Pavlovian Pattern Learning by Nonlinear Neural Networks

Abstract

This note describes laws for the anatomy, potentials, spiking rules, and transmitters of some networks of formal neurons that enable them to learn spatial patterns by Pavlovian conditioning. Applications to spacetime pattern learning and operant conditioning are then possible, if the conditioning is viewed as multi-channel Pavlovian conditioning in a highly inhomogeneous anatomy. In suitable anatomies, biases in learning because of axon collaterals with nonuniformly distributed diameters can be corrected ifone properly couples the action potential to transmitter potentiation, and chooses signal velocity proportional to axon diameter. These anatomies can contain any number of cells. Anatomies exist in which patterns may be learned without their being practiced overtly, whereas persistent recall of old patterns without the learning of newly imposed patterns is impossible. Physiologically, this constraint has the trivial interpretation that signals from one cell to another first pass through the intervening synaptic knob. Mechanisms that control learning rates at times important to the network (e.g., reward and punishment times) can be discussed. Serial behavior like that described by Lashley is possible: this consists of sequential learning and performance of patterns faster than would be allowed by a motor-feedback control, at velocities influenced by arousal level, with the possibility of abrupt termination of performance if conflicting environmental demands arise. Analogs of pattern completion and mass action exist, as do phase transitions in memory (for some rate parameters and anatomies, memory is rigid, for others, it is plastic). The laws limit the ways in which these networks can be interconnected to yield specific discrimination, learning, memory, and recall capabilities.

How Does the Brain Solve the Computational Problems of Spatial Navigation?

“…In this view, the role of the hippocampus in the brain is akin to the role of a librarian (Buzsáki 2006): given vague or partial information about a book (or an event or thing), the librarian (hippocampus) can retrieve the full record and return a pointer to the book (or the full memory of the event or thing). This is consistent with the autoassociative pattern-completion role usually ascribed to CA3 (Grossberg 1969(Grossberg , 1971Hopfield 1982;Amit 1994;McClelland and Rumelhart 1985;McNaughton and Morris 1987;Treves and Rolls 1992). To understand the elevation of the spatial variable, we might build on the analogy.…”

Distinctive features, categorical perception, and probability learning: Some applications of a neural model.

“…In the past few years a number of related realizations of distributed memories applied to brain models have been put forward by several groups of investigators (Anderson, 1970(Anderson, , 1972Cooper, 1974;Grossberg, 1971;Kohonen, 1972Kohonen, , 1977Little & Shaw, 1975;Willshaw, Buneman, & Longuet-Higgins, 1969). One form of the central learning assumptions of these models was first proposed by Hebb (1949) but, as is often the case in an active field of science, many of the fundamental assumptions of the models have been arrived at independently by different groups.…”

Principles of cortical synchronization

“…These learning laws arc like those of Artola and Singer ( 1993). I proved, under general conditions of cell signal processing, feedback, and modulation of learning that "The unit of long-term memory is a spatial pattern"; that is, associative networks learn contextually-informative synchronized patterns of activation (Grossberg, 1968(Grossberg, , 1971(Grossberg, , 1982.…”