newer NN algorithms, so I'm not sure to what extent they suffer from the same problems as traditional NN's. [1] http://en.wikipedia.org/wiki/Neural_network#Recent_improvements http://en.wikipedia.org/wiki/Neural_network#Recent_improveme...
- niels_olson 12y ago
  Is it safe to say that in ML, use of NNs is more about writing code that designs NNs, evaluates the results, and modifies the designs to optimize some desired meta-values, like accuracy, efficiency, etc?
- billderose 12y ago
  Hinton's DropOut [1] and Wan's DropConnect [2] have ameliorated some of the overfitting issues present in traditional NN's. In fact, DropConnect in conjunction with deep learning are responsible for new records being set on classical datasets such as MNIST. [1] http://arxiv.org/pdf/1207.0580.pdf http://arxiv.org/pdf/1207.0580.pdf [2] http://cs.nyu.edu/~wanli/dropc/ http://cs.nyu.edu/~wanli/dropc/
  - im3w1l 12y ago
    It's pretty funny, I saw DropConnect described in a stackoverflow answer that predated the paper you reference. It was an incorrect answer on how to do dropout. I shall try to find it tomorrow.
  - agibsonccc 12y ago
    Dropout is actually a knob on any neural network. These are used in image recognition as well as text and other areas. The fuzzing creates a very similar effect to convolutional nets where it can learn different poses of an image.
thegeomaster 12y ago
Looks like an interesting text, but to be honest I didn't understand a substantial portion of it.
- sillysaurus3 12y ago
  You're 17; get to work understanding it! The more you learn now, the more you'll be able to do for the rest of your life. Plus, diving into random topics and understanding them more deeply than anyone else is a ton of fun.
dlsym 12y ago
"What does a neural network actually do?" This is a fundamental Question: Can we really say and predict what a neural network does? Contrary to an engineered / constructed algorithm a neural network is 'trained'. Whenever we will present a 'known' input pattern it will reposnd with a 'learned' response. This however introduces interesting problems: How can we _debug_ a neural network? How can we debug a correlation? Sure we can tune its paramters, we can train it some more to again show the desired response. But reaching this point we just abandoned knowing how the intrinsic algorithm works in favor to just focussing on the result. Okay - now if we follow this argument - this would lead to: If we simulate the whole brain by simulating the neural network, we won't gain any knowlege about the intrinsic workings of the brain. We won't find any enlightenment about the innermost algorithm _represented_ by the neural network we call our brain.
- ShardPhoenix 12y ago
  I can't find an example on Google right now, but I've seen demonstrations that it's possible to visualize the intermediate layers of a neural network - for example you can see how an image recognition network is first breaking down an image into horizontal and vertical lines, then combining those into more complex shapes, etc.
  - agibsonccc 12y ago
    These are called filters. This is from my deep learning framework: Debugging a net visually: http://deeplearning4j.org/debug.html http://deeplearning4j.org/debug.html An example of doing facial reconstruction: http://deeplearning4j.org/facial-reconstruction-tutorial.html http://deeplearning4j.org/facial-reconstruction-tutorial.htm...
  - joe_the_user 12y ago
    But visualizing is quite a ways from debugging. To debug a program you actually verify that it's logic is correct (at least the good kind of debugging). Consider a spectrum: 1. Natural language - we humans combine fragments of natural language easily and on an ad-hoc basis. We can get a fairly amount of use from reusing Shakespeare quotes and neologisms while spending rather little effort. 2. Trained programmers can reuse and combine general purpose libraries - with difficulty and often after considerable debugging. 3. AI algorithms like Neural Networks. These are just plopped in and tweaked, not combining seems possible. It seem like "intelligent behavior" should be going more towards #1 but the process of Machine Learning seems to move things more towards #3. The "learn once, understand never" approach means that for each significant case, you'll need to do a re-tweaking and re-learning. The potential to get harder rather than easier over time might well be there.
oldspiceman 12y ago
A less mathy explanation with some real examples: http://neuralnetworksanddeeplearning.com/chap1.html http://neuralnetworksanddeeplearning.com/chap1.html Coding a digit recognizer using a neural network is an extremely rewarding exercise and there's a lot of help on the web to get you started.
- agibsonccc 12y ago
  This is a great example of a hello world application. Keep in mind there are several kinds of neural nets that allow you to do this. This includes convolutional RBMs (recognizes parts of an image) and normal RBMs (learns everything at once)
robert_tweed 12y ago
This is a pretty good article, but I'm seeing a lot of confusion in this thread because the article is maybe one step ahead of the basic intuition needed to understand why ANNs are not magical and are not artificial intelligence (at least not feed-forward networks). Perhaps a simpler way to look at it is to understand that a feed-forward ANN is basically just a really fancy transformation matrix. OK, so unless you know linear algebra, you're probably now asking what's a transformation matrix? Without the full explanation, the important understanding is why they are so important in 3D graphics: they can perform essentially arbitrary operations (translation, rotation, scaling) on points/vectors. Once you have set up your matrix, it will dutifully perform the same transformations on every point/vector you give it. In graphics programming, we use 4x4 matrices to perform these transformations on 3D points (vertices) but the same principle works in any number of dimensions - you just need a matrix that is one bigger than the number of dimensions in your data*. Edit: For NNs the matrices don't always have to be square. For instance you might want your output space to have far fewer dimensions that your input. If you want a simple yes/no decision then your output space is