Cumulative-Goodness Free-Riding in Forward-Forward Networks: Real, Repairable, but Not Accuracy-Dominant
Forward-Forward (FF) training lets each layer learn from a local goodness criterion. In cumulative-goodness variants, later layers can inherit a task that earlier layers have partly separated. We formalize this as layer free-riding: under the softplus FF criterion, the class-discrimination gradient reaching block $d$ decays exponentially with the positive margin accumulated by earlier blocks (Theorem 3.1); a squared-hinge barrier reproduces the pathology. History-free and hardness-gated repairs raise deeper-layer separation by up to $5\times$ on CIFAR-100 and $45\times$ in an 8-block CIFAR-10 model, yet these and a depth-scaled auxiliary term move accuracy by under one percentage point am...
| Authors | Amirhossein Yousefiramandi |
|---|---|
| Primary category | cs.LG |
| Published | 7 May 2026 |
| Last updated at source | 28 September 2026 |
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