# 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](<https://pmc.ncbi.nlm.nih.gov/articles/PMC1392413/> "A quantitative description of membrane current and its application to conduction and excitation in nerve; J. Physiol.").
- **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](<https://www.columbia.edu/cu/neurotheory/Larry/AbbottBrResBul99.pdf> "Lapicque’s introduction of the integrate-and-fire model neuron (1907); Brain Res. Bull."), [Brunel and van Rossum 2007 🔒](<https://doi.org/10.1007/s00422-007-0190-0> "Lapicque’s 1907 paper: from frogs to integrate-and-fire; Biol. Cybern.").
- **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](<https://izhikevich.org/publications/spikes.pdf> "Simple Model of Spiking Neurons; IEEE Trans. Neural Netw.").

## Local plasticity and temporal readouts

- **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](<https://www.jneurosci.org/content/18/24/10464> "Synaptic Modifications in Cultured Hippocampal Neurons: Dependence on Spike Timing, Synaptic Strength, and Postsynaptic Cell Type; J. Neurosci.").
- **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 🔒](<https://doi.org/10.1038/nn1643> "The tempotron: a neuron that learns spike timing–based decisions; Nat. Neurosci.").
- **Spiking reservoirs** - Trains a readout of a fixed recurrent circuit's transient responses. See [liquid state machines](https://mlpapers.org/neural-nets/#reservoir-computing); this trains a different component from plasticity throughout the recurrent network.

## Learning through spikes

- **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](<https://zenkelab.org/wp-content/uploads/2018/03/ZenkeGanguli2018_SuperSpike.pdf> "SuperSpike: Supervised Learning in Multilayer Spiking Neural Networks; Neural Comput.").
- **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](<https://www.nature.com/articles/s41467-020-17236-y> "A solution to the learning dilemma for recurrent networks of spiking neurons; Nat. Commun.").
- **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](<https://www.nature.com/articles/s41598-021-91786-z> "Event-based backpropagation can compute exact gradients for spiking neural networks; Sci. Rep.").
- **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](<https://pmc.ncbi.nlm.nih.gov/articles/PMC7619566/> "The Remarkable Robustness of Surrogate Gradient Learning for Instilling Complex Function in Spiking Neural Networks; Neural Comput.").

## Conversion and deep architectures

- **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](<https://www.frontiersin.org/journals/neuroscience/articles/10.3389/fnins.2017.00682/full> "Conversion of Continuous-Valued Deep Networks to Efficient Event-Driven Networks for Image Classification; Front. Neurosci.").
- **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](<https://papers.neurips.cc/paper_files/paper/2021/hash/afe434653a898da20044041262b3ac74-Abstract.html> "Deep Residual Learning in Spiking Neural Networks; NeurIPS").

## Hardware learning and evaluation

- **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](<https://paulmerolla.com/merolla_main_som.pdf> "A million spiking-neuron integrated circuit with a scalable communication network and interface; Science").
- **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](<https://redwood.berkeley.edu/wp-content/uploads/2021/08/Davies2018.pdf> "Loihi: A Neuromorphic Manycore Processor with On-Chip Learning; IEEE Micro").
- **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](<https://pmc.ncbi.nlm.nih.gov/articles/PMC8794842/> "Surrogate gradients for analog neuromorphic computing; PNAS").
- **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](<https://www.nature.com/articles/s41467-025-56739-4> "The neurobench framework for benchmarking neuromorphic computing algorithms and systems; Nat. Commun."); [code](<https://github.com/NeuroBench/neurobench>).

## Software

- **SpikingJelly** - Provides spiking-neuron simulation, surrogate-gradient training and ANN-to-SNN conversion with PyTorch interfaces and accelerated kernels. [Fang et al. 2023](<https://pmc.ncbi.nlm.nih.gov/articles/PMC10558124/> "SpikingJelly: An open-source machine learning infrastructure platform for spike-based intelligence; Sci. Adv."); [code](<https://github.com/fangwei123456/spikingjelly>).

## Related topics

- [Neural Networks and Deep Learning](https://mlpapers.org/neural-nets/)
- [Time Series Forecasting](https://mlpapers.org/time-series-forecasting/)
- [Computer Vision](https://mlpapers.org/computer-vision/)
- [Optimization](https://mlpapers.org/optimization/)
- [Model Evaluation and Comparison](https://mlpapers.org/evaluation/)