A gradient descent method for a neural fractal memory

It has been demonstrated that higher order recurrent neural networks exhibit an underlying fractal attractor as an artifact of their dynamics. These fractal attractors offer a very efficient mechanism to encode visual memories in a neural substrate, since even a simple twelve weight network can encode a very large set of different images. The main problem in this memory model, which so far has remained unaddressed, is how to train the networks to learn these different attractors. Following other neural training methods this paper proposes a gradient descent method to learn the attractors. The method is based on an error function which examines the effects of the current network transform on the desired fractal attractor. It is tested across a bank of different target fractal attractors and at different noise levels. The results show positive performance across three error measures