# Geometric Causal Models

arXiv: https://arxiv.org/abs/2607.05153 · HTML: https://mlsanity.com/paper/2607.05153/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 59 of its 95 references that are in the map.
- First posted on arXiv 6 Jul 2026.

## Builds on (most cited first, 30 of 59)

- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [Deformable DETR: Deformable Transformers for End-to-End Object Detection](https://mlsanity.com/paper/2010.04159/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [FCOS: Fully Convolutional One-Stage Object Detection](https://mlsanity.com/paper/1904.01355/) (2019)
- [Deformable Convolutional Networks](https://mlsanity.com/paper/1703.06211/) (2017)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [DINO: DETR with Improved DeNoising Anchor Boxes for End-to-End Object Detection](https://mlsanity.com/paper/2203.03605/) (2022)
- [Cascade R-CNN: Delving into High Quality Object Detection](https://mlsanity.com/paper/1712.00726/) (2017)
- [ImageBind: One Embedding Space To Bind Them All](https://mlsanity.com/paper/2305.05665/) (2023)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Deformable ConvNets v2: More Deformable, Better Results](https://mlsanity.com/paper/1811.11168/) (2018)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [Bridging the Gap Between Anchor-based and Anchor-free Detection via Adaptive Training Sample Selection](https://mlsanity.com/paper/1912.02424/) (2019)
- [InternImage: Exploring Large-Scale Vision Foundation Models with Deformable Convolutions](https://mlsanity.com/paper/2211.05778/) (2022)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [YOLOv12: Attention-Centric Real-Time Object Detectors](https://mlsanity.com/paper/2502.12524/) (2025)
- [DETRs with Collaborative Hybrid Assignments Training](https://mlsanity.com/paper/2211.12860/) (2022)
- [RepPoints: Point Set Representation for Object Detection](https://mlsanity.com/paper/1904.11490/) (2019)
- [VarifocalNet: An IoU-aware Dense Object Detector](https://mlsanity.com/paper/2008.13367/) (2020)
- [Oriented R-CNN for Object Detection](https://mlsanity.com/paper/2108.05699/) (2021)
- [LLVIP: A Visible-infrared Paired Dataset for Low-light Vision](https://mlsanity.com/paper/2108.10831/) (2021)
- [TOOD: Task-aligned One-stage Object Detection](https://mlsanity.com/paper/2108.07755/) (2021)
- [ReDet: A Rotation-equivariant Detector for Aerial Object Detection](https://mlsanity.com/paper/2103.07733/) (2021)
- [RTMDet: An Empirical Study of Designing Real-Time Object Detectors](https://mlsanity.com/paper/2212.07784/) (2022)
- [R3Det: Refined Single-Stage Detector with Feature Refinement for Rotating Object](https://mlsanity.com/paper/1908.05612/) (2019)
- [Align Deep Features for Oriented Object Detection](https://mlsanity.com/paper/2008.09397/) (2020)
- [Rethinking Rotated Object Detection with Gaussian Wasserstein Distance Loss](https://mlsanity.com/paper/2101.11952/) (2021)
- [Drone-based RGB-Infrared Cross-Modality Vehicle Detection via Uncertainty-Aware Learning](https://mlsanity.com/paper/2003.02437/) (2020)
- [Gliding vertex on the horizontal bounding box for multi-oriented object detection](https://mlsanity.com/paper/1911.09358/) (2019)

## Abstract (arXiv)

Scientists often seek to draw causal inferences from structured data that is not independently and identically distributed, such as spatial data, network data, or molecular data. We develop geometric causal models (GCMs), a framework for causal inference from dependent data that exploits underlying symmetries of the data generating process. For example, in spatial data, we consider processes that are symmetric under translations, or in graph data, symmetric under permutations of the nodes. We show how symmetries, formalized with group theory, can enable causal identification and estimation. We deploy ergodic theory for amenable groups to establish identification, and combine geometric deep learning with scalable Bayesian inference for estimation. We recover i.i.d. causal models and do-calculus when the data is a sequence and the symmetry is permutation equivariance, and find novel types of causal models when we use alternate structures and symmetries. As an example, we construct a causal model that satisfies the symmetries of DNA. This GCM enables new estimators for the effects of genetic variation, combining deep functional genomics models to describe outcomes and DNA language models to describe propensities. We illustrate on semisynthetic data.