The adaptive leaky integrate-and-fire (ALIF) model is fundamental within computational neuroscience and has been instrumental in studying our brains $\textit{in silico}$. Due to the sequential nature of simulating these neural models, a commonly faced issue is the speed-accuracy trade-off: either accurately simulate a neuron using a small discretisation time-step (DT), which is slow, or more quickly simulate a neuron using a larger DT and incur a loss in simulation accuracy. Here we provide a solution to this dilemma, by algorithmically reinterpreting the ALIF model, reducing the sequential simulation complexity and permitting a more efficient parallelisation on GPUs. We computationally validate our implementation to obtain over a $50\times$ training speedup using small DTs on synthetic benchmarks. We also obtained a comparable performance to the standard ALIF implementation on different supervised classification tasks - yet in a fraction of the training time. Lastly, we showcase how our model makes it possible to quickly and accurately fit real electrophysiological recordings of cortical neurons, where very fine sub-millisecond DTs are crucial for capturing exact spike timing.

翻译：自适应泄露积分点火（ALIF）模型是计算神经科学的基础模型，对于通过$\textit{计算机模拟}$研究大脑机制至关重要。由于这些神经模型的模拟具有顺序特性，一个常见问题是速度与精度之间的权衡：要么使用小离散化时间步长（DT）精确模拟神经元（但速度慢），要么使用较大DT快速模拟神经元（但会损失模拟精度）。本文通过从算法上重新解释ALIF模型，降低了顺序模拟的复杂度并提升了GPU上的并行化效率，从而解决了这一困境。我们通过计算验证表明，在合成基准测试中使用小DT可获得超过50倍的训练加速。在不同监督分类任务中，我们的实现与标准ALIF实现性能相当，但训练时间大幅缩短。最后，我们展示了该模型如何能够快速且精确地拟合真实皮层神经元的电生理记录数据——其中亚毫秒级极细DT对于捕捉精确的脉冲时序至关重要。