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This paper identifies a structural bottleneck in Forward-Forward (FF) learning: the standard sum-of-squares goodness function collapses feature volumes, omitting critical second-order dependencies. To address this, they introduce Bi-axis Covariance Goodness (BiCovG), a Logistic Fusion module, and a Feature Alignment Layer (FAL) to capture feature covariance and mitigate representation misalignment. The resulting BP-free model achieves 73.01% on ImageNet-100 and 50.30% on Tiny-ImageNet, with a hybrid approach nearly matching backpropagation performance while reducing memory.
Forward-Forward learning can finally compete with backpropagation on complex image tasks, thanks to a novel covariance-aware goodness function that captures crucial second-order feature dependencies.
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.
