Rescuing Points Trapped Inside Incorrect Decision Regions: A target for Evaluating and Improving Forward-Forward Learning

Abstract

Forward-Forward learning replaces end-to-end backpropagation with local, layer-wise training objectives. Its variants are evaluated primarily by classification accuracy, often measured with linear probes trained on their representations. We show that this evaluation can over-credit the learning method: a linear probe on the representations of an untrained convolutional neural network already reaches accuracy well above chance. Moreover, a single accuracy value does not reveal which datapoints become correctly classified after training and which remain misclassified. To examine what learning contributes beyond the random, untrained baseline, we present an analysis methodology built on the Boundary Proximity Index (BPI), a multiclass margin normalized by a class-centroid reference. We apply our analysis to seven Forward-Forward variants and related layer-local methods and find that initially misclassified points near the probe's decision boundary generally have higher rescue rates than those farther inside incorrect decision regions. Rescue rates vary substantially across methods, with some correcting a substantial fraction of these deeply embedded points. Together, these analyses offer a way to evaluate representation learning beyond accuracy and identify the rescue of points far inside incorrect decision regions as a target for improving local learning methods.