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

arXiv: https://arxiv.org/abs/2511.18567 · HTML: https://mlsanity.com/paper/2511.18567/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 42 references that are in the map.
- First posted on arXiv 23 Nov 2025.

## Builds on (most cited first, 18 of 18)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Exploring Simple Siamese Representation Learning](https://mlsanity.com/paper/2011.10566/) (2020)
- [Unsupervised Learning of Visual Features by Contrasting Cluster Assignments](https://mlsanity.com/paper/2006.09882/) (2020)
- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [Energy and Policy Considerations for Deep Learning in NLP](https://mlsanity.com/paper/1906.02243/) (2019)
- [Carbon Emissions and Large Neural Network Training](https://mlsanity.com/paper/2104.10350/) (2021)
- [Large-Margin Softmax Loss for Convolutional Neural Networks](https://mlsanity.com/paper/1612.02295/) (2016)
- [Equilibrium Propagation: Bridging the Gap Between Energy-Based Models and Backpropagation](https://mlsanity.com/paper/1602.05179/) (2016)
- [Difference Target Propagation](https://mlsanity.com/paper/1412.7525/) (2014)
- [Decoupled Neural Interfaces using Synthetic Gradients](https://mlsanity.com/paper/1608.05343/) (2016)
- [The Mechanics of n-Player Differentiable Games](https://mlsanity.com/paper/1802.05642/) (2018)
- [Reducing Overfitting in Deep Networks by Decorrelating Representations](https://mlsanity.com/paper/1511.06068/) (2015)
- [How Auto-Encoders Could Provide Credit Assignment in Deep Networks via Target Propagation](https://mlsanity.com/paper/1407.7906/) (2014)
- [Towards Biologically Plausible Deep Learning](https://mlsanity.com/paper/1502.04156/) (2015)

## Built on by (most cited first, 2 of 2)

- [Selectivity and Shape in the Design of Forward-Forward Goodness Functions](https://mlsanity.com/paper/2604.13081/) (2026)
- [Gauge-Fixing the Forward-Forward Objective: A Whitened Goodness Derived from a Likelihood-Ratio Account](https://mlsanity.com/paper/2607.12501/) (2026)

## Abstract (arXiv)

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, textttgametheoreticlocal achieved 97.15% accuracy on MNIST, textttsoftmaxenergymarginlocal reached 82.84% on FashionMNIST, and texttttripletmarginlocal 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 hrefhttps://github.com/aryashah2k/In-Search-of-GoodnessGithub for reference and reproducibility.