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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2605.06240 |
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| _version_ | 1866917468279144448 |
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| author | Yousefiramandi, Amirhossein |
| author_facet | Yousefiramandi, Amirhossein |
| contents | Forward-Forward (FF) training allows each layer to learn from a local goodness criterion. In cumulative-goodness variants, however, later layers can inherit a task that earlier layers have already partially separated. We formalize this phenomenon as layer free-riding: under the softplus FF criterion, the class-discrimination gradient reaching block $d$ decays exponentially with the positive margin accumulated by preceding blocks. We then study three local remedies -- per-block, hardness-gated, and depth-scaled -- that recover current-layer separation measures without relying on backpropagated gradients. On CIFAR-10 and CIFAR-100, these remedies dramatically improve layer-separation statistics, with $4\times$--$45\times$ gains in deeper layers, while changing accuracy by less than one percentage point for non-degenerate training procedures. Tiny ImageNet provides a tougher cross-dataset check for our selected block-wise configuration and reveals the same qualitative gap between layer-health diagnostics and final accuracy. Calibration experiments further show that architecture and augmentation choices have a larger effect on final accuracy than the training-rule modifications studied here. Cumulative free-riding is therefore a real and repairable optimization pathology. Nonetheless, for the FF training rules, architectures, and datasets we study, it is not the dominant factor limiting achievable accuracy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_06240 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Cumulative-Goodness Free-Riding in Forward-Forward Networks: Real, Repairable, but Not Accuracy-Dominant Yousefiramandi, Amirhossein Machine Learning Artificial Intelligence Forward-Forward (FF) training allows each layer to learn from a local goodness criterion. In cumulative-goodness variants, however, later layers can inherit a task that earlier layers have already partially separated. We formalize this phenomenon as layer free-riding: under the softplus FF criterion, the class-discrimination gradient reaching block $d$ decays exponentially with the positive margin accumulated by preceding blocks. We then study three local remedies -- per-block, hardness-gated, and depth-scaled -- that recover current-layer separation measures without relying on backpropagated gradients. On CIFAR-10 and CIFAR-100, these remedies dramatically improve layer-separation statistics, with $4\times$--$45\times$ gains in deeper layers, while changing accuracy by less than one percentage point for non-degenerate training procedures. Tiny ImageNet provides a tougher cross-dataset check for our selected block-wise configuration and reveals the same qualitative gap between layer-health diagnostics and final accuracy. Calibration experiments further show that architecture and augmentation choices have a larger effect on final accuracy than the training-rule modifications studied here. Cumulative free-riding is therefore a real and repairable optimization pathology. Nonetheless, for the FF training rules, architectures, and datasets we study, it is not the dominant factor limiting achievable accuracy. |
| title | Cumulative-Goodness Free-Riding in Forward-Forward Networks: Real, Repairable, but Not Accuracy-Dominant |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2605.06240 |