For single- and two-index neural hypotheses in the deep Ritz method for the Schrödinger equation, gradient descent converges in O(log(1/ε)) iterations and the Ritz minimizer aligns with the source feature; a second feature emerges as regularization varies.
Survey on Algorithms for multi-index models
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abstract
We review the literature on algorithms for estimating the index space in a multi-index model. The primary focus is on computationally efficient (polynomial-time) algorithms in Gaussian space, the assumptions under which consistency is guaranteed by these methods, and their sample complexity. In many cases, a gap is observed between the sample complexity of the best known computationally efficient methods and the information-theoretical minimum. We also review algorithms based on estimating the span of gradients using nonparametric methods, and algorithms based on fitting neural networks using gradient descent
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math.OC 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Feature Learning for the High Dimensional Stationary Sch\"odinger Equation with Deep Ritz Method
For single- and two-index neural hypotheses in the deep Ritz method for the Schrödinger equation, gradient descent converges in O(log(1/ε)) iterations and the Ritz minimizer aligns with the source feature; a second feature emerges as regularization varies.