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.
Deep neural networks trained with backpropagation have achieved outstanding performance in vision tasks but remain biologically implausible, computationally demanding, and difficult to interpret. The Forward-Forward (FF) algorithm offers a promising alternative by training each layer independently through local goodness objectives. However, its purely local optimization lacks hierarchical coordination across layers, and the decoupling of goodness from features leaves the representations unconstrained and semantically ambiguous. We propose a Hierarchical and Contrastive Learning FF framework (HCL-FF) to address these limitations. HCL-FF introduces (1) a coarse-to-fine hierarchical learning strategy that guides representations from low-level cues to high-level semantics, and (2) a supervised contrastive objective that enforces class-discriminative alignment after goodness decoupling. Experiments on CIFAR-10, CIFAR-100, and Tiny-ImageNet demonstrate that HCL-FF achieves new state-of-the-art performance among FF-based methods, with notable accuracy gains of +5.46%, +17.00%, and +12.51%, respectively.
The Forward-Forward (FF) algorithm presents a compelling, bio-inspired alternative to backpropagation. However, while efficient in training, it has a computationally prohibitive inference process that requires a separate forward pass for every class that is evaluated. In this work, we introduce the Hyperspherical Forward-Forward (HFF), a novel reformulation that resolves this critical bottleneck. Our core innovation is to reframe the local objective of each layer from a binary goodness-of-fit task to a direct multi-class classification problem within a hyperspherical feature space. We achieve this by learning a set of class-specific, unit-norm prototypes that act as geometric anchors and implicit negatives. This architectural innovation preserves the benefits of local training while enabling weight update and inference in a single forward pass, making it >40x faster than the original FF algorithm. Our method is simple to implement, scales effectively to modern convolutional architectures, and achieves superior accuracy on standard image classification benchmarks, closing the gap with backpropagation. Most notably, we are among the first greedy local-learning methods to report over 25% top-1 accuracy on ImageNet-1k, and 65.96% with transfer learning.
Forward-Forward (FF) learning [Hinton, 2022] replaces backpropagation with strictly layer-local goodness updates. Recent FF-CNN work has narrowed the gap to BP on 32x32 benchmarks, raising the question of whether layer-local training is becoming a viable alternative at realistic scale. To probe this rigorously, we develop DTG-FF -- dynamic temperature goodness, decoupled normalization, and multi-layer fusion -- as an instrument that sets FF-family state of the art across nine real-data benchmarks (91.8% CIFAR-10 and the first FF baseline at ImageNet-100 224x224), and use it to audit how far layer-local training actually scales. (1) Real-data scaling. Under identical recipe and backbone, an architecture-matched BP-DeepSup baseline beats DTG-FF by 2.40/5.93 pp on CIFAR-10/CIFAR-100, and the gap widens with class count. At 224x224 the same instrument reaches only 49.4% -- the first FF baseline at this scale, versus typical BP above 75% [Tian et al., 2020] -- exposing a real-data ceiling invisible at 32x32. (2) Synthetic vs. real K-conflict. DTG-FF increasingly outperforms BP as class count K grows on synthetic teacher-student tasks, yet on real images the FF-BP gap reverses sign and widens with K. A within-dataset CIFAR-100 coarse vs. fine probe isolates label-hierarchy from image distribution: synthetic K-sweeps confound output dimensionality with fine-grained discrimination difficulty and thereby overstate FF transferability. (3) Systems audit. FF can be implemented without storing depth-wide activations, but on commodity 8 GB hardware standard BP+gradient-accumulation reaches 4.18 GB / 157 imgs/s versus DTG-FF's 7.90 GB / 138 imgs/s, so a memory-based justification for FF at this scale is not supported under fair baselines.