Two neural networks that are trained on their mutual output synchronize to an identical time dependant weight vector. This novel phenomenon can be used for creation of a secure cryptographic secret-key using a public channel. Several models for this cryptographic system have been suggested, and have been tested for their security under different sophis- ticated attack strategies. The most promising models are networks that involve chaos synchronization. The synchronization process of mutual learning is described analytically using statistical physics methods.

For any discrete-state sequence prediction algorithm A, it is always possible, using an algorithm B no more complicated than A, to generate a sequence for which A's prediction is always wrong. For any prediction algorithm A and sequence x, there exists a sequence y no more complicated than x, such that if A performs better than random on x, then it will perform worse than random on y by the same margin. An example of a simple neural network predicting a bit sequence is used to illustrate this very general but not widely recognized phenomenon. This implies that any predictor with good performance must rely on some (usually implicitly) assumed prior distributions of the problem.