FFR：面向回归任务的 Forward-Forward 学习框架

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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 lacks 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 realworld 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 a single-pass uncertainty score. Extensive experimental results show FFR recovers on average 98.5% of BP's accuracy across six 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.

Submission history

From: Xinyang Liu [view email]
[v1] Tue, 2 Jun 2026 17:15:59 UTC (6,591 KB)
[v2] Tue, 6 Oct 2026 16:18:54 UTC (7,047 KB)