Title: Ubiquitous Learning: Artificial Intelligence Governed by Pointwise Constraints

Abstract:

This paper introduces "everywhere learning," a novel framework in which Artificial Intelligence (AI) models are optimized to adhere to loss constraints with a probability of one across the entire data distribution. This approach diverges from the conventional methodology of minimizing average loss. To support this paradigm, we formulate an approximate duality theory that underpins a generalization analysis, demonstrating the closeness between solutions derived from empirical and statistical everywhere learning problems.

Our findings indicate that dual variables effectively reweight the data distribution, shifting focus toward regions where satisfying loss constraints is most challenging. Consequently, generalization performance is determined by the discrepancy between the overall mass concentration of the data distribution and the mass concentration at points where constraints are hardest to meet. Additionally, we demonstrate that generalization can be regulated by applying a sparse L1 penalty to constraint relaxations. To highlight the advantages of this approach, we present an experiment involving agentic classification for language model tasks.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC