Computationally Efficient Neural Field Dynamics

Abstract. We propose a modification of the dynamic neural field model of Amari [1], aiming at reducing the simulation effort by employing spaceand frequency representations of the dynamic state in parallel. Additionally, we show how the correct treatment of boundary conditions (wraparound, zero-padding) can be ensured, which is of particular importance for, e.g., vision processing. We present theoretical predictions as well as measurements of the performance differences between original and modified dynamics. In addition, we show analytically that key properties of the original model are retained by the modified version. This allows us to deduce simple conditions for the applicability and the computational advantage of the proposed model in any given application scenario.