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An assembly is a large population of neurons whose synchronous firing ishypothesized to represent a memory, concept, word, and other cognitivecategories. Assemblies are believed to provide a bridge between high-levelcognitive phenomena and low-level neural activity. Recently, a computationalsystem called the Assembly Calculus (AC), with a repertoire of biologicallyplausible operations on assemblies, has been shown capable of simulatingarbitrary space-bounded computation, but also of simulating complex cognitivephenomena such as language, reasoning, and planning. However, the mechanismwhereby assemblies can mediate learning has not been known. Here we presentsuch a mechanism, and prove rigorously that, for simple classification problemsdefined on distributions of labeled assemblies, a new assembly representingeach class can be reliably formed in response to a few stimuli from the class;this assembly is henceforth reliably recalled in response to new stimuli fromthe same class. Furthermore, such class assemblies will be distinguishable aslong as the respective classes are reasonably separated -- for example, whenthey are clusters of similar assemblies. To prove these results, we draw onrandom graph theory with dynamic edge weights to estimate sequences ofactivated vertices, yielding strong generalizations of previous calculationsand theorems in this field over the past five years. These theorems are backedup by experiments demonstrating the successful formation of assemblies whichrepresent concept classes on synthetic data drawn from such distributions, andalso on MNIST, which lends itself to classification through one assembly perdigit. Seen as a learning algorithm, this mechanism is entirely online,generalizes from very few samples, and requires only mild supervision -- allkey attributes of learning in a model of the brain.

Assemblies of neurons learn to classify well-separated distributions