Spiking Neural Networks and Neuromorphic Learning

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Neuron dynamics and temporal codes

Hodgkin-Huxley dynamics - Models membrane voltage with sodium, potassium and leak currents. Voltage-dependent conductances fitted to squid-axon measurements reproduce action-potential shape, propagation and refractoriness, supplying a biophysical basis for reduced neuron models. Hodgkin and Huxley 1952.
Leaky integrate-and-fire neurons - Integrates current with passive leak and resets at a spike threshold. Lapicque’s 1907 circuit modeled excitability; the modern spike-and-reset formulation developed later. Abbott 1999, Brunel and van Rossum 2007 🔒.
Izhikevich neuron model - Uses membrane-voltage and recovery equations with a spike reset. Four parameters reproduce different spiking and bursting patterns, providing richer cell dynamics than a basic integrate-and-fire model. Izhikevich 2003.

Spike-timing-dependent plasticity - In cultured hippocampal neurons, pre-before-post firing potentiated synapses and reversed timing depressed them within narrow windows. Initial synaptic strength and postsynaptic cell type also affected plasticity. Bi and Poo 1998.
Tempotron - Trains an integrate-and-fire neuron to classify temporal spike patterns by firing or remaining silent. Weight changes follow each input spike’s contribution at the peak postsynaptic voltage. Gütig and Sompolinsky 2006 🔒.
Spiking reservoirs - Trains a readout of a fixed recurrent circuit’s transient responses. See liquid state machines; this trains a different component from plasticity throughout the recurrent network.

SuperSpike - Replaces the hard spike derivative with a voltage-dependent surrogate, combining presynaptic traces, postsynaptic voltage and error feedback. Trains multilayer spiking networks on temporal input-output mappings. Zenke and Ganguli 2018.
E-prop - Combines local eligibility traces with neuron-specific learning signals. Replaces future-dependent credit with online approximations, avoiding time-unrolling; the practical update approximates the exact gradient decomposition. Bellec et al. 2020.
EventProp - Uses continuous-time adjoints and derivative jumps at spikes for exact gradients in leaky integrate-and-fire networks. Derivatives can diverge where spikes appear or disappear; the algorithm still backpropagates errors. Wunderlich and Pehle 2021.
Surrogate-gradient sensitivity - On synthetic spike-pattern classification, tested surrogate shapes reached similar peak accuracy after tuning. Large gradient scales impaired learning through recurrent connections and spike resets. Zenke and Vogels 2021.

ANN-to-SNN conversion - Maps trained continuous activations to firing rates using weight normalization and reset by subtraction. On image classifiers, longer simulation improves approximation, creating an accuracy-latency trade-off. Rueckauer et al. 2017.
SEW ResNet - Combines spikes in residual blocks to preserve identity paths. On ImageNet, deeper SEW models improved training and validation accuracy while the compared Spiking ResNets degraded with depth. Fang et al. 2021.

TrueNorth - Stores configurable synapses beside spiking neurons in 4,096 digital cores connected by spike routing. Offline-trained networks run on chip; synaptic learning remains off chip. Merolla et al. 2014.
Loihi - Integrates programmable synaptic learning with spiking dynamics across 128 cores. Local learning engines update weights from spike traces, supporting pairwise and triplet STDP and reward-dependent rules. Davies et al. 2018.
Training analog hardware - Runs forward dynamics on BrainScaleS-2 and inserts measured spikes and voltages into a software model for surrogate-gradient BPTT. Weight updates run on conventional compute; the loop compensates for analog mismatch. Cramer et al. 2022.
NeuroBench - Separates algorithm and system benchmarks. Xylo used 33.4-fold less dynamic inference energy than Arduino at comparable keyword-spotting accuracy. Xylo’s preprocessing was simulated; this measures inference energy only. Yik et al. 2025; code.

SpikingJelly - Provides spiking-neuron simulation, surrogate-gradient training and ANN-to-SNN conversion with PyTorch interfaces and accelerated kernels. Fang et al. 2023; code.