Attention Kernels for Learning Maps Between Heavy-Tailed Measures

Abstract:Operator learning on probability measures can be accomplished with transformers. For measures with polynomial tails, the exponential weighting in softmax can make the corresponding measure-level attention integrals diverge. This motivates replacing the exponential with slower-growing functions. We construct two benchmarks for operator learning on measures with closed-form targets. We use these benchmarks to study attention kernel growth and data transformation in post-norm transformers. Without data transformation, the softmax models exhibit ensemble collapse on both heavy-tailed benchmarks, while the three slower-growing kernels avoid collapse. Symlog preprocessing allows softmax to avoid collapse on the matrix inverse task but not on the sheared swap task. On the Gaussian control, all four kernels perform similarly. We also examine how sample size affects the sensitivity of empirical energy and Wasserstein distances to tail differences. These results support slower-growing attention kernels as an effective design choice for post-norm transformers learning from heavy-tailed ensembles.

Machine Learning (cs.LG)

arXiv:2610.00564 [cs.LG]

(or arXiv:2610.00564v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.00564 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.