Gauge-Fixing the Forward-Forward Objective: A Whitened Goodness Derived from a Likelihood-Ratio Account
The Forward-Forward algorithm trains each layer locally, so that a scalar goodness - the sum of squared activations - is high on real inputs and low on contrastive ones. Under an explicit generative model this goodness is the sufficient statistic of a likelihood-ratio test, and the pairwise form of the objective admits a gauge: a layer can lower its loss by inflating the scale of its weights rather than by separating the two populations. The analysis prescribes the repair - a whitened, scale-invariant goodness trained online within each layer - which we evaluate as a training procedure. Across three corpora, three depths and a fourfold range of layer width (13 seeds per cell), it raises l...
| Authors | Paolo Giannitrapani |
|---|---|
| Primary category | cs.LG |
| Published | 14 July 2026 |
| Last updated at source | 12 August 2026 |
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