# DeepMAD: Mathematical Architecture Design for Deep Convolutional Neural Network

arXiv: https://arxiv.org/abs/2303.02165 · HTML: https://mlsanity.com/paper/2303.02165/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 55 of its 92 references that are in the map.
- First posted on arXiv 5 Mar 2023.

## Builds on (most cited first, 30 of 55)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [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)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Pyramid Vision Transformer: A Versatile Backbone for Dense Prediction without Convolutions](https://mlsanity.com/paper/2102.12122/) (2021)
- [The Kinetics Human Action Video Dataset](https://mlsanity.com/paper/1705.06950/) (2017)
- [MMDetection: Open MMLab Detection Toolbox and Benchmark](https://mlsanity.com/paper/1906.07155/) (2019)
- [Cascade R-CNN: Delving into High Quality Object Detection](https://mlsanity.com/paper/1712.00726/) (2017)
- [Unified Perceptual Parsing for Scene Understanding](https://mlsanity.com/paper/1807.10221/) (2018)
- [Random Erasing Data Augmentation](https://mlsanity.com/paper/1708.04896/) (2017)
- [Learning Transferable Architectures for Scalable Image Recognition](https://mlsanity.com/paper/1707.07012/) (2017)
- [Tokens-to-Token ViT: Training Vision Transformers from Scratch on ImageNet](https://mlsanity.com/paper/2101.11986/) (2021)
- [Designing Network Design Spaces](https://mlsanity.com/paper/2003.13678/) (2020)
- [MnasNet: Platform-Aware Neural Architecture Search for Mobile](https://mlsanity.com/paper/1807.11626/) (2018)
- [Regularized Evolution for Image Classifier Architecture Search](https://mlsanity.com/paper/1802.01548/) (2018)
- [Temporal Segment Networks: Towards Good Practices for Deep Action Recognition](https://mlsanity.com/paper/1608.00859/) (2016)
- [Efficient Neural Architecture Search via Parameter Sharing](https://mlsanity.com/paper/1802.03268/) (2018)

## Built on by (most cited first, 14 of 14)

- [Automated Design of Agentic Systems](https://mlsanity.com/paper/2408.08435/) (2024)
- [AZ-NAS: Assembling Zero-Cost Proxies for Network Architecture Search](https://mlsanity.com/paper/2403.19232/) (2024)
- [Search for Efficient Large Language Models](https://mlsanity.com/paper/2409.17372/) (2024)
- [MathNAS: If Blocks Have a Role in Mathematical Architecture Design](https://mlsanity.com/paper/2311.04943/) (2023)
- [Merino: Entropy-driven Design for Generative Language Models on IoT Devices](https://mlsanity.com/paper/2403.07921/) (2024)
- [ZiCo-BC: A Bias Corrected Zero-Shot NAS for Vision Tasks](https://mlsanity.com/paper/2309.14666/) (2023)
- [Troublemaker Learning for Low-Light Image Enhancement](https://mlsanity.com/paper/2402.04584/) (2024)
- [SpiralMLP: A Lightweight Vision MLP Architecture](https://mlsanity.com/paper/2404.00648/) (2024)
- [DeepFedNAS: Efficient Hardware-Aware Architecture Adaptation for Heterogeneous IoT Federations via Pareto-Guided Supernet Training](https://mlsanity.com/paper/2601.15127/) (2026)
- [Depth-induced Saliency Comparison Network for Diagnosis of Alzheimer's Disease via Jointly Analysis of Visual Stimuli and Eye Movements](https://mlsanity.com/paper/2403.10124/) (2024)
- [Dense Optimizer : An Information Entropy-Guided Structural Search Method for Dense-like Neural Network Design](https://mlsanity.com/paper/2410.07499/) (2024)
- [Underwater object detection in sonar imagery with detection transformer and Zero-shot neural architecture search](https://mlsanity.com/paper/2505.06694/) (2025)
- [Efficient Deep Demosaicing with Spatially Downsampled Isotropic Networks](https://mlsanity.com/paper/2601.00703/) (2026)
- [AgentFactory: Towards Automated Agentic System Design and Optimization](https://mlsanity.com/paper/2609.01045/) (2026)

## Abstract (arXiv)

The rapid advances in Vision Transformer (ViT) refresh the state-of-the-art performances in various vision tasks, overshadowing the conventional CNN-based models. This ignites a few recent striking-back research in the CNN world showing that pure CNN models can achieve as good performance as ViT models when carefully tuned. While encouraging, designing such high-performance CNN models is challenging, requiring non-trivial prior knowledge of network design. To this end, a novel framework termed Mathematical Architecture Design for Deep CNN (DeepMAD) is proposed to design high-performance CNN models in a principled way. In DeepMAD, a CNN network is modeled as an information processing system whose expressiveness and effectiveness can be analytically formulated by their structural parameters. Then a constrained mathematical programming (MP) problem is proposed to optimize these structural parameters. The MP problem can be easily solved by off-the-shelf MP solvers on CPUs with a small memory footprint. In addition, DeepMAD is a pure mathematical framework: no GPU or training data is required during network design. The superiority of DeepMAD is validated on multiple large-scale computer vision benchmark datasets. Notably on ImageNet-1k, only using conventional convolutional layers, DeepMAD achieves 0.7% and 1.5% higher top-1 accuracy than ConvNeXt and Swin on Tiny level, and 0.8% and 0.9% higher on Small level.