one-dimensional. The only reason the matrices are square in 3D graphics is because the vertices are always 3-dimensional. What a neural network does is take a bunch of "points" (the input data) in some arbitrary, high number of dimensions and performs the same transformation on all of them, so as to distort that space. The reason it does this is so that the points go from being some complex intertwining that might appear random or intractable, into something where the points are linearly separable: i.e., we can now draw a series of planes in between the data that segments it into the classifications we care about. The only difference between a transformation matrix and a neural network is that a neural network has at least two layers. In other words, it is two (or more) transformation matrices bolted together. For reasons that are a bit too complex to get into here, allows an NN to perform more complex transformations than a single matrix can. In fact, it turns out that an arbitrarily large NN can perform any polynomial-based transformation on the data. The reason this is often seen as somewhat magic is that although you can tell what transformations a neural network is doing in trivial cases, NNs are generally used where the number of dimensions is so large that reasoning about what it is doing is difficult. Different training methods can give wildly different networks that seemingly give much the same results, or fairly similar networks that give wildly different results. How easy it is to understand the various convolutions that are taking place rather depends on what the input data represents. In the case of computer vision it can be quite easy to visualise the features that each neuron in the hidden layer is looking for. In cases where the data is more arbitrary, it can be much harder to reason about, so if your training algorithm isn't performing as you'd like, it can be difficult to understand why it isn't working, even if you already understand that the basic principle of a feed-forward network is just a bunch of simple algebra.
nsxwolf 12y ago
Title made me think it would be something for beginners. Either it is not or I am very dim.
nullc 12y ago
Another limit they don't address is that the training normally used is purely local— just a gradient descent. So even when the network can model your function well, there is no guarantee that it will find the solution. For me ANN's always seem to get stuck on not very helpful local minima— they're not one of the first tools in my bags of tricks by far. Often I associate them as being the sort of thing that someone who doesn't really know what they're talking about talks about. (Esp. if its clear that in their minds NN have magical powers. :) maybe they'll also mention something about "genetic algorithms")
- nanidin 12y ago
  Well, you could use an EA to take a stab at finding better minima :) And correct me if I'm wrong, but isn't the cost function for a feed forward neural networks that uses a sigmoid activation function convex wrt the parameters being trained, i.e. gradient descent is guaranteed to find the global minimum when small enough of a step size is used?
  - chestervonwinch 12y ago
    Mostly, no. Hidden units introduce non-convexity to the cost. How bout a simple counter-example? Take a simple classifier network with one input, one hidden unit and one output and no biases. To make things even simpler, tie the two weights, i.e. make the first weight equal to the second. Now, mathematically the output of the network can be written: z=f(w * f(w * x)) where f() is the sigmoid. Next, consider a dataset with two items: [(x_1, y_1), (x_2, y_2)] where x_i is the input and y_i is the class label, 0 or 1. Take as values: [(0.9, 1), (0.1,0)]. The cost function (loglikelihood in this case) is: L(w) = sum_i { y_i * log( f(w * f(w * x_i)) ) + (1-y_i) * log( 1-f(w * f(w * x_i)) ) } or L(w) = log( f(w * f(w * 0.9)) ) + log( 1-f(w * f(w * 0.1)) ) Plot that last guy replacing f with the sigmoid, and you'll see the result is non-convex - there's a kink near zero.
- alkonaut 12y ago
  > So even when the network can model your function well, there is no guarantee that it will find the solution. If it models the function over the input domain, then it is properly trained. If it is trained to a local minima then it doesn't model the underlying function well over the whole input domain. If you have good/representative training and validation sets you will be able to tell. > Esp. if its clear that in their minds NN have magical powers I know that type. When dealing with ANN's you realize quickly (just like in all data science) that all of the "magic" relies on the manual work and thought that goes into washing and adapting the data. Not very sexy work, and work that requires a fair bit of knowledge about the problem domain. > For me ANN's always seem to get stuck on not very helpful local minima That isn't the ANN that gets stuck, it's the training algorithm (using gradient descent) that gets stuck :) Training is orthogonal to the operation of the network itself (which is just a nonlinear function in the end!). Gradient descent via error backpropagation is the most common training method for MLP's, but you could imagine doing a random/brute force algorithm that is significantly simpler to implement, but slower. Since a network is often trained once and then used repeatedly, it is often plausible to train it for several weeks if needed! A pure random search is usually not feasible, but adding randomization to a gradient descent will help. There are many ways to avoid local minima for a gradient desccent, if you have time to wait. > maybe they'll also mention something about "genetic algorithms" The simple error backpropagation methods only work well for normal feed-forward networks. Other topologies e.g. recurrent networks require more exotic methods. In my (limited) experience genetic algorithms are rarely efficient as a training method though.
neuralnet 12y ago
http://www.dkriesel.com/en/science/neural_networks http://www.dkriesel.com/en/science/neural_networks about 200 page bilingual ebook about neural networks containing lots of illustrations, in case some guys of you want to read further. There's also a nice java framework to try out for the coders.

