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Survey on Algorithms for multi-index models

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arxiv 2504.05426 v2 pith:R5OILMP3 submitted 2025-04-07 stat.ML cs.LGstat.ME

Joan Bruna , Daniel Hsu This is my paper · ORCID
classification stat.MLcs.LGstat.ME
keywords algorithmsmethodscomplexitycomputationallyefficientestimatingmulti-indexreview
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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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Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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    Randomly initialized Bayes-optimal AMP provably achieves the weak-recovery threshold δ=1/2 and arbitrarily accurate recovery for δ>1.13 in proportional-regime noiseless phase retrieval.

  2. Feature Learning for the High Dimensional Stationary Sch\"odinger Equation with Deep Ritz Method

    math.OC 2026-07 unverdicted novelty 7.0 of 10

    Gradient descent on single-index and two-neuron models provably recovers feature directions of the Schrödinger equation source term in the deep Ritz framework.

  3. Limitations of SGD for Multi-Index Models Beyond Statistical Queries

    cs.LG 2026-02 conditional novelty 7.0 of 10

    Vanilla SGD provably fails to learn periodic and low-information-exponent single/multi-index targets unless the input dimension is small or the number of iterations is large.

  4. AI4SLT: Empirical Processes in Lean 4 for Formal Statistical Learning Theory

    cs.LG 2026-02 conditional novelty 7.0 of 10

    The authors built a roughly 30,000-line Lean 4 library formalizing Gaussian Lipschitz concentration, Dudley's entropy integral, and localized least-squares regression rates.

  5. The Generative Leap: Sharp Sample Complexity for Efficiently Learning Gaussian Multi-Index Models

    cs.LG 2025-06 conditional novelty 7.0 of 10

    For any Gaussian multi-index model, the generative leap exponent k⋆ sharply characterizes the sample complexity of efficient subspace recovery as Θ(d^(1∨k⋆/2)).

  6. Joint Learning in the Gaussian Single Index Model

    cs.LG 2025-05 conditional novelty 6.0 of 10

    In Gaussian single-index models, joint gradient flow over direction and link function converges to the true regression function from either sign of initial alignment, with rate governed by the information exponent.

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