AI 中文总结
本文提出激活匹配的Bregman预测编码，消除激活导数，实现模拟友好的局部推理与学习规则，在分类和生成任务上性能与标准预测编码及反向传播相当。
AI 中文摘要
预测编码（PC）是反向传播（BP）的一种局部、基于能量的替代方案，其迭代推理动态使其在模拟硬件上实现具有吸引力。然而，标准的非线性预测编码在推理和学习过程中都需要评估激活函数的导数，这在物理上可能难以实现。在此，我们引入了“激活匹配的Bregman预测编码”，用与激活函数匹配的Bregman散度替代标准平方误差能量。该公式消除了激活导数，并与通过镜像下降进行的推理相结合，产生了仅需要加权和、局部预测误差、状态积分和激活函数的局部推理与学习规则。在数字实验中，Bregman预测编码在分类和生成任务上的表现与标准预测编码和反向传播相当，同时保留了预测编码的特征性学习动态及其在稳定大规模模型参数化下收敛到反向传播的特性。这些结果为非线性预测编码提供了一种更模拟友好的公式，同时保留了其关键计算特性。
英文摘要
Predictive coding (PC) is a local, energy-based alternative to backpropagation (BP) whose iterative inference dynamics make it attractive for implementation on analog hardware. However, standard nonlinear PC requires evaluating the derivative of the activation function during both inference and learning, which can be difficult to realise physically. Here, we introduce \textit{activation-matched Bregman PC}, replacing standard squared-error energies with Bregman divergences matched to the activation function. This formulation eliminates activation derivatives and, when combined with inference via mirror descent, yields local inference and learning rules requiring only weighted sums, local prediction errors, state integration, and the activation function. In digital experiments, Bregman PC performs comparably to standard PC and BP on classification and generative tasks, while preserving characteristic learning dynamics of PC and its convergence to BP under stable large-model parameterisations. These results provide a more analog-friendly formulation of nonlinear PC while retaining its key computational properties.
Comments20 pages, 14 figures
