# Spatial Knowledge-Infused Hierarchical Learning: An Application in Flood Mapping on Earth Imagery

arXiv: https://arxiv.org/abs/2312.07767 · HTML: https://mlsanity.com/paper/2312.07767/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 37 references that are in the map.
- First posted on arXiv 12 Dec 2023.

## Builds on (most cited first, 18 of 18)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [A Semantic Loss Function for Deep Learning with Symbolic Knowledge](https://mlsanity.com/paper/1711.11157/) (2017)
- [Neural-Symbolic Learning and Reasoning: A Survey and Interpretation](https://mlsanity.com/paper/1711.03902/) (2017)
- [Harnessing Deep Neural Networks with Logic Rules](https://mlsanity.com/paper/1603.06318/) (2016)
- [Improving model calibration with accuracy versus uncertainty optimization](https://mlsanity.com/paper/2012.07923/) (2020)
- [Tile2Vec: Unsupervised representation learning for spatially distributed data](https://mlsanity.com/paper/1805.02855/) (2018)
- [Logic Tensor Networks for Semantic Image Interpretation](https://mlsanity.com/paper/1705.08968/) (2017)
- [A Survey on Uncertainty Quantification Methods for Deep Learning](https://mlsanity.com/paper/2302.13425/) (2023)
- [Probabilistic Logic Neural Networks for Reasoning](https://mlsanity.com/paper/1906.08495/) (2019)
- [Hinge-Loss Markov Random Fields and Probabilistic Soft Logic](https://mlsanity.com/paper/1505.04406/) (2015)
- [Closed Loop Neural-Symbolic Learning via Integrating Neural Perception, Grammar Parsing, and Symbolic Reasoning](https://mlsanity.com/paper/2006.06649/) (2020)
- [Efficient Probabilistic Logic Reasoning with Graph Neural Networks](https://mlsanity.com/paper/2001.11850/) (2020)
- [Embedding Symbolic Knowledge into Deep Networks](https://mlsanity.com/paper/1909.01161/) (2019)
- [NLProlog: Reasoning with Weak Unification for Question Answering in Natural Language](https://mlsanity.com/paper/1906.06187/) (2019)
- [Neural Markov Logic Networks](https://mlsanity.com/paper/1905.13462/) (2019)
- [Clinical Temporal Relation Extraction with Probabilistic Soft Logic Regularization and Global Inference](https://mlsanity.com/paper/2012.08790/) (2020)
- [Geographical Hidden Markov Tree for Flood Extent Mapping (With Proof Appendix)](https://mlsanity.com/paper/1805.09757/) (2018)

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

- [Geospatial Artificial Intelligence for Satellite-Based Flood Extent Mapping: Concepts, Advances, and Future Perspectives](https://mlsanity.com/paper/2504.02214/) (2025)

## Abstract (arXiv)

Deep learning for Earth imagery plays an increasingly important role in geoscience applications such as agriculture, ecology, and natural disaster management. Still, progress is often hindered by the limited training labels. Given Earth imagery with limited training labels, a base deep neural network model, and a spatial knowledge base with label constraints, our problem is to infer the full labels while training the neural network. The problem is challenging due to the sparse and noisy input labels, spatial uncertainty within the label inference process, and high computational costs associated with a large number of sample locations. Existing works on neuro-symbolic models focus on integrating symbolic logic into neural networks (e.g., loss function, model architecture, and training label augmentation), but these methods do not fully address the challenges of spatial data (e.g., spatial uncertainty, the trade-off between spatial granularity and computational costs). To bridge this gap, we propose a novel Spatial Knowledge-Infused Hierarchical Learning (SKI-HL) framework that iteratively infers sample labels within a multi-resolution hierarchy. Our framework consists of a module to selectively infer labels in different resolutions based on spatial uncertainty and a module to train neural network parameters with uncertainty-aware multi-instance learning. Extensive experiments on real-world flood mapping datasets show that the proposed model outperforms several baseline methods. The code is available at urlhttps://github.com/ZelinXu2000/SKI-HL.