State-of-the-art methods for backpropagation-free learning employ local error feedback to direct iterative optimisation via gradient descent. In this study, we examine the more restrictive setting where retrograde communication from neuronal outputs is unavailable for pre-synaptic weight optimisation. To address this challenge, we propose Forward Projection (FP). This randomised closed-form training method requires only a single forward pass over the entire dataset for model fitting, without retrograde communication. Our method generates target values for pre-activation membrane potentials at each layer through randomised nonlinear projections of pre-synaptic inputs and the labels, thereby encoding information from both sources. Local loss functions are optimised over pre-synaptic inputs using closed-form regression, without feedback from neuronal outputs or downstream layers. Interpretability is a key advantage of FP training; membrane potentials of hidden neurons in FP-trained networks encode information which are interpretable layer-wise as label predictions. We demonstrate the effectiveness of FP across four biomedical datasets, comparing it with backpropagation and local learning techniques such as Forward-Forward training and Local Supervision in multi-layer perceptron and convolutional architectures. In some few-shot learning tasks, FP yielded more generalisable models than those optimised via backpropagation. In large-sample tasks, FP-based models achieve generalisation comparable to gradient descent-based local learning methods while requiring only a single forward propagation step, achieving significant speed up for training.

翻译：当前最先进的无反向传播学习方法采用局部误差反馈通过梯度下降指导迭代优化。本研究探讨了更严格的场景：神经元输出无法用于突触前权重优化的逆向通信。为解决这一挑战，我们提出正向投影（FP）。这种随机闭式训练方法仅需对整个数据集进行一次前向传播即可完成模型拟合，无需逆向通信。该方法通过突触前输入和标签的随机非线性投影，为每一层的激活前膜电位生成目标值，从而编码来自两个源的信息。局部损失函数通过闭式回归在突触前输入上进行优化，无需神经元输出或下游层的反馈。可解释性是FP训练的关键优势：FP训练网络中隐藏神经元的膜电位所编码的信息，可在逐层意义上解释为标签预测。我们在四个生物医学数据集上验证了FP的有效性，将其与反向传播及局部学习技术（如多层感知机和卷积架构中的前向-前向训练与局部监督）进行比较。在某些小样本学习任务中，FP相比反向传播优化模型展现出更强的泛化能力。在大样本任务中，基于FP的模型实现了与基于梯度下降的局部学习方法相当的泛化性能，同时仅需单次前向传播步骤，显著提升了训练速度。