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.
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) 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.
The Forward-Forward (FF) algorithm offers a biologically inspired alternative to backpropagation by replacing gradient-based credit assignment with local, forward-only objectives. While recent extensions have adapted FF to convolutional neural networks (CNNs), existing formulations rely on static channel-class partitions and struggle to perform effectively in complex tasks. In this work, we introduce a learnable channel-class assignment mechanism that enables adaptive, data-driven specialization of convolutional channels, supported by entropy and orthogonality regularization to promote learning performance. We further propose a loss-aware layer contribution strategy that adaptively weights intermediate-layer predictions based on their validation performance, enhancing the effectiveness of forward-only inference. Integrated into residual CNNs, the proposed method achieves consistently superior performance across CIFAR-10, CIFAR-100, and Tiny-ImageNet compared to existing similar forward-only methods. Notably, it establishes new state-of-the-art performance among FF-based models, substantially narrowing the gap with backpropagation. These findings demonstrate that introducing learnable channel specialization and layer contribution weighting significantly enhances the representational capacity of forward-only learning in deep CNNs.