Neural network models offer a theoretical testbed for the study of learning at the cellular level. The only experimentally verified learning rule, Hebb's rule, is extremely limited in its ability to train networks to perform complex tasks. An identified cellular mechanism responsible for Hebbian-type long-term potentiation, the NMDA receptor, is highly versatile. Its function and efficacy are modulated by a wide variety of compounds and conditions and are likely to be directed by non-local phenomena. Furthermore, it has been demonstrated that NMDA receptors are not essential for some types of learning. We have shown that another neural network learning rule, the chemotaxis algorithm, is theoretically much more powerful than Hebb's rule and is consistent with experimental data. A biased random-walk in synaptic weight space is a learning rule immanent in nervous activity and may account for some types of learning -- notably the acquisition of skilled movement.