Training networks consisting of biophysically accurate neuron models could allow for new insights into how brain circuits can organize and solve tasks. We begin by analyzing the extent to which the central algorithm for neural network learning -- stochastic gradient descent through backpropagation (BP) -- can be used to train such networks. We find that properties of biophysically based neural network models needed for accurate modelling such as stiffness, high nonlinearity and long evaluation timeframes relative to spike times makes BP unstable and divergent in a variety of cases. To address these instabilities and 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, allowing for discrete loss formulations, and potentially facilitating a more global exploration of parameters. We apply our method to train a recurrent network of Morris-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 expand on the viability of EAs in general, we apply them to a general neural ODE problem and a stiff neural ODE benchmark and find again that EAs can out-perform direct BP here, especially for the over-parameterized regime. Our findings suggest that biophysical neurons could provide useful benchmarks for testing the limits of BP-adjacent methods, and demonstrate the viability of EAs for training networks with complex components.

翻译：训练由生物物理精确神经元模型构成的网络，可能为理解大脑回路如何组织并解决任务提供新见解。我们首先分析了神经网络学习的核心算法——通过反向传播的随机梯度下降（BP）——用于训练此类网络的可能性。研究发现，生物物理神经网络模型为精确建模所需的关键特性（如刚性、高非线性和相对于尖峰时间较长的评估时间），导致反向传播在多种情况下出现不稳定性与发散。为解决这些不稳定性，并受近期研究启发，我们探索了使用“梯度估计”进化算法（EAs）训练生物物理神经网络。我们发现，进化算法具有若干优势使其优于直接反向传播，包括仅需前向传播、对噪声和刚性损失具有鲁棒性、支持离散损失函数设计，并可能促进参数的全局探索。我们应用该方法在刺激整合与工作记忆任务中训练了由Morris-Lecar神经元模型组成的循环网络，并展示了其在直接反向传播不可行情况下的成功应用。为验证进化算法的广泛适用性，我们将其应用于通用神经常微分方程问题及刚性神经常微分方程基准测试，结果再次表明进化算法在此类场景中优于直接反向传播，尤其在过参数化条件下。我们的研究结果表明，生物物理神经元可为测试反向传播相关方法的局限性提供有效基准，同时验证了进化算法在训练含复杂组件的网络中的可行性。