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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 if one 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.

Pavlovian Pattern Learning by Nonlinear Neural Networks