# LLS: Local Learning Rule for Deep Neural Networks Inspired by Neural Activity Synchronization

arXiv: https://arxiv.org/abs/2405.15868 · HTML: https://mlsanity.com/paper/2405.15868/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 34 references that are in the map.
- First posted on arXiv 24 May 2024.

## Builds on (most cited first, 16 of 16)

- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [Random Erasing Data Augmentation](https://mlsanity.com/paper/1708.04896/) (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)
- [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)
- [Revisiting Locally Supervised Learning: an Alternative to End-to-end Training](https://mlsanity.com/paper/2101.10832/) (2021)
- [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)
- [Visual Wake Words Dataset](https://mlsanity.com/paper/1906.05721/) (2019)
- [DNN+NeuroSim V2.0: An End-to-End Benchmarking Framework for Compute-in-Memory Accelerators for On-chip Training](https://mlsanity.com/paper/2003.06471/) (2020)
- [Direct Feedback Alignment with Sparse Connections for Local Learning](https://mlsanity.com/paper/1903.02083/) (2019)
- [PANTHER: A Programmable Architecture for Neural Network Training Harnessing Energy-efficient ReRAM](https://mlsanity.com/paper/1912.11516/) (2019)
- [Convergence and Alignment of Gradient Descent with Random Backpropagation Weights](https://mlsanity.com/paper/2106.06044/) (2021)

## Built on by (most cited first, 5 of 5)

- [TESS: A Scalable Temporally and Spatially Local Learning Rule for Spiking Neural Networks](https://mlsanity.com/paper/2502.01837/) (2025)
- [Adaptive Spatial Goodness Encoding: Advancing and Scaling Forward-Forward Learning Without Backpropagation](https://mlsanity.com/paper/2509.12394/) (2025)
- [LANCE: Low Rank Activation Compression for Efficient On-Device Continual Learning](https://mlsanity.com/paper/2509.21617/) (2025)
- [Closed-Form Feedback-Free Learning with Forward Projection](https://mlsanity.com/paper/2501.16476/) (2025)
- [Stochastic Layer-wise Learning: Scalable and Efficient Alternative to Backpropagation](https://mlsanity.com/paper/2505.05181/) (2025)

## Abstract (arXiv)

Training deep neural networks (DNNs) using traditional backpropagation (BP) presents challenges in terms of computational complexity and energy consumption, particularly for on-device learning where computational resources are limited. Various alternatives to BP, including random feedback alignment, forward-forward, and local classifiers, have been explored to address these challenges. These methods have their advantages, but they can encounter difficulties when dealing with intricate visual tasks or demand considerable computational resources. In this paper, we propose a novel Local Learning rule inspired by neural activity Synchronization phenomena (LLS) observed in the brain. LLS utilizes fixed periodic basis vectors to synchronize neuron activity within each layer, enabling efficient training without the need for additional trainable parameters. We demonstrate the effectiveness of LLS and its variations, LLS-M and LLS-MxM, on multiple image classification datasets, achieving accuracy comparable to BP with reduced computational complexity and minimal additional parameters. Specifically, LLS achieves comparable performance with up to 300 × fewer multiply-accumulate (MAC) operations and half the memory requirements of BP. Furthermore, the performance of LLS on the Visual Wake Word (VWW) dataset highlights its suitability for on-device learning tasks, making it a promising candidate for edge hardware implementations.