# GraIP: A Benchmarking Framework For Neural Graph Inverse Problems

arXiv: https://arxiv.org/abs/2601.18917 · HTML: https://mlsanity.com/paper/2601.18917/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 55 of its 82 references that are in the map.
- First posted on arXiv 26 Jan 2026.

## Builds on (most cited first, 30 of 55)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Strategies for Pre-training Graph Neural Networks](https://mlsanity.com/paper/1905.12265/) (2019)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Recipe for a General, Powerful, Scalable Graph Transformer](https://mlsanity.com/paper/2205.12454/) (2022)
- [Learning Combinatorial Optimization Algorithms over Graphs](https://mlsanity.com/paper/1704.01665/) (2017)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [Neural Relational Inference for Interacting Systems](https://mlsanity.com/paper/1802.04687/) (2018)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [An Efficient Graph Convolutional Network Technique for the Travelling Salesman Problem](https://mlsanity.com/paper/1906.01227/) (2019)
- [Combinatorial optimization and reasoning with graph neural networks](https://mlsanity.com/paper/2102.09544/) (2021)
- [Long Range Graph Benchmark](https://mlsanity.com/paper/2206.08164/) (2022)
- [DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimization](https://mlsanity.com/paper/2302.08224/) (2023)
- [On the Role of Sparsity and DAG Constraints for Learning Linear DAGs](https://mlsanity.com/paper/2006.10201/) (2020)
- [A Survey on Diffusion Models for Inverse Problems](https://mlsanity.com/paper/2410.00083/) (2024)
- [Solving ill-posed inverse problems using iterative deep neural networks](https://mlsanity.com/paper/1704.04058/) (2017)
- [DIMES: A Differentiable Meta Solver for Combinatorial Optimization Problems](https://mlsanity.com/paper/2210.04123/) (2022)
- [Erdos Goes Neural: an Unsupervised Learning Framework for Combinatorial Optimization on Graphs](https://mlsanity.com/paper/2006.10643/) (2020)
- [Connecting the Dots: Identifying Network Structure via Graph Signal Processing](https://mlsanity.com/paper/1810.13066/) (2018)
- [FoSR: First-order spectral rewiring for addressing oversquashing in GNNs](https://mlsanity.com/paper/2210.11790/) (2022)

## Abstract (arXiv)

A wide range of graph learning tasks, such as structure discovery, temporal graph analysis, and combinatorial optimization, focus on inferring graph structures from data, rather than making predictions on given graphs. However, the respective methods to solve such problems are often developed in an isolated, task-specific manner and thus lack a unifying theoretical foundation. Here, we provide a stepping stone towards the formation of such a foundation and further development by introducing the Neural Graph Inverse Problem (GraIP) conceptual framework, which formalizes and reframes a broad class of graph learning tasks as inverse problems. Unlike discriminative approaches that directly predict target variables from given graph inputs, the GraIP paradigm addresses inverse problems, i.e., it relies on observational data and aims to recover the underlying graph structure by reversing the forward process, such as message passing or network dynamics, that produced the observed outputs. We demonstrate the versatility of GraIP across various graph learning tasks, including rewiring, causal discovery, and neural relational inference. We also propose benchmark datasets and metrics for each GraIP domain considered, and characterize and empirically evaluate existing baseline methods used to solve them. Overall, our unifying perspective bridges seemingly disparate applications and provides a principled approach to structural learning in constrained and combinatorial settings while encouraging cross-pollination of existing methods across graph inverse problems.