School of Informatics, University of Edinburgh, Edinburgh EH8 9AB, U.K.
Sackler Center for Consciousness Science, School of Engineering and Informatics, University of Sussex, Brighton BN1 9QJ, U.K.
Neural Comput. 2022 May 19;34(6):1329-1368. doi: 10.1162/neco_a_01497.
Backpropagation of error (backprop) is a powerful algorithm for training machine learning architectures through end-to-end differentiation. Recently it has been shown that backprop in multilayer perceptrons (MLPs) can be approximated using predictive coding, a biologically plausible process theory of cortical computation that relies solely on local and Hebbian updates. The power of backprop, however, lies not in its instantiation in MLPs but in the concept of automatic differentiation, which allows for the optimization of any differentiable program expressed as a computation graph. Here, we demonstrate that predictive coding converges asymptotically (and in practice, rapidly) to exact backprop gradients on arbitrary computation graphs using only local learning rules. We apply this result to develop a straightforward strategy to translate core machine learning architectures into their predictive coding equivalents. We construct predictive coding convolutional neural networks, recurrent neural networks, and the more complex long short-term memory, which include a nonlayer-like branching internal graph structure and multiplicative interactions. Our models perform equivalently to backprop on challenging machine learning benchmarks while using only local and (mostly) Hebbian plasticity. Our method raises the potential that standard machine learning algorithms could in principle be directly implemented in neural circuitry and may also contribute to the development of completely distributed neuromorphic architectures.
反向传播误差（backprop）是一种通过端到端微分来训练机器学习体系结构的强大算法。最近表明，多层感知器（MLP）中的反向传播可以使用预测编码来近似，预测编码是一种依赖于局部和海伯更新的皮质计算的合理生物过程理论。然而，反向传播的强大之处不在于它在 MLP 中的实例化，而在于自动微分的概念，该概念允许对任何可微分的程序进行优化，这些程序表示为计算图。在这里，我们证明，使用仅基于局部学习规则的预测编码可以渐近地（在实践中，快速地）收敛到任意计算图上的精确反向传播梯度。我们将这一结果应用于开发一种将核心机器学习体系结构直接转换为其预测编码等效形式的简单策略。我们构建了预测编码卷积神经网络、递归神经网络和更复杂的长短期记忆网络，包括非分层的分支内部图结构和乘法交互。我们的模型在具有挑战性的机器学习基准上的表现与反向传播相当，同时仅使用局部和（主要）海伯可塑性。我们的方法提出了一种可能性，即标准的机器学习算法原则上可以直接在神经电路中实现，并且还可能有助于完全分布式神经形态架构的发展。
