For the comp neuro readers:
CLAPP++ is still a three-factor Hebbian plasticity rule:
plasticity = (neuromodulator) × (dendritic prediction) × (Hebbian term)
When there is direct feedback, the dendritic prediction comes from the top layer — matching findings in neuroscience experiments.
In supervised setups, many local learning algorithms are proposed to approximate the gradient of BP in theory and approach BP performance on benchmarks. However, for self-supervised learning, the performance gap is larger, and we miss a theory to compare gradients between local-SSL and BP.