BIOLOGICALLY PLAUSIBLE ERROR-DRIVEN LEARNING USING LOCAL ACTIVATION DIFFERENCES - THE GENERALIZED RECIRCULATION ALGORITHM

The error backpropagation learning algorithm (BP) is generally conside red biologically implausible because it does not use locally available , activation-based variables. A version of BP that can be computed loc ally using bidirectional activation recirculation (Hinton and McClella nd 1988) instead of backpropagated error derivatives is more biologica lly plausible. This paper presents a generalized version of the recirc ulation algorithm (GeneRec), which overcomes several limitations of th e earlier algorithm by using a generic recurrent network with sigmoida l units that can learn arbitrary input/output mappings. However, the c ontrastive Hebbian learning algorithm (CHL, also known as DBM or mean field learning) also uses local variables to perform error-driven lear ning in a sigmoidal recurrent network. CHL was derived in a stochastic framework (the Boltzmann machine), but has been extended to the deter ministic case in various ways, all of which rely on problematic approx imations and assumptions, leading some to conclude that it is fundamen tally flawed. This paper shows that CHL can be derived instead from wi thin the BP framework via the GeneRec algorithm. CHL is a symmetry-pre serving version of GeneRec that uses a simple approximation to the mid point or second-order accurate Runge-Kutta method of numerical integra tion, which explains the generally faster learning speed of CHL compar ed to BP, Thus, all known fully general error-driven learning algorith ms that use local activation-based variables in deterministic networks can be considered variations of the GeneRec algorithm (and indirectly , of the backpropagation algorithm). GeneRec therefore provides a prom ising framework for thinking about how the brain might perform error-d riven learning. To further this goal, an explicit biological mechanism is proposed that would be capable of implementing GeneRec-style learn ing. This mechanism is consistent with available evidence regarding sy naptic modification in neurons in the neocortex and hippocampus, and m akes further predictions.