An established normative approach for understanding the algorithmic basis of neural computation is to derive online algorithms from principled computational objectives and evaluate their compatibility with anatomical and physiological observations. Similarity matching objectives have served as successful starting points for deriving online algorithms that map onto neural networks (NNs) with point neurons and Hebbian/anti-Hebbian plasticity. These NN models account for many anatomical and physiological observations; however, the objectives have limited computational power and the derived NNs do not explain multi-compartmental neuronal structures and non-Hebbian forms of plasticity that are prevalent throughout the brain. In this article, we unify and generalize recent extensions of the similarity matching approach to address more complex objectives, including a large class of unsupervised and self-supervised learning tasks that can be formulated as symmetric generalized eigenvalue problems or nonnegative matrix factorization problems. Interestingly, the online algorithms derived from these objectives naturally map onto NNs with multi-compartmental neurons and local, non-Hebbian learning rules. Therefore, this unified extension of the similarity matching approach provides a normative framework that facilitates understanding multi-compartmental neuronal structures and non-Hebbian plasticity found throughout the brain.

翻译：一种理解神经计算算法基础的公认规范方法，是从原则性计算目标中导出在线算法，并评估其与解剖学和生理学观察的兼容性。相似性匹配目标已成功作为导出映射到具有点神经元和赫布/反赫布可塑性的神经网络(Neural Networks, NNs)的在线算法的出发点。这些神经网络模型解释了许多解剖学和生理学观察；然而，这些目标的计算能力有限，且导出的神经网络无法解释在大脑中普遍存在的多室神经元结构和非赫布可塑性形式。在本文中，我们统一并推广了相似性匹配方法的最新扩展，以处理更复杂的目标，包括一大类可表述为对称广义特征值问题或非负矩阵分解问题的无监督和自监督学习任务。有趣的是，从这些目标导出的在线算法自然映射到具有多室神经元和局部、非赫布学习规则的神经网络。因此，这种相似性匹配方法的统一扩展提供了一个规范框架，有助于理解在大脑中广泛存在的多室神经元结构和非赫布可塑性。