{"ID":3004662,"CreatedAt":"2026-06-03T03:09:48.883664427Z","UpdatedAt":"2026-06-05T11:43:53.432517148Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.03927","arxiv_id":"2606.03927","title":"FFR: Forward-Forward Learning for Regression","abstract":"The Forward-Forward (FF) algorithm offers a computationally efficient and biologically plausible alternative to backpropagation (BP) by training neural networks through purely local, layer-wise optimization. However, FF is inherently designed for classification via contrastive positive-negative sample pairs, and extending it to regression poses fundamental challenges: continuous target space lack natural \"opposites\" for contrastive learning, and the standard goodness function carries no information about target magnitude or ordering. We propose FFR (Forward-Forward for Regression), to our knowledge, the first framework to extend FF to real-world regression and demonstrate competitive performance across diverse real-world datasets. FFR introduces three key innovations: (1) an ordinal competitive goodness function that replaces contrastive pairs with competitive learning between partitioned neuron groups under distance-aware ordinal supervision; (2) a stratified ladder architecture where shallow layers learn coarse ordinal discrimination and deeper layers refine into fine-grained regression, with multi-scale feature aggregation for inter-layer collaboration; and (3) hierarchical prediction with uncertainty estimation, where multi-scale predictors jointly provide robust predictions and prediction confidence as a free-lunch. Extensive experimental results show FFR recovers on average 98.6% of BP's accuracy across five real-world regression benchmarks while reducing peak training memory to only 27% of BP's at depth 8 and 8% at depth 32, with per-iteration time around 72% of BP's, and substantially outperforms all BP-free competitors.","short_abstract":"The Forward-Forward (FF) algorithm offers a computationally efficient and biologically plausible alternative to backpropagation (BP) by training neural networks through purely local, layer-wise optimization. However, FF is inherently designed for classification via contrastive positive-negative sample pairs, and extend...","url_abs":"https://arxiv.org/abs/2606.03927","url_pdf":"https://arxiv.org/pdf/2606.03927v1","authors":"[\"Xinyang Liu\",\"Xuanyu Liang\",\"Shiqi Ding\",\"Boyang Li\",\"Zhiqiang Que\",\"Jiayang Li\",\"Guosheng Hu\"]","published":"2026-06-02T17:15:59Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.AI\"]","methods":"[]","has_code":false}