# Replacing Folk Psychology with a Neurocomputational Model

The Churchlands reject the symbolic AI conception of mental processes in terms of symbols and rules because it does not adequately reflect the brain’s computational architecture. They see the brain as a parallel-processing machine, performing mathematical calculations in neural networks. The Churchlands’ view builds on artificial neural networks research as pioneered in AI. Let us look at an example of a simple network that implements a logical function called XOR (“exclusive or”) to illustrate how artificial neural networks function. The network has five nodes (n1-n5).

The network has an input layer, a hidden layer, and an output layer. The nodes have connections, and each connection has a strength. Whatever values are given to nodes n1 and n2 are propagated through the network by multiplication and summation over the links. If we assume that the input values (of n1 and n2) can be either 1 or 0, then this network returns a 1 in the output node (n5) only if n1 = 1 or n2 = 1 but not when both are equal to 0 or both are equal to 1. This is called an “exclusive or” or, more briefly, an XOR operation. Let us look at an example. We begin with giving the input vector {0, 1} as a test. An input vector is a set of numbers that gives values to the input nodes. An input vector of {0, 1} instantiates n1 with 0 and n2 with 1. Four multiplications over the links from n1 and n2 (n1n3, n2n3, n1n4, n2n4) and two summations over the same links (n3 = n1n3 + n2n3 and n4 = n1n4 + n2n4) propagate values to n3 and n4. n3 is going to assume the value n1n3 + n2n3 = 0 x 1 + -1 x 1 = -1, so n3 = -1. n4 assumes the value n2n4 + n1n4 = 1 x 1 + 0 x -1 = 1. If we assume that nodes in the hidden layer propagate values only if they have a value greater than 0, then n3 will not propagate any value to n5 but n4 will propagate the value 1 x 1 = 1 to n5. You can try other input vectors to verify that the following XOR table is correct:

According to the table, you get a 1 in n5 only when either n1 or n2 = 1 but not both at the same time. Let us now consider the Churchlands’ neurocomputational approach in more detail.

Paul gives an example of how to think about vector-based representation and processing in visual perception, using a television metaphor (Churchland and Churchland 1998, p. 13). Suppose we are watching a tree on a TV screen. Perception begins with a vector-based representation, electrochemically transduced by rods and cones into a neural vector pattern in the space of 130 million retinal cells. This vector is mapped onto the smaller vector of the optic nerve (approximately 1.2 million fibers) through vector processing. Further transformations are done at the lateral geniculate nucleus (LGN), which has a slightly larger vector size of about 1.4 million neurons. This vector is then mapped onto a 200 million vector in the primary visual cortex (V1), where further vector processing is done and mapped onto other vectors in the visual processing areas (V1, V2, V3, and so on).

More transformations occur throughout the visual system until, finally, you consciously experience the tree as a neurally instantiated vector.