Summary of Optimization Can Learn Johnson Lindenstrauss Embeddings, by Nikos Tsikouras et al.
Optimization Can Learn Johnson Lindenstrauss Embeddings
by Nikos Tsikouras, Constantine Caramanis, Christos Tzamos
First submitted to arxiv on: 10 Dec 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG)
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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 This paper explores the use of embeddings in various fields and their role in providing compact representations of complex data structures. The authors investigate whether randomized methods, such as Johnson-Lindenstrauss (JL), are indeed necessary for achieving these representations. JL provides state-of-the-art theoretical guarantees, but they do not take into account any structural information about the data. The paper shows that the distance-preserving objective of JL has a non-convex landscape over the space of projection matrices, with many bad stationary points. This challenges the idea that we must randomize to achieve embeddings. Instead, the authors propose an optimization-based approach that works directly with the data. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Imagine you have a big box of puzzle pieces, and you want to find a way to represent each piece in a small amount of space. This is called embedding. A special method called Johnson-Lindenstrauss (JL) helps us do this, but it’s not perfect. JL doesn’t take into account how the puzzle pieces are actually shaped or connected. The question is: can we find a better way to embed these pieces without using JL? The answer is no, at least for now. But the researchers also found that there are some problems with using JL, so they’re working on new approaches. |
Keywords
» Artificial intelligence » Embedding » Optimization
