Summary of On the Sample Complexity Of One Hidden Layer Networks with Equivariance, Locality and Weight Sharing, by Arash Behboodi et al.
On the Sample Complexity of One Hidden Layer Networks with Equivariance, Locality and Weight Sharing
by Arash Behboodi, Gabriele Cesa
First submitted to arxiv on: 21 Nov 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Statistics Theory (math.ST); Machine Learning (stat.ML)
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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 abstract discusses how different design choices in neural networks contribute to their sample efficiency. Weight sharing, equivariance, and local filters are believed to be important, but it’s unclear how each one affects the generalization error. The authors use statistical learning theory to provide insight into this question by characterizing the relative impact of each choice on the sample complexity. They obtain bounds for single hidden layer networks with certain activation functions, as well as for max-pooling and multi-layer networks. The results show that non-equivariant weight-sharing can have similar generalization bounds as equivariant ones, while locality has generalization benefits but is traded off against expressivity. Experiments are conducted to highlight consistent trends. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Neural networks have special designs that help them learn quickly from few examples. But how do these designs affect how well they generalize? Researchers used a math framework called statistical learning theory to figure out the answers. They found that some design choices can make neural networks better at generalizing, like using local filters. Other design choices, like weight sharing, don’t seem to matter as much. The results show that making neural networks less special in certain ways can actually help them generalize better. |
Keywords
* Artificial intelligence * Generalization
