4 problems

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Computational lower-bound conjecture for learning spherical multi-index models
Computational lower-bound conjecture. No polynomial-time algorithm can recover the latent subspace with $\Theta_d(d)$ samples for general link functions $ud$ .
Conjectureopenharmonic-analysis multi-index-models statistical-computational-gapsarXiv posted 2 days ago
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Extension of RFM theory to multi-index models
Let $\mathtt{RFM}(\alpha)$ be the modified Recursive Feature Machines algorithm that draws fresh samples and reweights the data using an average of the Average Gradient Outer Produ…
Conjectureopenfeature-learning kernel-methods multi-index-modelsarXiv posted 2 days ago
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Optimality conjecture for spectral estimators in multi-index models
Consider a multi-index model with Gaussian design, and spectral estimators based on the linearization of approximate message passing. Optimality conjecture. Such spectral estimator…
Conjectureopenmulti-index-models spectral-methods weak-recoveryarXiv posted 2 days ago
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The adaptivity conjecture for two-scale neural network training
Adaptivity conjecture. Decoupling the learning scales in this way should be more adaptive to the problem than learning the two layers jointly.
Conjectureopengradient-flow multi-index-models neural-networksarXiv posted 2 days ago

Computational lower-bound conjecture for learning spherical multi-index models