Brain-Plausible Local Learning in SNNs: Training Hodgkin–Huxley Spiking Neural Networks with Predictive Coding

Almost all deep spiking neural networks (SNNs) use Leaky Integrate-and-Fire (LIF) neurons and are trained by backpropagation through time (BPTT) with surrogate gradients. Both choices are made for tractability, not biology: LIF throws away the ion-channel dynamics that generate real action potentials, and BPTT needs a global error signal no cortical mechanism is known to implement. Conductance-based models such as Hodgkin–Huxley (HH) are avoided because unrolling their coupled nonlinear dynamics through time is expensive and numerically fragile. We show the trade-off is avoidable. Our method trains a network of HH neurons for classification with no backpropagation, no surrogate gradients, and no unrolling, using predictive coding (PC) to supply layer-local errors. One design choice makes this work: a rate proxy, the spike count of each HH population divided by the simulation window, which gives PC the continuous states it needs. No gradient ever crosses spike generation, so the cost of learning does not depend on how complex the neuron is. Across MNIST, Fashion-MNIST, N-MNIST and the Spiking Heidelberg Digits, HH matches a LIF baseline trained under the same objective while firing fewer spikes in 26 of 28 window-matched comparisons. Our learning interface allows biophysically realistic neurons to retain competitive accuracy.