The search for ``biologically plausible'' learning algorithms has converged on the idea of representing gradients as activity differences. However, most approaches require a high degree of synchronization (distinct phases during learning) and introduce substantial computational overhead, which raises doubts regarding their biological plausibility as well as their potential utility for neuromorphic computing. Furthermore, they commonly rely on applying infinitesimal perturbations (nudges) to output units, which is impractical in noisy environments. Recently it has been shown that by modelling artificial neurons as dyads with two oppositely nudged compartments, it is possible for a fully local learning algorithm named ``dual propagation'' to bridge the performance gap to backpropagation, without requiring separate learning phases or infinitesimal nudging. However, the algorithm has the drawback that its numerical stability relies on symmetric nudging, which may be restrictive in biological and analog implementations. In this work we first provide a solid foundation for the objective underlying the dual propagation method, which also reveals a surprising connection with adversarial robustness. Second, we demonstrate how dual propagation is related to a particular adjoint state method, which is stable regardless of asymmetric nudging.

翻译：寻找"生物学合理"的学习算法已聚焦于将梯度表示为活动差异的思想。然而，大多数方法需要高度同步（学习过程中的不同阶段）并引入大量计算开销，这引发了对其生物学合理性及在神经形态计算中潜在实用性的质疑。此外，它们通常依赖于对输出单元施加无穷小扰动（微调），这在噪声环境中并不实用。最近研究表明，通过将人工神经元建模为具有两个相反微调区室的二元体，一种名为"双重传播"的完全局部学习算法能够弥合与反向传播的性能差距，且无需独立的学习阶段或无穷小微调。然而，该算法的缺陷在于其数值稳定性依赖于对称微调，这在生物和模拟实现中可能具有限制性。本工作首先为双重传播方法的基础目标建立了坚实理论基础，同时揭示了其与对抗鲁棒性的惊人联系。其次，我们论证了双重传播如何与特定伴随状态方法相关联，该方法在非对称微调条件下仍能保持稳定性。