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 o er a very e cent mechanism to encode visual memories in a neural substrate, since even a simple twelve weight network can encode a very large set of di erent images. The main problem in this memory model, which so far has remained unaddressed, is how to train the networks to learn these di erent 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 e ects of the current network transform on the desired fractal attractor. It is tested across a bank of di erent target fractal attractors and at di erent noise levels. The results show positive performance across three error measures. Keywords| Recurrent Neural Networks, Dynamical Systems, Fractals, Iterated Function Systems, Inverse Fractal Problem, Learning Rules, Gradient Descent.