# Adaptive Spatial Goodness Encoding: Advancing and Scaling Forward-Forward Learning Without Backpropagation

arXiv: https://arxiv.org/abs/2509.12394 · HTML: https://mlsanity.com/paper/2509.12394/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 42 references that are in the map.
- First posted on arXiv 15 Sep 2025.

## Builds on (most cited first, 23 of 23)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [The Forward-Forward Algorithm: Some Preliminary Investigations](https://mlsanity.com/paper/2212.13345/) (2022)
- [Direct Feedback Alignment Provides Learning in Deep Neural Networks](https://mlsanity.com/paper/1609.01596/) (2016)
- [Training Neural Networks with Local Error Signals](https://mlsanity.com/paper/1901.06656/) (2019)
- [Greedy Layerwise Learning Can Scale to ImageNet](https://mlsanity.com/paper/1812.11446/) (2018)
- [Assessing the Scalability of Biologically-Motivated Deep Learning Algorithms and Architectures](https://mlsanity.com/paper/1807.04587/) (2018)
- [How Auto-Encoders Could Provide Credit Assignment in Deep Networks via Target Propagation](https://mlsanity.com/paper/1407.7906/) (2014)
- [Error-driven Input Modulation: Solving the Credit Assignment Problem without a Backward Pass](https://mlsanity.com/paper/2201.11665/) (2022)
- [Understanding Synthetic Gradients and Decoupled Neural Interfaces](https://mlsanity.com/paper/1703.00522/) (2017)
- [Towards Scaling Difference Target Propagation by Learning Backprop Targets](https://mlsanity.com/paper/2201.13415/) (2022)
- [Learned-Norm Pooling for Deep Feedforward and Recurrent Neural Networks](https://mlsanity.com/paper/1311.1780/) (2013)
- [SoftHebb: Bayesian Inference in Unsupervised Hebbian Soft Winner-Take-All Networks](https://mlsanity.com/paper/2107.05747/) (2021)
- [SymBa: Symmetric Backpropagation-Free Contrastive Learning with Forward-Forward Algorithm for Optimizing Convergence](https://mlsanity.com/paper/2303.08418/) (2023)
- [Direct Feedback Alignment with Sparse Connections for Local Learning](https://mlsanity.com/paper/1903.02083/) (2019)
- [Convolutional Channel-wise Competitive Learning for the Forward-Forward Algorithm](https://mlsanity.com/paper/2312.12668/) (2023)
- [Layer Collaboration in the Forward-Forward Algorithm](https://mlsanity.com/paper/2305.12393/) (2023)
- [Training Convolutional Neural Networks with the Forward-Forward algorithm](https://mlsanity.com/paper/2312.14924/) (2023)
- [LLS: Local Learning Rule for Deep Neural Networks Inspired by Neural Activity Synchronization](https://mlsanity.com/paper/2405.15868/) (2024)
- [A Contrastive Symmetric Forward-Forward Algorithm (SFFA) for Continual Learning Tasks](https://mlsanity.com/paper/2409.07387/) (2024)

## Built on by (most cited first, 3 of 3)

- [Cumulative-Goodness Free-Riding in Forward-Forward Networks: Real, Repairable, but Not Accuracy-Dominant](https://mlsanity.com/paper/2605.06240/) (2026)
- [Synthetic Benchmarks Overstate Forward-Forward Scaling: Real-Data Limits of Layer-Local Training](https://mlsanity.com/paper/2606.06539/) (2026)
- [Rescuing Points Trapped Inside Incorrect Decision Regions: A target for Evaluating and Improving Forward-Forward Learning](https://mlsanity.com/paper/2610.16347/) (2026)

## Abstract (arXiv)

The Forward-Forward (FF) algorithm offers a promising alternative to backpropagation (BP). Despite advancements in recent FF-based extensions, which have enhanced the original algorithm and adapted it to convolutional neural networks (CNNs), they often suffer from limited representational capacity and poor scalability to large-scale datasets, primarily due to exploding channel dimensionality. In this work, we propose adaptive spatial goodness encoding (ASGE), a new FF-based training framework tailored for CNNs. ASGE leverages feature maps to compute spatially-aware goodness representations at each layer, enabling layer-wise supervision. Crucially, this approach decouples classification complexity from channel dimensionality, thereby addressing the issue of channel explosion and achieving competitive performance compared to other BP alternatives. ASGE outperforms all other FF-based approaches across multiple benchmarks, delivering test accuracies of 99.65% on MNIST, 93.41% on FashionMNIST, 90.62% on CIFAR-10, and 65.42% on CIFAR-100. Moreover, we present the first successful application of FF-based training to ImageNet, with Top-1 and Top-5 accuracies of 51.58% and 75.23%. Furthermore, we propose three prediction strategies to achieve flexible trade-offs among accuracy, parameters and memory usage, enabling deployment under diverse resource constraints.