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Training networks consisting of biophysically accurate neuron models couldallow for new insights into how brain circuits can organize and solve tasks. Webegin by analyzing the extent to which the central algorithm for neural networklearning -- stochastic gradient descent through backpropagation (BP) -- can beused to train such networks. We find that properties of biophysically basedneural network models needed for accurate modelling such as stiffness, highnonlinearity and long evaluation timeframes relative to spike times makes BPunstable and divergent in a variety of cases. To address these instabilitiesand inspired by recent work, we investigate the use of "gradient-estimating"evolutionary algorithms (EAs) for training biophysically based neural networks.We find that EAs have several advantages making them desirable over direct BP,including being forward-pass only, robust to noisy and rigid losses, allowingfor discrete loss formulations, and potentially facilitating a more globalexploration of parameters. We apply our method to train a recurrent network ofMorris-Lecar neuron models on a stimulus integration and working memory task,and show how it can succeed in cases where direct BP is inapplicable. To expandon the viability of EAs in general, we apply them to a general neural ODEproblem and a stiff neural ODE benchmark and find again that EAs canout-perform direct BP here, especially for the over-parameterized regime. Ourfindings suggest that biophysical neurons could provide useful benchmarks fortesting the limits of BP-adjacent methods, and demonstrate the viability of EAsfor training networks with complex components.

Evolutionary algorithms as an alternative to backpropagation for supervised training of Biophysical Neural Networks and Neural ODEs