In Search of Goodness: Large Scale Benchmarking of Goodness Functions for the Forward-Forward Algorithm

TL;DR

This paper systematically benchmarks 21 goodness functions for the Forward-Forward algorithm across multiple datasets, revealing that alternative functions can significantly improve accuracy and efficiency, emphasizing the importance of choosing the right goodness measure.

Contribution

It introduces a comprehensive benchmarking of diverse goodness functions for FF, identifying superior alternatives to the standard sum-of-squares and analyzing their impact on performance and environmental cost.

Findings

Certain goodness functions outperform the baseline in accuracy.

Trade-offs exist between predictive performance and energy consumption.

The choice of goodness function critically affects FF's effectiveness.

Abstract

The Forward-Forward (FF) algorithm offers a biologically plausible alternative to backpropagation, enabling neural networks to learn through local updates. However, FF's efficacy relies heavily on the definition of "goodness", which is a scalar measure of neural activity. While current implementations predominantly utilize a simple sum-of-squares metric, it remains unclear if this default choice is optimal. To address this, we benchmarked 21 distinct goodness functions across four standard image datasets (MNIST, FashionMNIST, CIFAR-10, STL-10), evaluating classification accuracy, energy consumption, and carbon footprint. We found that certain alternative goodness functions inspired from various domains significantly outperform the standard baseline. Specifically, \texttt{game\_theoretic\_local} achieved 97.15\% accuracy on MNIST, \texttt{softmax\_energy\_margin\_local} reached 82.84\% on FashionMNIST, and \texttt{triplet\_margin\_local} attained 37.69\% on STL-10. Furthermore, we observed substantial variability in computational efficiency, highlighting a critical trade-off between predictive performance and environmental cost. These findings demonstrate that the goodness function is a pivotal hyperparameter in FF design. We release our code on \href{https://github.com/aryashah2k/In-Search-of-Goodness}{Github} for reference and reproducibility.