# Open Problem: Learning with Variational Objectives on Measures

arXiv: https://arxiv.org/abs/2306.11928 · HTML: https://mlsanity.com/paper/2306.11928/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 41 references that are in the map.
- First posted on arXiv 20 Jun 2023.

## Builds on (most cited first, 12 of 12)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Semantics derived automatically from language corpora contain human-like biases](https://mlsanity.com/paper/1608.07187/) (2016)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Snorkel: Rapid Training Data Creation with Weak Supervision](https://mlsanity.com/paper/1711.10160/) (2017)
- [Multi-task Self-Supervised Visual Learning](https://mlsanity.com/paper/1708.07860/) (2017)
- [A General Theory for Structured Prediction with Smooth Convex Surrogates](https://mlsanity.com/paper/1902.01958/) (2019)
- [Epi-Convergence of Expectation Functions under Varying Measures and Integrands](https://mlsanity.com/paper/2208.03805/) (2022)

## Abstract (arXiv)

The theory of statistical learning has focused on variational objectives expressed on functions. In this note, we discuss motivations to write similar objectives on measures, in particular to discuss out-of-distribution generalization and weakly-supervised learning. It raises a natural question: can one cast usual statistical learning results to objectives expressed on measures? Does the resulting construction lead to new algorithms of practical interest?