Summary of Defining Neural Network Architecture Through Polytope Structures Of Dataset, by Sangmin Lee et al.
Defining Neural Network Architecture through Polytope Structures of Dataset
by Sangmin Lee, Abbas Mammadov, Jong Chul Ye
First submitted to arxiv on: 4 Feb 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Computer Vision and Pattern Recognition (cs.CV); Neural and Evolutionary Computing (cs.NE)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The paper investigates the relationship between neural network architecture size and dataset complexity. It defines upper and lower bounds for network widths based on the polytope structure of the dataset, and applies these principles to simplicial complexes and manifold shapes. The study also develops an algorithm to infer the polytope structure of a dataset from its trained neural networks, showing that popular datasets like MNIST, Fashion-MNIST, and CIFAR10 can be efficiently represented using just two polytopes with a small number of faces. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Neural networks need to get bigger to understand complex data. But how big do they need to be? This paper figures out the answer by looking at the shapes of the data itself. It shows that if you know the shape, you can guess how big the network needs to be, and vice versa. The researchers tested this idea on popular datasets like pictures of cats and dogs, and found that just two simple shapes are enough to capture all the information. |
Keywords
* Artificial intelligence * Neural network
