发表机构
University of Alberta; Alberta Machine Intelligence Institute (Amii)（阿尔伯塔大学; 阿尔伯塔机器智能研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究针对预测编码中层间路由误差依赖雅可比转置乘积的问题，提出将精确的$J^\top$分解为局部可用项的方法，恢复权重反馈修正，得到 WF-Act-PC，消除自动求导反向传播，在多个数据集上取得较好效果。
AI 中文摘要
预测编码（PC）通过局部权重更新为反向传播提供了一种受生物学启发的替代方案，但层间路由误差仍依赖自动求导雅可比转置（$J^\top$）乘积——PC 中的最后一个非局部操作。研究表明这种依赖很大程度上可避免。对于具有冻结归一化统计量的层$f(x)=\mathrm{Act}(\mathrm{Norm}(L(x)))$，精确的$J^\top$可分解为三个局部可用项。先前的权重反馈方法省略了修正，恢复这些修正可缩小此类层的传输差距。局部性有三个假设。将恒等代入 PC 得到 WF-Act-PC，它消除了误差传输中的自动求导反向传播。在 CIFAR-10/100 上，WF-Act-PC 是唯一准确率随深度提高的 PC 方法，在 CIFAR-10 上比最强经典 PC 基线 iPC 高 2.7 - 22.3 个百分点。在更深的 CIFAR-10 架构和更难的 Tiny-ImageNet 基准测试中，WF-Act-PC 与调优后的反向传播基线匹配或超过，在更深的 CIFAR-100 VGG 单元上落后于调优后的 BP。WF-Act-PC 实现可公开获取。
英文摘要
Predictive Coding (PC) offers a biologically motivated alternative to backpropagation via local weight updates, yet routing error between layers still relies on an autograd Jacobian-transpose ($J^\top$) product - the last non-local operation in PC. We show that this dependency is largely avoidable. For any layer $f(x)=\mathrm{Act}(\mathrm{Norm}(L(x)))$ with frozen normalization statistics, the exact $J^\top$ factors into three locally available terms, $J^\top v = L^\top(s \odot σ'(z) \odot v)$, where $σ'$ is the activation derivative, $z$ is the pre-activation, and $s=γ/σ_{\mathrm{run}}$ is the normalization gain. Prior weight-feedback methods omitted both corrections; restoring them closes the transport gap for this layer class. Locality here holds up to three assumptions, which we state upfront: weight symmetry ($L^\top$ mirrors the forward operator, as assumed by all PC), a soft spectral-norm control that is not synapse-local, and a nearest-neighbour approximation for MaxPool. Substituting the identity into PC yields WF-Act-PC, which removes the autograd backward pass from error transport. On CIFAR-10/100 (50 epochs, 5 seeds), WF-Act-PC is the only PC method whose accuracy improves with depth, surpassing iPC - the strongest classical PC baseline - by 2.7-22.3 pp on CIFAR-10. With both methods tuned per architecture, it matches or exceeds a comparably-tuned backpropagation baseline on the deeper CIFAR-10 architectures (VGG-9: 93.57% vs. 92.43%; ResNet-18: 92.76% vs. 91.54%) and on the harder Tiny-ImageNet benchmark, while trailing tuned BP on the deeper CIFAR-100 VGG cells. Our WF-Act-PC implementation is publicly available at https://github.com/jlshen025/pcax
