# Grassmanian Interpolation of Low-Pass Graph Filters: Theory and Applications

arXiv: https://arxiv.org/abs/2510.23235 · HTML: https://mlsanity.com/paper/2510.23235/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 41 references that are in the map.
- First posted on arXiv 27 Oct 2025.

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

- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Revisiting Graph Neural Networks: All We Have is Low-Pass Filters](https://mlsanity.com/paper/1905.09550/) (2019)
- [Is Homophily a Necessity for Graph Neural Networks?](https://mlsanity.com/paper/2106.06134/) (2021)
- [An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists](https://mlsanity.com/paper/1710.04019/) (2017)
- [Contextual Stochastic Block Models](https://mlsanity.com/paper/1807.09596/) (2018)
- [Handling Missing Data with Graph Representation Learning](https://mlsanity.com/paper/2010.16418/) (2020)
- [Graph Wavelet Neural Network](https://mlsanity.com/paper/1904.07785/) (2019)
- [Connecting the Dots: Identifying Network Structure via Graph Signal Processing](https://mlsanity.com/paper/1810.13066/) (2018)
- [Statistical inference on random dot product graphs: a survey](https://mlsanity.com/paper/1709.05454/) (2017)
- [Flow Smoothing and Denoising: Graph Signal Processing in the Edge-Space](https://mlsanity.com/paper/1808.02111/) (2018)
- [Signal Processing on Cell Complexes](https://mlsanity.com/paper/2110.05614/) (2021)
- [A Survey on Spectral Graph Neural Networks](https://mlsanity.com/paper/2302.05631/) (2023)
- [A User Guide to Low-Pass Graph Signal Processing and its Applications](https://mlsanity.com/paper/2008.01305/) (2020)
- [Strong Consistency, Graph Laplacians, and the Stochastic Block Model](https://mlsanity.com/paper/2004.09780/) (2020)
- [Signal processing on simplicial complexes](https://mlsanity.com/paper/2106.07471/) (2021)
- [Learning time-dependent PDE solver using Message Passing Graph Neural Networks](https://mlsanity.com/paper/2204.07651/) (2022)
- [Online Change Point Detection for Weighted and Directed Random Dot Product Graphs](https://mlsanity.com/paper/2201.11222/) (2022)

## Abstract (arXiv)

Low-pass graph filters are fundamental for signal processing on graphs and other non-Euclidean domains. However, the computation of such filters for parametric graph families can be prohibitively expensive as computation of the corresponding low-frequency subspaces, requires the repeated solution of an eigenvalue problem. We suggest a novel algorithm of low-pass graph filter interpolation based on Riemannian interpolation in normal coordinates on the Grassmann manifold. We derive an error bound estimate for the subspace interpolation and suggest two possible applications for induced parametric graph families. First, we argue that the temporal evolution of the node features may be translated to the evolving graph topology via a similarity correction to adjust the homophily degree of the network. Second, we suggest a dot product graph family induced by a given static graph which allows to infer improved message passing scheme for node classification facilitated by the filter interpolation.