When Does Margin Clamping Affect Training Variance? Dataset-Dependent Effects in Contrastive Forward-Forward Learning

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.

Forward-Forward (FF) training lets each layer learn from a local goodness criterion. In cumulative-goodness variants, later layers can inherit a task that earlier layers have partly separated. We formalize this as layer free-riding: under the softplus FF criterion, the class-discrimination gradient reaching block $d$ decays exponentially with the positive margin accumulated by earlier blocks (Theorem 3.1); a squared-hinge barrier reproduces the pathology. History-free and hardness-gated repairs raise deeper-layer separation by up to $5\times$ on CIFAR-100 and $45\times$ in an 8-block CIFAR-10 model, yet these and a depth-scaled auxiliary term move accuracy by under one percentage point among non-degenerate variants; on Tiny ImageNet, a harder cross-dataset check of the selected configuration, layer health likewise does not track accuracy. A theory-derived attenuation-compensated objective raises deepest-block separation $5.9\times$ at a consistent cost in the FF classifier's own accuracy that a probe trained on the frozen features recovers; in a smaller CIFAR-10 control, most of its separation gain comes from dropping the depth-scaled auxiliary term it replaces. Accuracy invariance is a property of the deployed sum-based scoring rule under redistribution (Proposition 3.2) and, empirically, of the structured trained readouts we test, not of what the network learns: retrained variants disagree on 13-26% of test predictions. Architecture and augmentation matter far more than the non-degenerate training rules studied. Cumulative free-riding is therefore a real and repairable pathology, but for the softplus and squared-hinge objectives, architectures, and datasets we study, it is not the dominant factor limiting accuracy.

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 at the time of our submission (91.8% CIFAR-10 and an 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% on ImageNet-100, versus 75.6% even for a self-supervised BP-trained ResNet-50 with linear evaluation [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.