mlsanityData to 7 Oct 2026

The Cascaded Forward Algorithm for Neural Network Training

arXiv 2303.09728 ↗First posted 17 Mar 2023cs.CVcited by 17

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Abstract (arXiv)

Backpropagation algorithm has been widely used as a mainstream learning procedure for neural networks in the past decade, and has played a significant role in the development of deep learning. However, there exist some limitations associated with this algorithm, such as getting stuck in local minima and experiencing vanishing/exploding gradients, which have led to questions about its biological plausibility. To address these limitations, alternative algorithms to backpropagation have been preliminarily explored, with the Forward-Forward (FF) algorithm being one of the most well-known. In this paper we propose a new learning framework for neural networks, namely Cascaded Forward (CaFo) algorithm, which does not rely on BP optimization as that in FF. Unlike FF, our framework directly outputs label distributions at each cascaded block, which does not require generation of additional negative samples and thus leads to a more efficient process at both training and testing. Moreover, in our framework each block can be trained independently, so it can be easily deployed into parallel acceleration systems. The proposed method is evaluated on four public image classification benchmarks, and the experimental results illustrate significant improvement in prediction accuracy in comparison with the baseline.

Key facts. Cited by 17 papers in the map (data through 7 Oct 2026). Builds on 16 of its 29 references that are in the map. First posted on arXiv 17 Mar 2023.

Builds on

16 of 29 references.

References · 16

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2015Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networkscited by 9,617
  3. 2015Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shiftcited by 6,979
  4. 2015Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classificationcited by 3,590
  5. 2016Matching Networks for One Shot Learningcited by 2,246
  6. 2017Random Erasing Data Augmentationcited by 1,235
  7. 2021Segmenter: Transformer for Semantic Segmentationcited by 855
  8. 2021CrossViT: Cross-Attention Multi-Scale Vision Transformer for Image Classificationcited by 806
  9. 2016From Softmax to Sparsemax: A Sparse Model of Attention and Multi-Label Classificationcited by 337
  10. 2019Why gradient clipping accelerates training: A theoretical justification for adaptivitycited by 335
  11. 2014Identifying and attacking the saddle point problem in high-dimensional non-convex optimizationcited by 286
  12. 2022The Forward-Forward Algorithm: Some Preliminary Investigationscited by 262
4 more
  1. 2018Which Neural Net Architectures Give Rise To Exploding and Vanishing Gradients?cited by 94
  2. 2020The Neural Coding Framework for Learning Generative Modelscited by 44
  3. 2018Biologically Motivated Algorithms for Propagating Local Target Representationscited by 43
  4. 2023The Predictive Forward-Forward Algorithmcited by 35

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 5; 2024: 4; 2025: 4; 2026: 4.

17 papers.

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  1. 2023Brain-Inspired Machine Intelligence: A Survey of Neurobiologically-Plausible Credit Assignmentcited by 13
  2. 2023Training Convolutional Neural Networks with the Forward-Forward algorithmcited by 13
  3. 2023Contrastive-Signal-Dependent Plasticity: Self-Supervised Learning in Spiking Neural Circuitscited by 10
  4. 2023Block-local learning with probabilistic latent representationscited by 6
  5. 2025Stochastic Forward-Forward Learning through Representational Dimensionality Compressioncited by 4
  6. 2024LightFF: Lightweight Inference for Forward-Forward Algorithmcited by 3
  7. 2025Mono-Forward: Revisiting Forward-Forward through Objective-Locality Decompositioncited by 3
  8. 2024DFA-GNN: Forward Learning of Graph Neural Networks by Direct Feedback Alignmentcited by 2
  9. 2026Covariance-Aware Goodness for Scalable Forward-Forward Learningcited by 2
  10. 2024Forward Learning of Graph Neural Networkscited by 1
  11. 2024Going Forward-Forward in Distributed Deep Learningcited by 1
  12. 2026HCL-FF: Hierarchical and Contrastive Learning for Forward-Forward Algorithmcited by 1
5 more
  1. 2023Using Linear Regression for Iteratively Training Neural Networkscited by 0
  2. 2025Forward-Cooperation-Backward (FCB) learning in a Multi-Encoding Uni-Decoding neural network architecturecited by 0
  3. 2025Energy-Efficient Supervised Learning with a Binary Stochastic Forward-Forward Algorithmcited by 0
  4. 2026Gauge-Fixing the Forward-Forward Objective: A Whitened Goodness Derived from a Likelihood-Ratio Accountcited by 0
  5. 2026Emergent Hierarchical Monosemantic Neurons from the Group-Contrastive Forward-Forward Algorithmcited by 0