Local Synaptic Rules Can Implement a SIGReg Gradient Without Backpropagation

What the math gives to ML

The paper provides a constructive bridge from biologically local plasticity to an exact gradient of a SIGReg-like self-supervised objective: encoder synapses use only pre/post activity, local sigmoid gain, temporal adjacency, and a fixed random projection circuit. The transferable asset is not STDP in isolation, but the decomposition of a global representation-learning gradient into an online Hebbian term plus a homeostatic correction and a fixed feedback projection, avoiding backpropagation and weight transport. A practical first transfer is a two-step temporal representation learner whose encoder update uses a fixed random projection to generate a locally available modulatory error, then compares it against a backpropagation baseline on temporally ordered and randomly shuffled data.