Summary of Tempered Calculus For Ml: Application to Hyperbolic Model Embedding, by Richard Nock and Ehsan Amid and Frank Nielsen and Alexander Soen and Manfred K. Warmuth
Tempered Calculus for ML: Application to Hyperbolic Model Embedding
by Richard Nock, Ehsan Amid, Frank Nielsen, Alexander Soen, Manfred K. Warmuth
First submitted to arxiv on: 6 Feb 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: None
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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 A novel approach to improving mathematical distortions used in machine learning is introduced. The authors generalize Riemann integration to encompass t-additive functions, which recovers Volterra’s product integral as a special case. This framework is then extended to derive the Fundamental Theorem of calculus and other results that enable simple design, alteration, or change of distortion measures with emphasis on geometric and machine learning-related properties such as metricity, hyperbolicity, and encoding. Applications include hyperbolic embeddings for boosted combinations of decision trees trained using log-loss or logistic loss. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary A new way to improve mathematical tools used in machine learning is discovered. It starts by expanding a math concept called Riemann integration to make it work with different types of functions. This helps create a foundation for understanding how to change the properties of these tools. The authors use this framework to show how to design, modify, or adjust distortion measures in a simple way. This has applications in machine learning, such as creating embeddings that are more efficient and accurate. |
Keywords
* Artificial intelligence * Machine learning
