Structural Adaptation of Boolean Higher Order Neurons: Classification with Parsimonious Topologies for Superior Generalization

We present alternative algorithms that avoid the combinatorial explosion problem, and that emerge robust generalization within Boolean higher order neurons. We report simulation results for difficult classification benchmarks. Our algorithms efficiently determine parsimonious classifier topologies that exhibit striking generalization capabilities. 1. INTRODUCTION Standard neural net repertoire (back-prop, layered feed-forward, sum-and-squash units) lacks efficiency for highly nonlinear mappings. Improvements are possible with special purpose nets including product units, higher order neurons, or Boolean gates: designed in a task-oriented way, these architectures capture specific nonlinearities more closely. Our parsimonious higher order neuron model exploits dendritic modeling for automatic identification, and effective processing of the relevant nonlinearities. 2. FULLY CONNECTED MODEL Consider a binary Higher Order Neuron (HON) with K bipolar inputs x 1 ; :::; xK 2 P = f\Gamma1;..