Can neural network can be used to predict pseudo-random numbers? Given list of numbers which looks pseudo-random (like lotto numbers, stock prices, pseudo-random), is it is possible to train the network to attempt to predict the next numbers?
Which network would be more suitable for this task? Feedforward, recurrent or any other neural network?
Especially the one which will work without memorizing the entire training set, but the one which can find some patterns or statistical association.
 A: A recent paper in this vein can be found in "Learning from Pseudo-Randomness with an Artificial Neural Network – Does God Play Pseudo-Dice?" by Fenglei Fan & Ge Wang.

Inspired by the fact that the neural network, as the mainstream method for machine learning, has brought successes in many application areas, here we propose to use this approach for decoding hidden correlation among pseudo-random data and predicting events accordingly. With a simple neural network structure and a typical training procedure, we demonstrate the learning and prediction power of the neural network in pseudorandom environments. Finally, we postulate that the high sensitivity and efficiency of the neural network may allow to learn on a low-dimensional manifold in a high-dimensional space of pseudo-random events and critically test if there could be any fundamental difference between quantum randomness and pseudo randomness, which is equivalent to the classic question: Does God play dice? 

Moreover, the references cited in the paper comprise a partial literature review of other efforts to model PRNGs using neural networks.
