Predictive coding (PC) is a biologically inspired algorithm for training neural networks that relies only on local updates, allowing parallel learning across layers. However, practical implementations face two key limitations: error signals must still propagate from the output to early layers through multiple inference-phase steps, and feedback decays exponentially during this process, leading to vanishing updates in early layers. We propose direct Kolen-Pollack predictive coding (DKP-PC), which simultaneously addresses both feedback delay and exponential decay, yielding a more efficient and scalable variant of PC while preserving update locality. Leveraging direct feedback alignment and direct Kolen-Pollack algorithms, DKP-PC introduces learnable feedback connections from the output layer to all hidden layers, establishing a direct pathway for error transmission. This yields an algorithm that reduces the theoretical error propagation time complexity from O(L), with L being the network depth, to O(1), removing depth-dependent delay in error signals. Moreover, empirical results demonstrate that DKP-PC achieves performance at least comparable to, and often exceeding, that of standard PC, while offering improved latency and computational performance, supporting its potential for custom hardware-efficient implementations.

翻译：预测编码（PC）是一种受生物学启发的神经网络训练算法，仅依赖局部更新，可实现跨层并行学习。然而，实际应用面临两个关键局限：误差信号仍需通过多个推理阶段步骤从输出层传播至早期层，且在此过程中反馈呈指数衰减，导致早期层更新消失。我们提出直接Kolen-Pollack预测编码（DKP-PC），该方法同时解决了反馈延迟与指数衰减问题，在保持更新局部性的同时，实现了更高效、可扩展的PC变体。通过结合直接反馈对齐与直接Kolen-Pollack算法，DKP-PC引入从输出层到所有隐藏层的可学习反馈连接，建立了误差传输的直接通路。该算法将理论误差传播时间复杂度从O(L)（L为网络深度）降低至O(1)，消除了误差信号对深度的依赖延迟。此外，实验结果表明，DKP-PC在性能上至少与标准PC相当，且往往更优，同时具有更低的延迟与更高的计算性能，这为其在定制化硬件高效实现中的潜力提供了支持。