# Efficient and Flexible Neural Network Training through Layer-wise Feedback Propagation

arXiv: https://arxiv.org/abs/2308.12053 · HTML: https://mlsanity.com/paper/2308.12053/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 78 of its 132 references that are in the map.
- First posted on arXiv 23 Aug 2023.

## Builds on (most cited first, 30 of 78)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [Striving for Simplicity: The All Convolutional Net](https://mlsanity.com/paper/1412.6806/) (2014)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [Analyzing Multi-Head Self-Attention: Specialized Heads Do the Heavy Lifting, the Rest Can Be Pruned](https://mlsanity.com/paper/1905.09418/) (2019)
- [Network Dissection: Quantifying Interpretability of Deep Visual Representations](https://mlsanity.com/paper/1704.05796/) (2017)
- [Interpretable Explanations of Black Boxes by Meaningful Perturbation](https://mlsanity.com/paper/1704.03296/) (2017)
- [Evolution Strategies as a Scalable Alternative to Reinforcement Learning](https://mlsanity.com/paper/1703.03864/) (2017)
- [Skin Lesion Analysis Toward Melanoma Detection: A Challenge at the 2017 International Symposium on Biomedical Imaging (ISBI), Hosted by the International Skin Imaging Collaboration (ISIC)](https://mlsanity.com/paper/1710.05006/) (2017)
- [Pruning neural networks without any data by iteratively conserving synaptic flow](https://mlsanity.com/paper/2006.05467/) (2020)
- [High-Performance Large-Scale Image Recognition Without Normalization](https://mlsanity.com/paper/2102.06171/) (2021)
- [Incorporating Learnable Membrane Time Constant to Enhance Learning of Spiking Neural Networks](https://mlsanity.com/paper/2007.05785/) (2020)
- [The Forward-Forward Algorithm: Some Preliminary Investigations](https://mlsanity.com/paper/2212.13345/) (2022)

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

- [Relevance-driven Input Dropout: an Explanation-guided Regularization Technique](https://mlsanity.com/paper/2505.21595/) (2025)
- [Structural Compactness as a Complementary Criterion for Explanation Quality](https://mlsanity.com/paper/2603.29491/) (2026)

## Abstract (arXiv)

Gradient-based optimization has been a cornerstone of machine learning that enabled the vast advances of Artificial Intelligence (AI) development over the past decades. However, this type of optimization requires differentiation, and with recent evidence of the benefits of non-differentiable (e.g. neuromorphic) architectures over classical models w.r.t. efficiency, such constraints can become limiting in the future. We present Layer-wise Feedback Propagation (LFP), a novel training principle for neural network-like predictors that utilizes methods from the domain of explainability to decompose a reward to individual neurons based on their respective contributions. Leveraging these neuron-wise rewards, our method then implements a greedy approach reinforcing helpful parts of the network and weakening harmful ones. While having comparable computational complexity to gradient descent, LFP does not require gradient computation and generates sparse and thereby memory- and energy-efficient parameter updates and models. We establish the convergence of LFP theoretically and empirically, demonstrating its effectiveness on various models and datasets. Via two applications - neural network pruning and the approximation-free training of Spiking Neural Networks (SNNs) - we demonstrate that LFP combines increased efficiency in terms of computation and representation with flexibility w.r.t. choice of model architecture and objective function. Our code is available at https://github.com/leanderweber/layerwise-feedback-propagation.