  We present the Evolving Graph Fourier Transform (EFT), the first invertible
spectral transform that captures evolving representations on temporal graphs.
We motivate our work by the inadequacy of existing methods for capturing the
evolving graph spectra, which are also computationally expensive due to the
temporal aspect along with the graph vertex domain. We view the problem as an
optimization over the Laplacian of the continuous time dynamic graph.
Additionally, we propose pseudo-spectrum relaxations that decompose the
transformation process, making it highly computationally efficient. The EFT
method adeptly captures the evolving graph's structural and positional
properties, making it effective for downstream tasks on evolving graphs. Hence,
as a reference implementation, we develop a simple neural model induced with
EFT for capturing evolving graph spectra. We empirically validate our
theoretical findings on a number of large-scale and standard temporal graph
benchmarks and demonstrate that our model achieves state-of-the-art
performance.
