# HCL-FF: Hierarchical and Contrastive Learning for Forward-Forward Algorithm

arXiv: https://arxiv.org/abs/2605.24797 · HTML: https://mlsanity.com/paper/2605.24797/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 57 references that are in the map.
- First posted on arXiv 24 May 2026.

## Builds on (most cited first, 30 of 37)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [CosFace: Large Margin Cosine Loss for Deep Face Recognition](https://mlsanity.com/paper/1801.09414/) (2018)
- [SphereFace: Deep Hypersphere Embedding for Face Recognition](https://mlsanity.com/paper/1704.08063/) (2017)
- [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)
- [NormFace: L2 Hypersphere Embedding for Face Verification](https://mlsanity.com/paper/1704.06369/) (2017)
- [Difference Target Propagation](https://mlsanity.com/paper/1412.7525/) (2014)
- [Decoupled Neural Interfaces using Synthetic Gradients](https://mlsanity.com/paper/1608.05343/) (2016)
- [Assessing the Scalability of Biologically-Motivated Deep Learning Algorithms and Architectures](https://mlsanity.com/paper/1807.04587/) (2018)
- [Deep Learning without Weight Transport](https://mlsanity.com/paper/1904.05391/) (2019)
- [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)
- [Hebbian Deep Learning Without Feedback](https://mlsanity.com/paper/2209.11883/) (2022)
- [NBDT: Neural-Backed Decision Trees](https://mlsanity.com/paper/2004.00221/) (2020)
- [Biologically Motivated Algorithms for Propagating Local Target Representations](https://mlsanity.com/paper/1805.11703/) (2018)
- [The Predictive Forward-Forward Algorithm](https://mlsanity.com/paper/2301.01452/) (2023)
- [Towards Scaling Difference Target Propagation by Learning Backprop Targets](https://mlsanity.com/paper/2201.13415/) (2022)
- [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)
- [Convolutional Channel-wise Competitive Learning for the Forward-Forward Algorithm](https://mlsanity.com/paper/2312.12668/) (2023)
- [Signal Propagation: A Framework for Learning and Inference In a Forward Pass](https://mlsanity.com/paper/2204.01723/) (2022)
- [Principled Training of Neural Networks with Direct Feedback Alignment](https://mlsanity.com/paper/1906.04554/) (2019)
- [Layer Collaboration in the Forward-Forward Algorithm](https://mlsanity.com/paper/2305.12393/) (2023)
- [Hebbian Semi-Supervised Learning in a Sample Efficiency Setting](https://mlsanity.com/paper/2103.09002/) (2021)
- [Hebbian learning with gradients: Hebbian convolutional neural networks with modern deep learning frameworks](https://mlsanity.com/paper/2107.01729/) (2021)
- [The Cascaded Forward Algorithm for Neural Network Training](https://mlsanity.com/paper/2303.09728/) (2023)
- [Self-Contrastive Forward-Forward Algorithm](https://mlsanity.com/paper/2409.11593/) (2024)

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

- [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)

Deep neural networks trained with backpropagation have achieved outstanding performance in vision tasks but remain biologically implausible, computationally demanding, and difficult to interpret. The Forward-Forward (FF) algorithm offers a promising alternative by training each layer independently through local goodness objectives. However, its purely local optimization lacks hierarchical coordination across layers, and the decoupling of goodness from features leaves the representations unconstrained and semantically ambiguous. We propose a Hierarchical and Contrastive Learning FF framework (HCL-FF) to address these limitations. HCL-FF introduces (1) a coarse-to-fine hierarchical learning strategy that guides representations from low-level cues to high-level semantics, and (2) a supervised contrastive objective that enforces class-discriminative alignment after goodness decoupling. Experiments on CIFAR-10, CIFAR-100, and Tiny-ImageNet demonstrate that HCL-FF achieves new state-of-the-art performance among FF-based methods, with notable accuracy gains of +5.46%, +17.00%, and +12.51%, respectively.