Summary of Fundamental Computational Limits Of Weak Learnability in High-dimensional Multi-index Models, by Emanuele Troiani et al.
Fundamental computational limits of weak learnability in high-dimensional multi-index models
by Emanuele Troiani, Yatin Dandi, Leonardo Defilippis, Lenka Zdeborová, Bruno Loureiro, Florent Krzakala
First submitted to arxiv on: 24 May 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Disordered Systems and Neural Networks (cond-mat.dis-nn); Computational Complexity (cs.CC)
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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 theoretical boundaries of efficient learnability in multi-index models, a useful benchmark for feature learning with neural nets. It explores the minimum sample complexity required to recover the low-dimensional structure of these models using first-order iterative algorithms in the high-dimensional regime where the number of samples is proportional to the covariate dimension. The findings unfold in three parts: (i) identifying conditions for learning a trivial subspace with a single step of a first-order algorithm, (ii) providing necessary and sufficient conditions for the existence of an easy subspace, and (iii) showing interactions between directions can result in hierarchical learning. The theory builds on the optimality of approximate message-passing among first-order iterative methods, delineating the fundamental learnability limit across various algorithms, including neural networks trained with gradient descent. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper looks at how well we can learn from data when using special types of models called multi-index models. These models are useful for testing how well artificial intelligence (AI) can find patterns in large datasets. The researchers want to know what’s the minimum amount of data needed to get a good result, and they’re interested in finding out if AI algorithms can do better or worse than human-made methods. They found that some directions are easy to learn, while others require more data, and that the order we try to learn these directions matters. |
Keywords
» Artificial intelligence » Gradient descent
