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 algorithm eliminates global gradient flow and full network activations storage. However, in convolutional settings, existing BP-free FF methods significantly under-perform backpropagation on complex benchmarks such as ImageNet-100 and Tiny-ImageNet. We identify this gap as a structural bottleneck in goodness extraction: standard sum-of-squares formulation collapses feature volumes into channel-wise activation energies which omits critical second-order dependencies. To address this, we propose a framework centered on three key components. First, Bi-axis Covariance Goodness(BiCovG) explicitly augments the standard goodness function with structured second-order information along two axes: cross-channel projections that model inter-feature covariance, and nested multi-scale aggregation that encodes spatial correlation statistics. This provides a tractable approximation to covariance-aware goodness without the prohibitive O(C^2) complexity of explicit matrix estimation. Second, a lightweight Logistic Fusion module aggregates layer-wise predictions, amplifying the contribution of deeper representations. Third, the Feature Alignment Layer(FAL) introduces a zero-initialized correction at block boundaries to mitigate representation misalignment in deep locally trained networks. By introducing these three components, we effectively double the depth of viable Forward-Forward learning, extending robust layer utilization from shallow baselines to 16 layer architectures like VGG-16. The resulting BP-free model achieves 73.01% on ImageNet-100 and 50.30% on Tiny-ImageNet. As a practical extension, Hybrid Goodness Blocks control the scope of gradient propagation via configurable block sizes, further narrowing the ImageNet-100 gap to 3.6% and matching BP on Tiny-ImageNet, while still reducing peak memory by approximately 50% relative to BP.
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.
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.