Summary of Neural Scaling Laws Of Deep Relu and Deep Operator Network: a Theoretical Study, by Hao Liu et al.
Neural Scaling Laws of Deep ReLU and Deep Operator Network: A Theoretical Study
by Hao Liu, Zecheng Zhang, Wenjing Liao, Hayden Schaeffer
First submitted to arxiv on: 1 Oct 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: 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 paper explores neural scaling laws for deep operator networks, which learn mappings between function spaces. It focuses on Chen and Chen style architectures, such as DeepONet, that approximate output functions using linear combinations of learnable basis functions and coefficients. The authors establish a theoretical framework to quantify the neural scaling laws by analyzing approximation and generalization errors, relating them to factors like network size and training data size. They also derive tighter error bounds for input functions with low-dimensional structures, which holds for deep ReLU networks and similar structures. The results provide a partial explanation of neural scaling laws in operator learning and offer a theoretical foundation for their applications. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper studies how big artificial intelligence models work when they get bigger or more complicated. It looks at special kinds of AI that learn from functions, not just numbers. These AI models, like DeepONet, are good at certain tasks, but nobody really understands why they’re so good. The researchers in this paper try to figure out the rules behind how well these AI models do their jobs. They find some patterns and rules that explain why bigger models might be better or worse than smaller ones, depending on what kind of data they’re trained on. This helps us understand how to make these AI models work even better in the future. |
Keywords
* Artificial intelligence * Generalization * Relu * Scaling laws
