Selectivity and Shape in the Design of Forward-Forward Goodness Functions

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Main Authors: Akkus, Talha Ruzgar, Kocabay, Suayp Talha, Yuksel, Kamer Ali, Sawaf, Hassan
Format: Preprint
Published: 2026
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author Akkus, Talha Ruzgar
Kocabay, Suayp Talha
Yuksel, Kamer Ali
Sawaf, Hassan
author_facet Akkus, Talha Ruzgar
Kocabay, Suayp Talha
Yuksel, Kamer Ali
Sawaf, Hassan
contents The Forward-Forward (FF) algorithm trains networks layer-by-layer using a local "goodness function," yet sum-of-squares (SoS) has remained the only choice studied. We systematically explore the goodness-function design space and identify a unifying principle: the goodness function must be sensitive to the shape of neural activity, not its total energy. This principle is motivated by the observation that deep network activations follow heavy-tailed distributions and that discriminative information is often concentrated in peak activities. We propose two complementary families: selective functions (top-k, entmax-weighted energy) that measure only peak activity, and shape-sensitive functions (excess kurtosis / "burstiness" and higher-order moments) that reward heavy-tailed distributions via scale-invariant statistics. Combined with separate label-feature forwarding (FFCL), controlled experiments across 13 goodness functions, 5 activations, 6 datasets, and three continuous sweeps, each tracing a characteristic inverted-U, yield 89.0% on Fashion-MNIST and 98.2+-0.1% on MNIST (4x2000), a +32.6pp gain over SoS, with consistent improvements across all benchmarks (+72pp USPS, +52pp SVHN). The scale-invariant nature of burstiness makes it particularly robust to magnitude shifts across layers and datasets.
format Preprint
id arxiv_https___arxiv_org_abs_2604_13081
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Selectivity and Shape in the Design of Forward-Forward Goodness Functions
Akkus, Talha Ruzgar
Kocabay, Suayp Talha
Yuksel, Kamer Ali
Sawaf, Hassan
Machine Learning
Artificial Intelligence
Neural and Evolutionary Computing
The Forward-Forward (FF) algorithm trains networks layer-by-layer using a local "goodness function," yet sum-of-squares (SoS) has remained the only choice studied. We systematically explore the goodness-function design space and identify a unifying principle: the goodness function must be sensitive to the shape of neural activity, not its total energy. This principle is motivated by the observation that deep network activations follow heavy-tailed distributions and that discriminative information is often concentrated in peak activities. We propose two complementary families: selective functions (top-k, entmax-weighted energy) that measure only peak activity, and shape-sensitive functions (excess kurtosis / "burstiness" and higher-order moments) that reward heavy-tailed distributions via scale-invariant statistics. Combined with separate label-feature forwarding (FFCL), controlled experiments across 13 goodness functions, 5 activations, 6 datasets, and three continuous sweeps, each tracing a characteristic inverted-U, yield 89.0% on Fashion-MNIST and 98.2+-0.1% on MNIST (4x2000), a +32.6pp gain over SoS, with consistent improvements across all benchmarks (+72pp USPS, +52pp SVHN). The scale-invariant nature of burstiness makes it particularly robust to magnitude shifts across layers and datasets.
title Selectivity and Shape in the Design of Forward-Forward Goodness Functions
topic Machine Learning
Artificial Intelligence
Neural and Evolutionary Computing
url https://arxiv.org/abs/2604.13081