<ul data-eligibleForWebStory="false"><li>Study on learning single-index models where the label depends on the input only through a one-dimensional projection.</li><li>Prior work uses Hermite polynomials for recovering the projection under Gaussian inputs.</li><li>A new perspective proposes using spherical harmonics due to the problem's rotational symmetry.</li><li>Complexity of learning single-index models under spherically symmetric input distributions is characterized.</li><li>Introduction of estimators based on tensor unfolding and online SGD to achieve optimal sample complexity or runtime.</li><li>No single estimator may achieve both optimal sample complexity and runtime in general.</li><li>Specializing to Gaussian inputs, the theory clarifies existing results and uncovers new phenomena.</li></ul>

Learning single-index models via harmonic decomposition

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