Summary of Transport Of Algebraic Structure to Latent Embeddings, by Samuel Pfrommer et al.
Transport of Algebraic Structure to Latent Embeddings
by Samuel Pfrommer, Brendon G. Anderson, Somayeh Sojoudi
First submitted to arxiv on: 27 May 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 Machine learning often aims to produce latent embeddings of inputs which lie in a larger, abstract mathematical space. For instance, in 3D modeling, subsets of Euclidean space can be embedded as vectors using implicit neural representations. To learn “union” two sets based on their latent embeddings while respecting associativity, we propose a general procedure for parameterizing latent space operations that are provably consistent with the input space’s laws. This is achieved by learning a bijection from the latent space to a carefully designed mirrored algebra constructed on Euclidean space in accordance with desired laws. We evaluate structural transport nets for various mirrored algebras against baselines operating directly on the latent space, providing strong evidence that respecting underlying algebraic structure is crucial for learning accurate and self-consistent operations. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper helps machines learn to combine two groups of things (like shapes or objects) in a way that makes sense. Imagine you have two sets of shapes, and you want to combine them while keeping the same rules as when you work with individual shapes. The researchers developed a new method to do this by mapping the group of shapes into a special space where you can apply the same operations as before. They tested this approach on different types of combinations and found that it works better than just working directly with the groups. |
Keywords
» Artificial intelligence » Latent space » Machine learning
