Efficient training of artificial neural networks remains a key challenge in deep learning. Backpropagation (BP), the standard learning algorithm, relies on gradient descent and typically requires numerous iterations for convergence. In this study, we introduce Expectation Reflection (ER), a novel learning approach that updates weights multiplicatively based on the ratio of observed to predicted outputs. Unlike traditional methods, ER maintains consistency without requiring ad hoc loss functions or learning rate hyperparameters. We extend ER to multilayer networks and demonstrate its effectiveness in performing image classification tasks. Notably, ER achieves optimal weight updates in a single iteration. Additionally, we reinterpret ER as a modified form of gradient descent incorporating the inverse mapping of target propagation. These findings suggest that ER provides an efficient and scalable alternative for training neural networks.

本研究解决了深度学习中人工神经网络训练效率低下的问题。我们提出了一种新的学习方法——期望反射（ER），通过观察与预测输出的比率乘法更新权重，避免了传统方法中对损失函数和学习率超参数的依赖。ER在多层网络中有效，能够在单次迭代中实现最优的权重更新，展现出训练神经网络的高效和可扩展性。

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