It is a common understanding that rotational cattle grazing provides better yields than continuous grazing, but a quantitative analysis is lacking in agricultural literature. In rotational grazing, cattle periodically move among paddocks in contrast to continuous grazing, in which the cattle graze on a single plot for the entire grazing season. We construct a differential equation model of vegetation grazing on a fixed area to show that production yields and stockpiled forage are greater for rotational grazing than continuous grazing. Our results show that both the number of cattle per acre and stockpiled forage increase for many rotational configurations.

Machine learning models are often deployed in different settings than they were trained and validated on, posing a challenge to practitioners who wish to predict how well the deployed model will perform on a target distribution. If an unlabeled sample from the target distribution is available, along with a labeled sample from a possibly different source distribution, standard approaches such as importance weighting can be applied to estimate performance on the target. However, importance weighting struggles when the source and target distributions have non-overlapping support or are high-dimensional. Taking inspiration from fields such as epidemiology and polling, we develop Mandoline, a new evaluation framework that mitigates these issues. Our key insight is that practitioners may have prior knowledge about the ways in which the distribution shifts, which we can use to better guide the importance weighting procedure. Specifically, users write simple "slicing functions"-noisy, potentially correlated binary functions intended to capture possible axes of distribution shift-to compute reweighted performance estimates. We further describe a density ratio estimation framework for the slices and show how its estimation error scales with slice quality and dataset size. Empirical validation on NLP and vision tasks shows that Mandoline can estimate performance on the target distribution up to 3× more accurately compared to standard baselines.

Entity retrieval-retrieving information about entity mentions in a query-is a key step in open-domain tasks, such as question answering or fact checking. However, state-of-the-art entity retrievers struggle to retrieve rare entities for ambiguous mentions due to biases towards popular entities. Incorporating knowledge graph types during training could help overcome popularity biases, but there are several challenges: (1) existing type-based retrieval methods require mention boundaries as input, but open-domain tasks run on unstructured text, (2) type-based methods should not compromise overall performance, and (3) type-based methods should be robust to noisy and missing types. In this work, we introduce TABi, a method to jointly train bi-encoders on knowledge graph types and unstructured text for entity retrieval for open-domain tasks. TABi leverages a typeenforced contrastive loss to encourage entities and queries of similar types to be close in the embedding space. TABi improves retrieval of rare entities on the Ambiguous Entity Retrieval (AmbER) sets, while maintaining strong overall retrieval performance on open-domain tasks in the KILT benchmark compared to state-of-the-art retrievers. TABi is also robust to incomplete type systems, improving rare entity retrieval over baselines with only 5% type coverage of the training dataset. We make our code publicly available. 1