151 points by zercool 12y ago

ctdavies 12y ago

They write comments on HN.

jacquesm 12y ago
Those are Markov-chain based text generators. (yes, I got the joke).
- Houshalter 12y ago
  Well recently a lot of work has gone into using NNs for natural language processing. Typically it's trained to do something like predict the next word or character in a sequence. Using that you could possibly create a far better generative model than markov chains, and create more realistic sentences. Perhaps you could even combine them (NN gets the output of the markov chain to help make it's prediction.)
- ctdavies 12y ago
  :( I wish everyone else did.

csense 12y ago

I've found that, in practice, traditional neural networks tend to be prone to overfitting and are finicky about their parameters (in particular the topology and number of nodes you choose). I use the word "traditional" to describe the NN architecture discussed in the article. Recent NN research has been promising [1], but this article strictly discusses traditional NN's. I don't really have much experience with the newer NN algorithms, so I'm not sure to what extent they suffer from the same problems as traditional NN's. [1] http://en.wikipedia.org/wiki/Neural_network#Recent_improvements http://en.wikipedia.org/wiki/Neural_network#Recent_improveme...

niels_olson 12y ago
Is it safe to say that in ML, use of NNs is more about writing code that designs NNs, evaluates the results, and modifies the designs to optimize some desired meta-values, like accuracy, efficiency, etc?
billderose 12y ago
Hinton's DropOut [1] and Wan's DropConnect [2] have ameliorated some of the overfitting issues present in traditional NN's. In fact, DropConnect in conjunction with deep learning are responsible for new records being set on classical datasets such as MNIST. [1] http://arxiv.org/pdf/1207.0580.pdf http://arxiv.org/pdf/1207.0580.pdf [2] http://cs.nyu.edu/~wanli/dropc/ http://cs.nyu.edu/~wanli/dropc/
- im3w1l 12y ago
  It's pretty funny, I saw DropConnect described in a stackoverflow answer that predated the paper you reference. It was an incorrect answer on how to do dropout. I shall try to find it tomorrow.
- agibsonccc 12y ago
  Dropout is actually a knob on any neural network. These are used in image recognition as well as text and other areas. The fuzzing creates a very similar effect to convolutional nets where it can learn different poses of an image.

thegeomaster 12y ago

Looks like an interesting text, but to be honest I didn't understand a substantial portion of it.

sillysaurus3 12y ago
You're 17; get to work understanding it! The more you learn now, the more you'll be able to do for the rest of your life. Plus, diving into random topics and understanding them more deeply than anyone else is a ton of fun.

