14 problems

Asymptotic covariance approximation conjecture. The population covariances can be asymptotically approximated by the last iterates of the corresponding linear recursions, with the…

Let the assumptions in Crefrange{asm:model}{asm:feat} hold. Define $\phi_n=p/n$. Let $k\le n$ be the subsample size and set $\bar{\psi}_n=p/k$. Suppose that $\varphi$ satisfies cer…

Let a double random feature model have two parts of random features with scale parameters whose difference is neither too small nor too large, and let…

Overparameterized randomly trained networks use a large feature space, and sparse regression seeks a subset of features that still approximates a target function accurately. Sparse…

Uniform correlated Gaussian equivalence conjecture. The Gaussian equivalence is valid for $(\nu_1,\nu_2,\dots,\nu_\ell)$ for every $\ell\geq 1$, uniformly over…

Correlated Gaussian equivalence conjecture. For Gaussian input and perturbation vectors, the learning formulation is asymptotically equivalent to the simpler optimization problem o…

Let $\boldsymbol{a}_t$ and $\boldsymbol{b}_t$ be the regressors of the kernel and Gaussian models, respectively, and let…

Let ${\sf M}$ denote either the random-feature (RF) or neural-tangent (NT) model, with $R_{{\sf M},N,n}(f_*;{\boldsymbol W})$ its test error for a target function $f_*$ at width…

Random-features/Gaussian-features equivalence conjecture. In the limit $p,n,d\to\infty$ with $p/d\to\psi_1$ and $n/d\to\psi_2$,

Let $p$, $n$, and $d$ tend to infinity, with $p/d\to\psi_1$ and $n/d\to\psi_2$. The random-features model uses nonlinear features generated from Gaussian covariates, while the nois…

The paper considers binary classification with random features obtained from Gaussian covariates and a nonlinear activation, and compares this model with an effective Gaussian-cova…

Let $R_{\rm RF}(f_d, {\boldsymbol X}, {\boldsymbol \Theta}, \lambda)$ denote the prediction risk of random-features ridge regression, with ridge parameter $\lambda>0$, and let the…

Smallest-sample-size conjecture. Beyond the proportional asymptotics, the limiting factor governing $R_{\sf RF}(f_d,\boldsymbol X,\boldsymbol W,\lambda)$ is given by the smallest o…

Fastfood replacement conjecture. The Hadamard matrix $\mathbf{H}$ can be replaced by any matrix $\mathbf{T}$ such that $\mathbf{T}/\sqrt{n}$ is orthonormal, the maximum entry in…