# MAN++: Scaling Momentum Auxiliary Network for Supervised Local Learning in Vision Tasks

arXiv: https://arxiv.org/abs/2507.16279 · HTML: https://mlsanity.com/paper/2507.16279/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 54 references that are in the map.
- First posted on arXiv 22 Jul 2025.

## Builds on (most cited first, 30 of 38)

- [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)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [The Cityscapes Dataset for Semantic Urban Scene Understanding](https://mlsanity.com/paper/1604.01685/) (2016)
- [Aggregated Residual Transformations for Deep Neural Networks](https://mlsanity.com/paper/1611.05431/) (2016)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [On the Convergence of Adam and Beyond](https://mlsanity.com/paper/1904.09237/) (2019)
- [Direct Feedback Alignment Provides Learning in Deep Neural Networks](https://mlsanity.com/paper/1609.01596/) (2016)
- [A Variational Inequality Perspective on Generative Adversarial Networks](https://mlsanity.com/paper/1802.10551/) (2018)
- [Decoupled Neural Interfaces using Synthetic Gradients](https://mlsanity.com/paper/1608.05343/) (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)
- [Deep Learning without Weight Transport](https://mlsanity.com/paper/1904.05391/) (2019)
- [Putting An End to End-to-End: Gradient-Isolated Learning of Representations](https://mlsanity.com/paper/1905.11786/) (2019)
- [Decoupled Greedy Learning of CNNs](https://mlsanity.com/paper/1901.08164/) (2019)
- [Greedy Hierarchical Variational Autoencoders for Large-Scale Video Prediction](https://mlsanity.com/paper/2103.04174/) (2021)
- [Revisiting Locally Supervised Learning: an Alternative to End-to-end Training](https://mlsanity.com/paper/2101.10832/) (2021)
- [Towards Biologically Plausible Deep Learning](https://mlsanity.com/paper/1502.04156/) (2015)
- [Scaling Forward Gradient With Local Losses](https://mlsanity.com/paper/2210.03310/) (2022)
- [Error-driven Input Modulation: Solving the Credit Assignment Problem without a Backward Pass](https://mlsanity.com/paper/2201.11665/) (2022)
- [LoCo: Local Contrastive Representation Learning](https://mlsanity.com/paper/2008.01342/) (2020)
- [Local plasticity rules can learn deep representations using self-supervised contrastive predictions](https://mlsanity.com/paper/2010.08262/) (2020)
- [Deep supervised learning using local errors](https://mlsanity.com/paper/1711.06756/) (2017)
- [Parallel Training of Deep Networks with Local Updates](https://mlsanity.com/paper/2012.03837/) (2020)
- [Credit Assignment Through Broadcasting a Global Error Vector](https://mlsanity.com/paper/2106.04089/) (2021)
- [Interlocking Backpropagation: Improving depthwise model-parallelism](https://mlsanity.com/paper/2010.04116/) (2020)

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

- [Rethinking Local Learning: A Cheaper and Faster Recipe for LLM Post-Training](https://mlsanity.com/paper/2605.04913/) (2026)
- [Correct Is Not Enough: Training Reasoning Planners with Executor-Grounded Rewards](https://mlsanity.com/paper/2605.03862/) (2026)
- [Replacement Learning: Training Neural Networks with Fewer Parameters](https://mlsanity.com/paper/2605.19533/) (2026)

## Abstract (arXiv)

Deep learning typically relies on end-to-end backpropagation for training, a method that inherently suffers from issues such as update locking during parameter optimization, high GPU memory consumption, and a lack of biological plausibility. In contrast, supervised local learning seeks to mitigate these challenges by partitioning the network into multiple local blocks and designing independent auxiliary networks to update each block separately. However, because gradients are propagated solely within individual local blocks, performance degradation occurs, preventing supervised local learning from supplanting end-to-end backpropagation. To address these limitations and facilitate inter-block information flow, we propose the Momentum Auxiliary Network++ (MAN++). MAN++ introduces a dynamic interaction mechanism by employing the Exponential Moving Average (EMA) of parameters from adjacent blocks to enhance communication across the network. The auxiliary network, updated via EMA, effectively bridges the information gap between blocks. Notably, we observed that directly applying EMA parameters can be suboptimal due to feature discrepancies between local blocks. To resolve this issue, we introduce a learnable scaling bias that balances feature differences, thereby further improving performance. We validate MAN++ through extensive experiments on tasks that include image classification, object detection, and image segmentation, utilizing multiple network architectures. The experimental results demonstrate that MAN++ achieves performance comparable to end-to-end training while significantly reducing GPU memory usage. Consequently, MAN++ offers a novel perspective for supervised local learning and presents a viable alternative to conventional training methods.