Can supervised learning be achieved without explicit error back-propagation?

We propose a new model for the implementation of supervised learning algorithms for networks of sigmoidal "neurons" which does not require that error feedback be explicitly provided by means of a dedicated feedback network. In this model, a locally-defined environmental gradient which is implicit in the strengths of synapses, their rates of change, and pre- and post-synaptic activity levels is used in the adaptation. This environmental gradient always exists and is generally non-zero, independently of the presence of a supervisor, so long as there is some change in synaptic strength, regardless of the driving force behind the modification, much as a Hebbian gradient always exists at any synapse.