Theories on the synaptic algoritihm

hello does anyone know about any recent advances in cracking the synaptic algorithm?

what are the current theories on this?

to be clear by the synaptic algorithm I mean the rules that govern the phenomenon of where input to one synapse affects the synaptic strength of nearby synapses.

synapses in general are the least understood part of neurons so solid theories on their function are essential to understanding 2 neuron and multi-neuron systems and the nonlinear properties they exhibit.