8 problems

Effective-dimension conjecture. The relevant sample complexity for the second kernel ridge regression fit is governed by $d_{\mathrm{eff}}$. This prediction is motivated by an anal…

Let $d$ be the ambient dimension, $n$ the sample size, and $v_i$ the strength of feature $i$. In the non-overfitting regime, let $\textsc{Adam}$ denote the training algorithm and l…

Consider the single-index model with fixed latent dimension $k=1$, sample-to-dimension ratio $\frac{n}{d}\to\delta$, and an even link function $h$. Let weak recovery mean estimatin…

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…

Let $d$ be the input dimension and $m$ the layer width, as in the stated feature-learning bound, whose approximation term contains the factor $\sqrt{d+m}$. Bietti et al.'s feature-…

Let a feature be rare when it occurs infrequently in the training data relative to a corresponding common feature, and suppose standard data augmentations such as rotations and fli…

Let $\tilde{\boldsymbol X}$ and $\tilde{\boldsymbol y}$ be new training data and labels independent of $\boldsymbol W_1$. Assume the activation $\sigma$ is odd, Assumption 1 holds,…

The paper considers feature extraction layers learned by directly optimizing the AUC margin loss from scratch and compares them with feature extraction layers learned by optimizing…