对比21种好坏函数，发现特定设计能显著提升前向-前向算法性能。
In Search of Goodness: Large Scale Benchmarking of Goodness Functions for the Forward-Forward Algorithm
- 测试21种好坏度量方式，寻找最优局部更新策略
- 某些新函数在MNIST上达97.15%准确率，超越传统方法
- 揭示性能与能耗间的权衡，适合关注效率的模型设计者
前向-前向（FF）算法为反向传播提供了生物可解释的替代方案，通过局部更新实现学习，但其效果高度依赖于“好坏”度量的定义——一种衡量神经活动的标量。尽管当前普遍采用简单的平方和度量，但其是否最优尚不明确。为此，我们在四个标准图像数据集（MNIST、FashionMNIST、CIFAR-10、STL-10）上对21种不同的好坏函数进行了大规模基准测试，评估分类准确率、能耗及碳足迹。结果表明，来自不同领域的若干替代函数显著优于默认基线：例如， exttt{game\_theoretic\_local} 在 MNIST 上达到 97.15% 准确率， exttt{softmax\_energy\_margin\_local} 在 FashionMNIST 上达 82.84%， exttt{triplet\_margin\_local} 在 STL-10 上取得 37.69% 的表现。此外，计算效率存在显著差异，凸显预测性能与环境成本之间的关键权衡。研究证明，好坏函数是前向-前向算法设计中的核心超参数。代码已开源以供复现。
原文摘要 · Abstract (English)
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.
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