无需反向传播的单次前向训练法，实现可解释的高效学习。
Closed-Form Feedback-Free Learning with Forward Projection
- 通过随机非线性投影生成膜电位目标值，闭式求解权重更新。
- 单次前向传播即达梯度下降性能，训练速度大幅提升。
- 模型可逐层解读，适合医学诊断等需可解释性的场景。
当前无反向传播的学习方法依赖局部误差反馈来指导迭代优化。本文研究更严格的情形：突触前权重更新无法获取下游神经元输出的回传信号。提出前向投影（Forward Projection, FP）方法，仅需对数据集进行一次前向传播，无需任何回传通信即可完成训练。FP通过随机非线性投影预突触输入与标签，生成突触前膜电位的目标值，并利用闭式回归优化局部损失函数。其关键优势在于可解释性：FP训练网络中各层的膜电位可逐层解读为标签预测结果。在多个生物医学数据集上，FP的泛化能力与基于梯度下降的局部学习方法相当，且仅需一次前向传播，显著提升训练效率。在少样本学习任务中，FP生成的模型比反向传播优化的模型更具泛化能力，且本地解释函数成功识别出具有临床意义的诊断特征。
原文摘要 · Abstract (English)
State-of-the-art backpropagation-free learning methods employ local error feedback to direct iterative optimisation via gradient descent. Here, we examine the more restrictive setting where retrograde communication from neuronal outputs is unavailable for pre-synaptic weight optimisation. We propose Forward Projection (FP), a randomised closed-form training method requiring only a single forward pass over the dataset without retrograde communication. FP generates target values for pre-activation membrane potentials through randomised nonlinear projections of pre-synaptic inputs and labels. Local loss functions are optimised using closed-form regression without feedback from downstream layers. A key advantage is interpretability: membrane potentials in FP-trained networks encode information interpretable layer-wise as label predictions. Across several biomedical datasets, FP achieves generalisation comparable to gradient descent-based local learning methods while requiring only a single forward propagation step, yielding significant training speedup. In few-shot learning tasks, FP produces more generalisable models than backpropagation-optimised alternatives, with local interpretation functions successfully identifying clinically salient diagnostic features.
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