dlsym 12y ago

"What does a neural network actually do?" This is a fundamental Question: Can we really say and predict what a neural network does? Contrary to an engineered / constructed algorithm a neural network is 'trained'. Whenever we will present a 'known' input pattern it will reposnd with a 'learned' response. This however introduces interesting problems: How can we _debug_ a neural network? How can we debug a correlation? Sure we can tune its paramters, we can train it some more to again show the desired response. But reaching this point we just abandoned knowing how the intrinsic algorithm works in favor to just focussing on the result. Okay - now if we follow this argument - this would lead to: If we simulate the whole brain by simulating the neural network, we won't gain any knowlege about the intrinsic workings of the brain. We won't find any enlightenment about the innermost algorithm _represented_ by the neural network we call our brain.

ShardPhoenix 12y ago
I can't find an example on Google right now, but I've seen demonstrations that it's possible to visualize the intermediate layers of a neural network - for example you can see how an image recognition network is first breaking down an image into horizontal and vertical lines, then combining those into more complex shapes, etc.
- agibsonccc 12y ago
  These are called filters. This is from my deep learning framework: Debugging a net visually: http://deeplearning4j.org/debug.html http://deeplearning4j.org/debug.html An example of doing facial reconstruction: http://deeplearning4j.org/facial-reconstruction-tutorial.html http://deeplearning4j.org/facial-reconstruction-tutorial.htm...
- joe_the_user 12y ago
  But visualizing is quite a ways from debugging. To debug a program you actually verify that it's logic is correct (at least the good kind of debugging). Consider a spectrum: 1. Natural language - we humans combine fragments of natural language easily and on an ad-hoc basis. We can get a fairly amount of use from reusing Shakespeare quotes and neologisms while spending rather little effort. 2. Trained programmers can reuse and combine general purpose libraries - with difficulty and often after considerable debugging. 3. AI algorithms like Neural Networks. These are just plopped in and tweaked, not combining seems possible. It seem like "intelligent behavior" should be going more towards #1 but the process of Machine Learning seems to move things more towards #3. The "learn once, understand never" approach means that for each significant case, you'll need to do a re-tweaking and re-learning. The potential to get harder rather than easier over time might well be there.

oldspiceman 12y ago

A less mathy explanation with some real examples: http://neuralnetworksanddeeplearning.com/chap1.html http://neuralnetworksanddeeplearning.com/chap1.html Coding a digit recognizer using a neural network is an extremely rewarding exercise and there's a lot of help on the web to get you started.

agibsonccc 12y ago
This is a great example of a hello world application. Keep in mind there are several kinds of neural nets that allow you to do this. This includes convolutional RBMs (recognizes parts of an image) and normal RBMs (learns everything at once)

robert_tweed 12y ago

This is a pretty good article, but I'm seeing a lot of confusion in this thread because the article is maybe one step ahead of the basic intuition needed to understand why ANNs are not magical and are not artificial intelligence (at least not feed-forward networks). Perhaps a simpler way to look at it is to understand that a feed-forward ANN is basically just a really fancy transformation matrix. OK, so unless you know linear algebra, you're probably now asking what's a transformation matrix? Without the full explanation, the important understanding is why they are so important in 3D graphics: they can perform essentially arbitrary operations (translation, rotation, scaling) on points/vectors. Once you have set up your matrix, it will dutifully perform the same transformations on every point/vector you give it. In graphics programming, we use 4x4 matrices to perform these transformations on 3D points (vertices) but the same principle works in any number of dimensions - you just need a matrix that is one bigger than the number of dimensions in your data*. Edit: For NNs the matrices don't always have to be square. For instance you might want your output space to have far fewer dimensions that your input. If you want a simple yes/no decision then your output space is one-dimensional. The only reason the matrices are square in 3D graphics is because the vertices are always 3-dimensional. What a neural network does is take a bunch of "points" (the input data) in some arbitrary, high number of dimensions and performs the same transformation on all of them, so as to distort that space. The reason it does this is so that the points go from being some complex intertwining that might appear random or intractable, into something where the points are linearly separable: i.e., we can now draw a series of planes in between the data that segments it into the classifications we care about. The only difference between a transformation matrix and a neural network is that a neural network has at least two layers. In other words, it is two (or more) transformation matrices bolted together. For reasons that are a bit too complex to get into here, allows an NN to perform more complex transformations than a single matrix can. In fact, it turns out that an arbitrarily large NN can perform any polynomial-based transformation on the data. The reason this is often seen as somewhat magic is that although you can tell what transformations a neural network is doing in trivial cases, NNs are generally used where the number of dimensions is so large that reasoning about what it is doing is difficult. Different training methods can give wildly different networks that seemingly give much the same results, or fairly similar networks that give wildly different results. How easy it is to understand the various convolutions that are taking place rather depends on what the input data represents. In the case of computer vision it can be quite easy to visualise the features that each neuron in the hidden layer is looking for. In cases where the data is more arbitrary, it can be much harder to reason about, so if your training algorithm isn't performing as you'd like, it can be difficult to understand why it isn't working, even if you already understand that the basic principle of a feed-forward network is just a bunch of simple algebra.

