  Machine learning is gaining popularity in a broad range of areas working with
geographic data, such as ecology or atmospheric sciences. Here, data often
exhibit spatial effects, which can be difficult to learn for neural networks.
In this study, we propose SXL, a method for embedding information on the
autoregressive nature of spatial data directly into the learning process using
auxiliary tasks. We utilize the local Moran's I, a popular measure of local
spatial autocorrelation, to "nudge" the model to learn the direction and
magnitude of local spatial effects, complementing the learning of the primary
task. We further introduce a novel expansion of Moran's I to multiple
resolutions, thus capturing spatial interactions over longer and shorter
distances simultaneously. The novel multi-resolution Moran's I can be
constructed easily and as a multi-dimensional tensor offers seamless
integration into existing machine learning frameworks. Throughout a range of
experiments using real-world data, we highlight how our method consistently
improves the training of neural networks in unsupervised and supervised
learning tasks. In generative spatial modeling experiments, we propose a novel
loss for auxiliary task GANs utilizing task uncertainty weights. Our proposed
method outperforms domain-specific spatial interpolation benchmarks,
highlighting its potential for downstream applications. This study bridges
expertise from geographic information science and machine learning, showing how
this integration of disciplines can help to address domain-specific challenges.
The code for our experiments is available on Github:
https://github.com/konstantinklemmer/sxl.
