11 problems

Let $c$ be the teacher model's coefficient vector, with $c$ sampled in the paper's model from $\{\pm 1/\sqrt{k}\}^k$. Worst-case fine-tuning tractability conjecture. Fine-tuning sh…

While the analysis concerns analytically tractable overparameterized linear regression, let signal-noise dynamics denote the interaction between denoising and signal forgetting dur…

Let $\mathcal{F}_k$ denote sieve spaces used for boosting, and let the associated hyperparameters be selected from the data, for example by sample-splitting or cross-validation. Da…

Let $\sigma$ be an activation function satisfying the monomial approximation property: for every integer $k\geq 0$ and every $\rho>0$, there is a bounded weight function…

Let $\rho_\infty(\cdot,t)$ be the limiting parameter distribution at time $t$, and suppose that the origin $0_{\mathrm{dim}\theta+\mathrm{dim}w}$ is an interior point of…

Let the data have modes satisfying the additional homogeneity assumption described in the paper, and let the training objective use a loss function that is not necessarily convex.…

Signal-strength tightness conjecture. The second condition on the signal strength is tight up to an extra $\sqrt{n}$ factor; this factor is believed to be an artifact of the analys…

Consider the polynomial approximation barrier in high-dimensional kernel regression, and allow different choices of the kernel scaling, including the standard scaling and the flat-…

Let a kernel be rotationally invariant, and consider kernel regression for challenging non-polynomial problems in high dimensions. The polynomial approximation barrier is a bias ph…

Let the counterexample constructed in the paper establish failure of initial-value stability for standard deterministic accelerated gradient descent, even for strongly convex and s…

Let a base learner predict by randomly selecting and averaging over points in a set $A$, and let $k$ denote the number of selected points. Write $\zeta_s$ and $\zeta_1$ for the cor…