Convection-Diffusion Equation: A Theoretically Certified Framework for Neural Networks
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Abstract (arXiv)
In this paper, we study the partial differential equation models of neural networks. Neural network can be viewed as a map from a simple base model to a complicate function. Based on solid analysis, we show that this map can be formulated by a convection-diffusion equation. This theoretically certified framework gives mathematical foundation and more understanding of neural networks. Moreover, based on the convection-diffusion equation model, we design a novel network structure, which incorporates diffusion mechanism into network architecture. Extensive experiments on both benchmark datasets and real-world applications validate the performance of the proposed model.
Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 65 of its 106 references that are in the map. First posted on arXiv 23 Mar 2024.
Builds on
65 of 106 references.
References · 65
- 2015Deep Residual Learning for Image Recognitioncited by 51,809
- 2014Very Deep Convolutional Networks for Large-Scale Image Recognitioncited by 15,267
- 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
- 2017Graph Attention Networkscited by 8,854
- 2014ImageNet Large Scale Visual Recognition Challengecited by 8,441
- 2014Explaining and Harnessing Adversarial Examplescited by 7,287
- 2016Densely Connected Convolutional Networkscited by 6,691
- 2017Inductive Representation Learning on Large Graphscited by 6,284
- 2017Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networkscited by 4,861
- 2018Neural Ordinary Differential Equationscited by 3,733
- 2016Wide Residual Networkscited by 3,057
- 2017Prototypical Networks for Few-shot Learningcited by 3,001
38 more
- 2018UMAP: Uniform Manifold Approximation and Projection for Dimension Reductioncited by 2,841
- 2016Aggregated Residual Transformations for Deep Neural Networkscited by 2,540
- 2016Matching Networks for One Shot Learningcited by 2,246
- 2016Identity Mappings in Deep Residual Networkscited by 1,960
- 2016Adversarial examples in the physical worldcited by 1,762
- 2019Simplifying Graph Convolutional Networkscited by 1,470
- 2019Certified Adversarial Robustness via Randomized Smoothingcited by 1,324
- 2017Learning to Compare: Relation Network for Few-Shot Learningcited by 1,139
- 2015Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)cited by 1,061
- 2018Pitfalls of Graph Neural Network Evaluationcited by 994
- 2018Predict then Propagate: Graph Neural Networks meet Personalized PageRankcited by 987
- 2016Deep Networks with Stochastic Depthcited by 973
- 2016Revisiting Semi-Supervised Learning with Graph Embeddingscited by 970
- 2016Temporal Segment Networks: Towards Good Practices for Deep Action Recognitioncited by 899
- 2019A Closer Look at Few-shot Classificationcited by 679
- 2018Meta-Learning with Latent Embedding Optimizationcited by 476
- 2019Meta-Learning with Differentiable Convex Optimizationcited by 461
- 2019EvolveGCN: Evolving Graph Convolutional Networks for Dynamic Graphscited by 443
- 2019Diffusion Improves Graph Learningcited by 414
- 2018TADAM: Task dependent adaptive metric for improved few-shot learningcited by 408
- 2018Dynamic Few-Shot Visual Learning without Forgettingcited by 385
- 2019Provably Robust Deep Learning via Adversarially Trained Smoothed Classifierscited by 328
- 2019A Baseline for Few-Shot Image Classificationcited by 298
- 2018Few-Shot Learning via Embedding Adaptation with Set-to-Set Functionscited by 293
- 2016Structured Sequence Modeling with Graph Convolutional Recurrent Networkscited by 273
- 2021GRAND: Graph Neural Diffusioncited by 258
- 2019Cross Attention Network for Few-shot Classificationcited by 218
- 2016FractalNet: Ultra-Deep Neural Networks without Residualscited by 216
- 2018Learning to Propagate Labels: Transductive Propagation Network for Few-shot Learningcited by 208
- 2017Beyond Finite Layer Neural Networks: Bridging Deep Architectures and Numerical Differential Equationscited by 203
- 2019SimpleShot: Revisiting Nearest-Neighbor Classification for Few-Shot Learningcited by 194
- 2018Certified Adversarial Robustness with Additive Noisecited by 178
- 2019Graph Neural Ordinary Differential Equationscited by 153
- 2019Neural Jump Stochastic Differential Equationscited by 147
- 2019Boosting Few-Shot Visual Learning with Self-Supervisioncited by 140
- 2017Few-Shot Image Recognition by Predicting Parameters from Activationscited by 122
- 2021PyTorch Geometric Temporal: Spatiotemporal Signal Processing with Neural Machine Learning Modelscited by 118
- 2019Continuous Graph Neural Networkscited by 114
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