One of the proposals for a biologically realistic alternative to backpropagation is feedback alignment: http://www.cs.toronto.edu/~tingwuwang/2546.pdf http://ww

One of the proposals for a biologically realistic alternative to backpropagation is feedback alignment: http://www.cs.toronto.edu/~tingwuwang/2546.pdf http://www.cs.toronto.edu/~tingwuwang/2546.pdf (randomly selected representative slides from Google search. See reference therein)