# Rethinking Inductive Bias in Geographically Neural Network Weighted Regression

arXiv: https://arxiv.org/abs/2507.09958 · HTML: https://mlsanity.com/paper/2507.09958/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 17 references that are in the map.
- First posted on arXiv 14 Jul 2025.

## Builds on (most cited first, 9 of 9)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Scalable GWR: A linear-time algorithm for large-scale geographically weighted regression with polynomial kernels](https://mlsanity.com/paper/1905.00266/) (2019)

## Abstract (arXiv)

Inductive bias is a key factor in spatial regression models, determining how well a model can learn from limited data and capture spatial patterns. This work revisits the inductive biases in Geographically Neural Network Weighted Regression (GNNWR) and identifies limitations in current approaches for modeling spatial non-stationarity. While GNNWR extends traditional Geographically Weighted Regression by using neural networks to learn spatial weighting functions, existing implementations are often restricted by fixed distance-based schemes and limited inductive bias. We propose to generalize GNNWR by incorporating concepts from convolutional neural networks, recurrent neural networks, and transformers, introducing local receptive fields, sequential context, and self-attention into spatial regression. Through extensive benchmarking on synthetic spatial datasets with varying heterogeneity, noise, and sample sizes, we show that GNNWR outperforms classic methods in capturing nonlinear and complex spatial relationships. Our results also reveal that model performance depends strongly on data characteristics, with local models excelling in highly heterogeneous or small-sample scenarios, and global models performing better with larger, more homogeneous data. These findings highlight the importance of inductive bias in spatial modeling and suggest future directions, including learnable spatial weighting functions, hybrid neural architectures, and improved interpretability for models handling non-stationary spatial data.