Adaptive Spatial Goodness Encoding: Advancing and Scaling Forward-Forward Learning Without Backpropagation

Qingchun Gong; Robert Bogdan Staszewski; Kai Xu

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arXiv · 2509.12394

Adaptive Spatial Goodness Encoding: Advancing and Scaling Forward-Forward Learning Without Backpropagation

Qingchun Gong·Robert Bogdan Staszewski·Kai Xu

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Abstract

The Forward-Forward (FF) algorithm offers a promising alternative to backpropagation (BP). Despite advancements in recent FF-based extensions, which have enhanced the original algorithm and adapted it to convolutional neural networks (CNNs), they often suffer from limited representational capacity and poor scalability to large-scale datasets, primarily due to exploding channel dimensionality. In this work, we propose adaptive spatial goodness encoding (ASGE), a new FF-based training framework tailored for CNNs. ASGE leverages feature maps to compute spatially-aware goodness representations at each layer, enabling layer-wise supervision. Crucially, this approach decouples classification complexity from channel dimensionality, thereby addressing the issue of channel explosion and achieving competitive performance compared to other BP alternatives. ASGE outperforms all other FF-based approaches across multiple benchmarks, delivering test accuracies of 99.65% on MNIST, 93.41% on FashionMNIST, 90.62% on CIFAR-10, and 65.42% on CIFAR-100. Moreover, we present the first successful application of FF-based training to ImageNet, with Top-1 and Top-5 accuracies of 51.58% and 75.23%. Furthermore, we propose three prediction strategies to achieve flexible trade-offs among accuracy, parameters and memory usage, enabling deployment under diverse resource constraints.

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Qingchun Gong, Robert Bogdan Staszewski, Kai Xu. 2026-01-22. Adaptive Spatial Goodness Encoding: Advancing and Scaling Forward-Forward Learning Without Backpropagation. https://arxiv.org/abs/2509.12394

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