反向传播的替代方案：增强拉格朗日预测编码算法问世

研究人员提出了PC-ALM（增强拉格朗日预测编码）算法，这是一种无需反向传播即可训练深层神经网络的局部学习方法1。该算法在每层引入拉格朗日乘数，用层局部动力学系统取代传统反向传播的前向和后向传递过程1。

PC-ALM在深度学习任务上展现了显著性能。该算法成功训练了深达1000层的多层感知机网络，在MNIST数据集上接近反向传播的性能水平1。在更复杂的基准测试中，使用ResNet-18架构在CIFAR-10和Tiny ImageNet上的表现均相比标准预测编码有所改进1。

算法的创新之处在于其生物可行性设计和高效的信息传播机制。PC-ALM仅依赖层间局部通信进行邻层消息传递1，避免了全局的误差反向传播。在线性网络的极限情况下，其对偶变量收敛到精确的反向传播信用信号1。相较于标准预测编码的扩散型信用传播，PC-ALM展现出更快速的"弹道式"信用传播动力学1。

Researchers have introduced PC-ALM (Augmented Lagrangian Predictive Coding), a local learning algorithm that eliminates the need for backpropagation while successfully training neural networks up to 1,000 layers deep.1 The method replaces the conventional forward and backward pass of backpropagation with layer-local dynamical systems by incorporating Lagrange multipliers, or dual variables, at each layer, achieving performance comparable to backpropagation while maintaining biological plausibility.1

Testing demonstrates that PC-ALM performs nearly as well as backpropagation on MNIST, while outperforming standard predictive coding on both CIFAR-10 and Tiny ImageNet when applied to ResNet-18 architectures.1 Each layer is equipped with feedback control dynamics that operate using only layer-local communication through messaging between neighboring layers.1 In the limiting case of linear networks, the dual variables converge to the exact credit signals produced by backpropagation,1 and PC-ALM exhibits "ballistic" credit propagation dynamics that spread significantly faster than the diffusive propagation characteristic of standard predictive coding.1