# Data-Driven Graph Filters via Adaptive Spectral Shaping

arXiv: https://arxiv.org/abs/2602.03698 · HTML: https://mlsanity.com/paper/2602.03698/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 21 references that are in the map.
- First posted on arXiv 3 Feb 2026.

## Builds on (most cited first, 15 of 15)

- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filters](https://mlsanity.com/paper/1705.07664/) (2017)
- [BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation](https://mlsanity.com/paper/2106.10994/) (2021)
- [Graph Neural Networks with convolutional ARMA filters](https://mlsanity.com/paper/1901.01343/) (2019)
- [Transferability of Spectral Graph Convolutional Neural Networks](https://mlsanity.com/paper/1907.12972/) (2019)
- [Diffusion Scattering Transforms on Graphs](https://mlsanity.com/paper/1806.08829/) (2018)
- [Autoregressive Moving Average Graph Filtering](https://mlsanity.com/paper/1602.04436/) (2016)
- [Interpretable Stability Bounds for Spectral Graph Filters](https://mlsanity.com/paper/2102.09587/) (2021)
- [Vertex-Frequency Analysis on Graphs](https://mlsanity.com/paper/1307.5708/) (2013)
- [Gaussian Processes on Graphs via Spectral Kernel Learning](https://mlsanity.com/paper/2006.07361/) (2020)
- [Do We Need Anisotropic Graph Neural Networks?](https://mlsanity.com/paper/2104.01481/) (2021)
- [Spectrum-Adapted Tight Graph Wavelet and Vertex-Frequency Frames](https://mlsanity.com/paper/1311.0897/) (2013)
- [Adaptive Gaussian Processes on Graphs via Spectral Graph Wavelets](https://mlsanity.com/paper/2110.12752/) (2021)
- [Fourier-based and Rational Graph Filters for Spectral Processing](https://mlsanity.com/paper/2011.04055/) (2020)

## Abstract (arXiv)

We introduce Adaptive Spectral Shaping, a data-driven framework for graph filtering that learns a reusable baseline spectral kernel and modulates it with a small set of Gaussian factors. The resulting multi-peak, multi-scale responses allocate energy to heterogeneous regions of the Laplacian spectrum while remaining interpretable via explicit centers and bandwidths. To scale, we implement filters with Chebyshev polynomial expansions, avoiding eigendecompositions. We further propose Transferable Adaptive Spectral Shaping (TASS): the baseline kernel is learned on source graphs and, on a target graph, kept fixed while only the shaping parameters are adapted, enabling few-shot transfer under matched compute. Across controlled synthetic benchmarks spanning graph families and signal regimes, Adaptive Spectral Shaping reduces reconstruction error relative to fixed-prototype wavelets and learned linear banks, and TASS yields consistent positive transfer. The framework provides compact spectral modules that plug into graph signal processing pipelines and graph neural networks, combining scalability, interpretability, and cross-graph generalization.