From STDP to SIGReg: Backpropagation-Free Representation Learning with Local Synaptic Rules

We show that two canonical local synaptic learning rules, the potentiation arm of spike-timing-dependent plasticity (STDP$^+$) and homeostatic plasticity (instantiated here via random-projection granule-cell-like “flashlight” neurons), together can implement the exact gradient of a SIGReg-like self-supervised learning objective whose collapse-prevention term is the second-order random-projection penalty of Weak-SIGReg. The equivalence requires no gradient calculations, no global error signals, no weight transport, and no labels entering any synaptic update: the only learning signals are pre- and post-synaptic firing rates, local firing statistics, and the temporal contiguity of the input stream. Synthetic and MNIST experiments support complementary roles for temporal STDP$^+$ and homeostatic plasticity in shaping representation geometry.