Using a learned Artificial Neural Network to solve inputs

Question

I've recently been delving into artificial neural networks again, both evolved and trained. I had a question regarding what methods, if any, to solve for inputs that would result in a target output set. Is there a name for this? Everything I try to look for leads me to backpropagation which isn't necessarily what I need. In my search, the closest thing I've come to expressing my question is

Is it possible to run a neural network in reverse?

Which told me that there, indeed, would be many solutions for networks that had varying numbers of nodes for the layers and they would not be trivial to solve for. I had the idea of just marching toward an ideal set of inputs using the weights that have been established during learning. Does anyone else have experience doing something like this?

In order to elaborate: Say you have a network with 401 input nodes which represents a 20x20 grayscale image and a bias, two hidden layers consisting of 100+25 nodes, as well as 6 output nodes representing a classification (symbols, roman numerals, etc). After training a neural network so that it can classify with an acceptable error, I would like to run the network backwards. This would mean I would input a classification in the output that I would like to see, and the network would imagine a set of inputs that would result in the expected output. So for the roman numeral example, this could mean that I would request it to run the net in reverse for the symbol 'X' and it would generate an image that would resemble what the net thought an 'X' looked like. In this way, I could get a good idea of the features it learned to separate the classifications. I feel as it would be very beneficial in understanding how ANNs function and learn in the grand scheme of things.

Answer 1

For a simple feed-forward fully connected NN, it is possible to project hidden unit activation into pixel space by taking inverse of activation function (for example Logit for sigmoid units), dividing it by sum of incoming weights and then multiplying that value by weight of each pixel. That will give visualization of average pattern, recognized by this hidden unit. Summing up these patterns for each hidden unit will result in average pattern, that corresponds to this particular set of hidden unit activities.Same procedure can be in principle be applied to to project output activations into hidden unit activity patterns.

This is indeed useful for analyzing what features NN learned in image recognition. For more complex methods you can take a look at this paper (besides everything it contains examples of patterns that NN can learn).

You can not exactly run NN in reverse, because it does not remember all information from source image - only patterns that it learned to detect. So network cannot "imagine a set inputs". However, it possible to sample probability distribution (taking weight as probability of activation of each pixel) and produce a set of patterns that can be recognized by particular neuron.

Answer 2

I know that you can, and I am working on a solution now. I have some code on my github here for imagining the inputs of a neural network that classifies the handwritten digits of the MNIST dataset, but I don't think it is entirely correct. Right now, I simply take a trained network and my desired output and multiply backwards by the learned weights at each layer until I have a value for inputs. This is skipping over the activation function and may have some other errors, but I am getting pretty reasonable images out of it. For example, this is the result of the trained network imagining a 3: number 3

Answer 3

Yes, you can run a probabilistic NN in reverse to get it to 'imagine' inputs that would match an output it's been trained to categorise.

I highly recommend Geoffrey Hinton's coursera course on NN's here: https://www.coursera.org/course/neuralnets

He demonstrates in his introductory video a NN imagining various "2"s that it would recognise having been trained to identify the numerals 0 through 9. It's very impressive!

I think it's basically doing exactly what you're looking to do.

Gruff