Two projects in theoretical neuroscience: A convolution-based metric for neural membrane potentials and a combinatorial connectionist semantic network method

In this work, I present two projects that both contribute to the aim of discovering how intelligence manifests in the brain.;The first project is a method for analyzing recorded neural signals, which takes the form of a convolution-based metric on neural membrane potential recordings. Relying only on integral and algebraic operations, the metric compares the timing and number of spikes within recordings as well as the recordings' subthreshold features: summarizing differences in these with a single "distance" between the recordings. Like van Rossum's (2001) metric for spike trains, the metric is based on a convolution operation that it performs on the input data. The kernel used for the convolution is carefully chosen such that it produces a desirable frequency space response and, unlike van Rossum's kernel, causes the metric to be first order both in differences between nearby spike times and in differences between same-time membrane potential values: an important trait.;The second project is a combinatorial syntax method for connectionist semantic network encoding. Combinatorial syntax has been a point on which those who support a symbol-processing view of intelligent processing and those who favor a connectionist view have had difficulty seeing eye-to-eye. Symbol-processing theorists have persuasively argued that combinatorial syntax is necessary for certain intelligent mental operations, such as reasoning by analogy. Connectionists have focused on the versatility and adaptability offered by self-organizing networks of simple processing units. With this project, I show that there is a way to reconcile the two perspectives and to ascribe a combinatorial syntax to a connectionist network. The critical principle is to interpret nodes, or units, in the connectionist network as bound integrations of the interpretations for nodes that they share links with. Nodes need not correspond exactly to neurons and may correspond instead to distributed sets, or assemblies, of neurons.