When Goodness Forgets Shape: Information Loss in Forward-Forward Learning

Forward-Forward (FF) learning replaces end-to-end backpropagation with local goodness objectives, but local supervision is only useful if the goodness function preserves the information needed for prediction. We identify a failure mode in spatial representations: mean-squared goodness is invariant to permutations of hidden spatial positions, making some shape-relevant distinctions invisible to the local objective. Under spurious correlations, this invariance can suppress shape evidence while allowing simpler nuisance cues to dominate. We study spatial goodness through controlled adaptations that expose spatial structure to local supervision while preserving block-local training and avoiding cross-block gradients. Capacity-matched and coordinate-randomization controls isolate stable spatial indexing as the relevant source of improvement. On Colored MNIST, spatial goodness increases reversed-color accuracy from 10.83% to 85.02%. In a controlled adaptation of Adaptive Spatial Goodness Encoding (ASGE), spatial local predictions achieve 77.48% reversed-color accuracy, whereas global-average fusion of the same trained representation reduces performance to 10.12%, showing that spatial evidence can be learned locally yet discarded during prediction. Experiments on Waterbirds extend the analysis to natural images and improve worst-group performance. These results show that robust local learning depends not only on what representations encode, but also on what local objectives and prediction rules preserve.