# Everywhere Learning: Artificial Intelligence with Pointwise Constraints

arXiv: https://arxiv.org/abs/2606.01557 · HTML: https://mlsanity.com/paper/2606.01557/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 50 references that are in the map.
- First posted on arXiv 1 Jun 2026.

## Builds on (most cited first, 24 of 24)

- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [A Survey on Multi-Task Learning](https://mlsanity.com/paper/1707.08114/) (2017)
- [Multi-Task Learning as Multi-Objective Optimization](https://mlsanity.com/paper/1810.04650/) (2018)
- [AFlow: Automating Agentic Workflow Generation](https://mlsanity.com/paper/2410.10762/) (2024)
- [Multi-Task Learning with Deep Neural Networks: A Survey](https://mlsanity.com/paper/2009.09796/) (2020)
- [Fairness Without Demographics in Repeated Loss Minimization](https://mlsanity.com/paper/1806.08010/) (2018)
- [Robust Learning Through Cross-Task Consistency](https://mlsanity.com/paper/2006.04096/) (2020)
- [Probably Approximately Correct Constrained Learning](https://mlsanity.com/paper/2006.05487/) (2020)
- [Train simultaneously, generalize better: Stability of gradient-based minimax learners](https://mlsanity.com/paper/2010.12561/) (2020)
- [Constrained Learning with Non-Convex Losses](https://mlsanity.com/paper/2103.05134/) (2021)
- [Generalization Bounds for Stochastic Saddle Point Problems](https://mlsanity.com/paper/2006.02067/) (2020)
- [GNNs as Predictors of Agentic Workflow Performances](https://mlsanity.com/paper/2503.11301/) (2025)
- [Multi-Objective Learning to Predict Pareto Fronts Using Hypervolume Maximization](https://mlsanity.com/paper/2102.04523/) (2021)
- [What is a Good Metric to Study Generalization of Minimax Learners?](https://mlsanity.com/paper/2206.04502/) (2022)
- [Robust Optimization using Machine Learning for Uncertainty Sets](https://mlsanity.com/paper/1407.1097/) (2014)
- [Composition and Alignment of Diffusion Models using Constrained Learning](https://mlsanity.com/paper/2508.19104/) (2025)
- [Near-Optimal Solutions of Constrained Learning Problems](https://mlsanity.com/paper/2403.11844/) (2024)
- [Alignment of large language models with constrained learning](https://mlsanity.com/paper/2505.19387/) (2025)
- [Feasible Learning](https://mlsanity.com/paper/2501.14912/) (2025)
- [Functional Nonlinear Sparse Models](https://mlsanity.com/paper/1811.00577/) (2018)
- [Strong Duality in Risk-Constrained Nonconvex Functional Programming](https://mlsanity.com/paper/2206.11948/) (2022)
- [AL-CoLe: Augmented Lagrangian for Constrained Learning](https://mlsanity.com/paper/2510.20995/) (2025)
- [Learning Optimal Power Flow with Pointwise Constraints](https://mlsanity.com/paper/2510.20777/) (2025)

## Built on by (most cited first, 1 of 1)

- [Learning Samples Importance: Parameterizing Dual Variables in Everywhere Learning](https://mlsanity.com/paper/2609.36310/) (2026)

## Abstract (arXiv)

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.