Fig. 5.
Cartoon summary of learning rules explored in this work. (A) The exact gradient: Updating weight wpq, the synaptic connection strength from presynaptic neuron q to postsynaptic neuron p, involves nonlocal information inaccessible to neural circuits, i.e., the knowledge of activity (e.g., voltage s) for all distant neurons j and l in the network. This is because wpq affects the activities of many other cells through indirect connections, which will then affect the network output at subsequent time steps (Eq. 17 in Methods). (B) E-prop, a state-of-the-art biologically plausible learning rule, restricts the weight update to depend only on presynaptic and postsynaptic activity and TD learning signal, as in a three-factor learning rule (Fig. 2A). (C) We allow the weight update to capture dependencies within one connection step, which are omitted in e-prop. The activity of neuron j could be delivered to p through local modulatory signaling. (D) For the signaling in C to be cell-type–specific, as consistent with experimental observation in ref. 42 and biologically plausible mechanisms, we approximate the cell-specific gain with cell-type–specific gain (Eq. 23), which leads to our MDGL. Effect of this cell-type approximation is explored in SI Appendix, Fig. S9. (E) NL-MDGL, where modulatory signal diffuses to all cells in the network without attenuation (Fig. 4).