Simulation of networks using multidimensional Fast Fourier Transforms

A fast method is presented for simulating a class of systems that includes certain regular neural networks based on neurons that perform a weighted spatial summation as a part of their operation. The method employs high-speed convolution via the Fast Fourier Transform. Some important aspects are emphasized: first, even though the FFT is essential, the neurons do not need to be completely linear (they can have time varying thresholds for example); second, simulations of networks with very dense interconnections are encouraged (they take no more time then sparse ones using this method); and finally, the method is suggestive of similar but more general computational schemes.