Summary of Hypothesis Spaces For Deep Learning, by Rui Wang et al.
Hypothesis Spaces for Deep Learning
by Rui Wang, Yuesheng Xu, Mingsong Yan
First submitted to arxiv on: 5 Mar 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Functional Analysis (math.FA)
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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 introduces a novel hypothesis space for deep learning, treating deep neural networks (DNNs) as functions of two variables. By analyzing the primitive set of DNNs for the parameter variable, located in weight matrices and biases determined by depth and widths, the authors construct a Banach space of functions for the physical variable. They prove this space is a reproducing kernel Banach space (RKBS) and derive its reproducing kernel. The paper investigates two learning models – regularized learning and minimum interpolation problem – in the RKBS, establishing representer theorems that show solutions can be expressed as linear combinations of kernel sessions determined by given data and the reproducing kernel. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper creates a new way to think about deep learning using special functions called reproducing kernel Banach spaces. This helps us solve problems like training neural networks. The authors take a big step forward in understanding how these problems work, giving us two new ways to approach them: regularized learning and minimum interpolation problem. They show that solutions can be broken down into smaller pieces, which is useful for making predictions. |
Keywords
* Artificial intelligence * Deep learning
