Local Synaptic Rules Can Implement a SIGReg Gradient Without Backpropagation

The paper proves that two local learning mechanisms, the potentiation arm of spike-timing-dependent plasticity (STDP+) and homeostatic plasticity implemented with flashlight granule-cell-like neurons, can realize the exact gradient of a SIGReg-like self-supervised objective. The method uses no backpropagation, global error signals, weight transport, or labels; it relies only on pre- and post-synaptic firing rates, local firing statistics, and temporal contiguity in sensory streams. On a synthetic clustering task, ordered inputs produced a cluster-separation ratio (CSR) of 2.49 versus 0.83 for random ordering. A two-layer network reached 87.3% linear-probe accuracy on temporally ordered MNIST.