Title: Learning DAGs from Fourier-Sparse Data. Abstract: We present a novel perspective on learning directed acyclic graphs (DAGs) from data, leveraging a recent novel form of causal Fourier analysis on DAGs. We build on prior work that learned DAGs from data generated by a structural equation model (SEM). First, we show that data generated by linear SEMs can be characterized in the frequency domain as having dense spectra with random coefficients. Then we propose the new problem of learning DAGs from approximately Fourier-sparse data, which we solve by minimizing the $L^1$ norm of the spectrum. We provide a motivation for this problem and compare our method to prior DAG learning methods, showing superior performance.