  In this work we propose Hebbian-descent as a biologically plausible learning
rule for hetero-associative as well as auto-associative learning in single
layer artificial neural networks. It can be used as a replacement for gradient
descent as well as Hebbian learning, in particular in online learning, as it
inherits their advantages while not suffering from their disadvantages. We
discuss the drawbacks of Hebbian learning as having problems with correlated
input data and not profiting from seeing training patterns several times. For
gradient descent we identify the derivative of the activation function as
problematic especially in online learning. Hebbian-descent addresses these
problems by getting rid of the activation function's derivative and by
centering, i.e. keeping the neural activities mean free, leading to a
biologically plausible update rule that is provably convergent, does not suffer
from the vanishing error term problem, can deal with correlated data, profits
from seeing patterns several times, and enables successful online learning when
centering is used. We discuss its relationship to Hebbian learning, contrastive
learning, and gradient decent and show that in case of a strictly positive
derivative of the activation function Hebbian-descent leads to the same update
rule as gradient descent but for a different loss function. In this case
Hebbian-descent inherits the convergence properties of gradient descent, but we
also show empirically that it converges when the derivative of the activation
function is only non-negative, such as for the step function for example.
Furthermore, in case of the mean squared error loss Hebbian-descent can be
understood as the difference between two Hebb-learning steps, which in case of
an invertible and integrable activation function actually optimizes a
generalized linear model. ...