nsxwolf 12y ago

Title made me think it would be something for beginners. Either it is not or I am very dim.

nullc 12y ago

Another limit they don't address is that the training normally used is purely local— just a gradient descent. So even when the network can model your function well, there is no guarantee that it will find the solution. For me ANN's always seem to get stuck on not very helpful local minima— they're not one of the first tools in my bags of tricks by far. Often I associate them as being the sort of thing that someone who doesn't really know what they're talking about talks about. (Esp. if its clear that in their minds NN have magical powers. :) maybe they'll also mention something about "genetic algorithms")

nanidin 12y ago
Well, you could use an EA to take a stab at finding better minima :) And correct me if I'm wrong, but isn't the cost function for a feed forward neural networks that uses a sigmoid activation function convex wrt the parameters being trained, i.e. gradient descent is guaranteed to find the global minimum when small enough of a step size is used?
- chestervonwinch 12y ago
  Mostly, no. Hidden units introduce non-convexity to the cost. How bout a simple counter-example? Take a simple classifier network with one input, one hidden unit and one output and no biases. To make things even simpler, tie the two weights, i.e. make the first weight equal to the second. Now, mathematically the output of the network can be written: z=f(w * f(w * x)) where f() is the sigmoid. Next, consider a dataset with two items: [(x_1, y_1), (x_2, y_2)] where x_i is the input and y_i is the class label, 0 or 1. Take as values: [(0.9, 1), (0.1,0)]. The cost function (loglikelihood in this case) is: L(w) = sum_i { y_i * log( f(w * f(w * x_i)) ) + (1-y_i) * log( 1-f(w * f(w * x_i)) ) } or L(w) = log( f(w * f(w * 0.9)) ) + log( 1-f(w * f(w * 0.1)) ) Plot that last guy replacing f with the sigmoid, and you'll see the result is non-convex - there's a kink near zero.
alkonaut 12y ago
> So even when the network can model your function well, there is no guarantee that it will find the solution. If it models the function over the input domain, then it is properly trained. If it is trained to a local minima then it doesn't model the underlying function well over the whole input domain. If you have good/representative training and validation sets you will be able to tell. > Esp. if its clear that in their minds NN have magical powers I know that type. When dealing with ANN's you realize quickly (just like in all data science) that all of the "magic" relies on the manual work and thought that goes into washing and adapting the data. Not very sexy work, and work that requires a fair bit of knowledge about the problem domain. > For me ANN's always seem to get stuck on not very helpful local minima That isn't the ANN that gets stuck, it's the training algorithm (using gradient descent) that gets stuck :) Training is orthogonal to the operation of the network itself (which is just a nonlinear function in the end!). Gradient descent via error backpropagation is the most common training method for MLP's, but you could imagine doing a random/brute force algorithm that is significantly simpler to implement, but slower. Since a network is often trained once and then used repeatedly, it is often plausible to train it for several weeks if needed! A pure random search is usually not feasible, but adding randomization to a gradient descent will help. There are many ways to avoid local minima for a gradient desccent, if you have time to wait. > maybe they'll also mention something about "genetic algorithms" The simple error backpropagation methods only work well for normal feed-forward networks. Other topologies e.g. recurrent networks require more exotic methods. In my (limited) experience genetic algorithms are rarely efficient as a training method though.

neuralnet 12y ago

http://www.dkriesel.com/en/science/neural_networks http://www.dkriesel.com/en/science/neural_networks about 200 page bilingual ebook about neural networks containing lots of illustrations, in case some guys of you want to read further. There's also a nice java framework to try out for the coders.