Reproduce “Transport of Algebraic Structure to Latent Embeddings” on OpenResearch

About this paper

Samuel Pfrommer, Brendon G. Anderson, Somayeh Sojoudi

A method termed structural transport nets enables machine learning models to perform algebraic operations directly on latent embeddings by inducing operations from a 'mirrored' space. This approach yields higher accuracy and perfect self-consistency when the mirrored space's operations provably satisfy the source algebra's laws, demonstrated through set operations on implicit neural representations.

Key insights

• Algebraic structures can be systematically "transported" to latent spaces using a learned bijection to a 'mirrored' space, enabling learned operations to inherit axiomatic laws.
• The alignment of the 'mirrored' algebra's laws with the source algebra's laws is crucial, with full adherence leading to higher accuracy and perfect self-consistency of learned latent operations.
• Directly parameterizing latent space operations with neural networks is less effective and consistent than explicitly structuring them through the proposed structural transport mechanism.

Summary by alphaXiv.