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This paper introduces "everywhere learning," a novel training paradigm where AI systems are optimized to satisfy loss constraints with probability one rather than minimizing average losses. By leveraging approximate duality theory and sparse L1 penalties, the authors demonstrate how this approach controls generalization through specific data distribution mismatches. The study validates these theoretical advances using agentic classification tasks for language models, offering a rigorous alternative to standard empirical risk minimization.
Everywhere Learning: Artificial Intelligence with Pointwise Constraints
arXiv:2606.01557v2 Announce Type: replace Abstract: Everywhere learning is a new paradigm whereby Artificial Intelligence (AI) systems are trained to satisfy loss constraints with probability one over the data distribution. This is in contrast to the standard paradigm of training AI systems to minimize average losses. We develop an approximate duality theory to substantiate a generalization analysis that establishes the proximity between solutions of empirical and statistical everywhere learning problems. Our results show that dual variables reweigh the data distribution towards points in which loss constraints are more difficult to satisfy and that generalization is controlled by the mismatch between the concentration of mass of the data distribution and the concentration of mass on points where constraints are more difficult to satisfy. We further show that we can control generalization with a sparse L1 penalty on constraint relaxations. We illustrate the merits of everywhere learning with an experiment in agentic classification for language model tasks.
Abstract:Everywhere learning is a new paradigm whereby Artificial Intelligence (AI) systems are trained to satisfy loss constraints with probability one over the data distribution. This is in contrast to the standard paradigm of training AI systems to minimize average losses. We develop an approximate duality theory to substantiate a generalization analysis that establishes the proximity between solutions of empirical and statistical everywhere learning problems. Our results show that dual variables reweigh the data distribution towards points in which loss constraints are more difficult to satisfy and that generalization is controlled by the mismatch between the concentration of mass of the data distribution and the concentration of mass on points where constraints are more difficult to satisfy. We further show that we can control generalization with a sparse L1 penalty on constraint relaxations. We illustrate the merits of everywhere learning with an experiment in agentic classification for language model tasks.
Machine Learning (cs.LG); Signal Processing (eess.SP)
arXiv:2606.01557 [cs.LG]
(or arXiv:2606.01557v2 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2606.01557 Focus to learn more arXiv-issued DOI via DataCite
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