A Computationally Universal Field Computer That is Purely Linear
David H. Wolpert, Bruce James MacLennan · 1993
As defined in MacLennan (1987), a field computer is a (spatial) continuum-limit neural net. This paper investigates field computers whose temporal dynamics is also continuum-limit, being governed by an integro-differential equation. Such systems are motivated both as a means of studying neural nets and as a model for cognitive processing. As this paper proves, even when they are purely linear. such systems are computationally universal. The "trick" used to get such universal nonlinear behavior from a purely linear system is quite similar to the way nonlinear macroscopic physics arises from the purely linear microscopic physics of Schrodinger's equation. More precisely, the "trick" involves interpreting the system in a non-linear way. That is, the meaning of the system's output is determined by which neurons have an activation exceeding a threshold (which in this paper is taken to be 0), rather than by the actual activation values of the neurons. (This The Santa Fe Institute, 1399 Hy...