5 problems

Let $\Omega$ be the continuum domain, let $\rho$ be the sampling density, and let $\Gamma$ be a set of continuum labels with label function $g$. Define $\overline g$ as the centere…

Proof-artifact conjecture. The extra $+2$ term in the condition is an artifact of the proof of the cited theorem; equivalently, the result should hold without that additional term.

Let $\mathcal{H}$ be a hypothesis class, and consider semi-supervised learning (SSL), where a learner uses labeled and unlabeled data, versus supervised learning, where it uses lab…

Positive-shift numerical-stability conjecture. Incorporating a positive shift already in the single-layer Laplacians $\boldsymbol{L}_{\mathrm{sym},\delta}^{(t)}$ should provide gre…

Let $p$ be the model exponent, let $\beta_n$ denote the label rate, let $\varepsilon_n$ denote the graph length scale, and let $n$ be the number of data points. The source identifi…