Surrogate Gradients for Gradient-Based Parameter Estimation in Simplified Neuron Models

Abstract

Simplified spiking neuron models such as the Adaptive Exponential Integrate-and-Fire (AdEx) model reproduce the firing behaviour of diverse neuron types at a fraction of the cost of biophysically detailed models, making them attractive for large-scale brain simulation. Fitting their parameters to recordings, however, still relies on derivative-free search such as grid search or evolutionary algorithms, because the discrete spike-and-reset mechanism renders these models non-differentiable. Surrogate gradients, used in deep spiking networks, replace the spike derivative with a smooth approximation on the backward pass. Whether they also enable efficient gradient-based parameter estimation for single simplified neurons is untested. We implement a differentiable AdEx model with a surrogate-gradient variant in the Jaxley framework. The implementation is on par with target-compiled C++ Brian2 code while remaining end-to-end differentiable, vmap-batchable and GPU/TPU-portable. It is 200 times faster than Brian2’s default runtime mode. Across a recovery-radius benchmark of 2,700 paired runs, gradient-based fitting never matched a gradient-free Nelder–Mead baseline. At sub-threshold levels, gradient descent instead beats Nelder–Mead. The obstacle is therefore the spike mechanism and the loss geometry it induces, not gradient descent itself.