# NM-Hebb: Coupling Local Hebbian Plasticity with Metric Learning for More Accurate and Interpretable CNNs

arXiv: https://arxiv.org/abs/2508.19896 · HTML: https://mlsanity.com/paper/2508.19896/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 41 references that are in the map.
- First posted on arXiv 27 Aug 2025.

## Builds on (most cited first, 28 of 28)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [FixMatch: Simplifying Semi-Supervised Learning with Consistency and Confidence](https://mlsanity.com/paper/2001.07685/) (2020)
- [Shortcut Learning in Deep Neural Networks](https://mlsanity.com/paper/2004.07780/) (2020)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [EfficientNetV2: Smaller Models and Faster Training](https://mlsanity.com/paper/2104.00298/) (2021)
- [SqueezeNet: AlexNet-level accuracy with 50x fewer parameters and <0.5MB model size](https://mlsanity.com/paper/1602.07360/) (2016)
- [ConvNeXt V2: Co-designing and Scaling ConvNets with Masked Autoencoders](https://mlsanity.com/paper/2301.00808/) (2023)
- [Network Dissection: Quantifying Interpretability of Deep Visual Representations](https://mlsanity.com/paper/1704.05796/) (2017)
- [A Fourier Perspective on Model Robustness in Computer Vision](https://mlsanity.com/paper/1906.08988/) (2019)
- [Proxy Anchor Loss for Deep Metric Learning](https://mlsanity.com/paper/2003.13911/) (2020)
- [SoftTriple Loss: Deep Metric Learning Without Triplet Sampling](https://mlsanity.com/paper/1909.05235/) (2019)
- [Interpretable Convolutional Neural Networks](https://mlsanity.com/paper/1710.00935/) (2017)
- [Scaling Up Your Kernels to 31x31: Revisiting Large Kernel Design in CNNs](https://mlsanity.com/paper/2203.06717/) (2022)
- [Hebbian Deep Learning Without Feedback](https://mlsanity.com/paper/2209.11883/) (2022)
- [Towards Learning Convolutions from Scratch](https://mlsanity.com/paper/2007.13657/) (2020)
- [Backpropamine: training self-modifying neural networks with differentiable neuromodulated plasticity](https://mlsanity.com/paper/2002.10585/) (2020)
- [Hebbian Semi-Supervised Learning in a Sample Efficiency Setting](https://mlsanity.com/paper/2103.09002/) (2021)
- [FastHebb: Scaling Hebbian Training of Deep Neural Networks to ImageNet Level](https://mlsanity.com/paper/2207.03172/) (2022)
- [Advancing the Biological Plausibility and Efficacy of Hebbian Convolutional Neural Networks](https://mlsanity.com/paper/2501.17266/) (2025)
- [Enhancing Interpretability Through Loss-Defined Classification Objective in Structured Latent Spaces](https://mlsanity.com/paper/2412.08515/) (2024)
- [Comparison of Embedded Spaces for Deep Learning Classification](https://mlsanity.com/paper/2408.01767/) (2024)

## Built on by (most cited first, 1 of 1)

- [Constrained Hebbian Learning Supports Efficient Representational Allocation under Structural Constraints](https://mlsanity.com/paper/2607.16027/) (2026)

## Abstract (arXiv)

Deep Convolutional Neural Networks (CNNs) achieve high accuracy but often rely on purely global, gradient-based optimisation, which can lead to overfitting, redundant filters, and reduced interpretability. To address these limitations, we propose NM-Hebb, a two-phase training framework that integrates neuro-inspired local plasticity with distance-aware supervision. Phase 1 extends standard supervised training by jointly optimising a cross-entropy objective with two biologically inspired mechanisms: (i) a Hebbian regulariser that aligns the spatial mean of activations with the mean of the corresponding convolutional filter weights, encouraging structured, reusable primitives; and (ii) a learnable neuromodulator that gates an elastic-weight-style consolidation loss, preserving beneficial parameters without freezing the network. Phase 2 fine-tunes the backbone with a pairwise metric-learning loss, explicitly compressing intra-class distances and enlarging inter-class margins in the embedding space. Evaluated on CIFAR-10, CIFAR-100, and TinyImageNet across five backbones (ResNet-18, VGG-11, MobileNet-v2, EfficientNet-V2, DenseNet-121), NM-Hebb achieves consistent gains over baseline and other methods: Top-1 accuracy improves by +2.0-10.0 pp (CIFAR-10), +2.0-9.0 pp (CIFAR-100), and up to +4.3-8.9 pp (TinyImageNet), with Normalised Mutual Information (NMI) increased by up to +0.15. Qualitative visualisations and filter-level analyses further confirm that NM-Hebb produces more structured and selective features, yielding tighter and more interpretable class clusters. Overall, coupling local Hebbian plasticity with metric-based fine-tuning yields CNNs that are not only more accurate but also more interpretable, offering practical benefits for resource-constrained and safety-critical AI deployments.