Sampling regime
Smooth non-log-concave + Fisher accuracy
Compare theorems by mathematical guarantee, rate, and source — not by raw crawler rows.
Theorem and frontier cases
best upper · Exact source theorem
Exact ULD / FORS
Theorem 6.2, using Theorem 6.1 and Theorem 3.2(ii)
Theorem statement
\[\mathsf{FI}(\widehat\pi\Vert\pi)\le\varepsilon^2,\qquad \widetilde O\!\left(M(d^{1/3}+\log(M/p))\right),\quad M=O\!\left(1+\frac{\beta\mathsf{KL}_0}{\varepsilon^2}\right)\]
best lower · Normalized SampleWiki statement
General first-order Fisher lower bound
Primary theorem audit pending — this is not presented as a verbatim paper theorem
Guarantee / accuracy
\[\operatorname{FI}\le\varepsilon^2\]
Complexity / rate
\[\varepsilon^{-2+o(1)}\]
upper/lower · Exact source theorem
Averaged LMC
Theorem 11.2.1
Theorem statement
\[\frac1{Nh}\int_0^{Nh}\mathrm{FI}(\widehat\mu_t\Vert\pi)\,dt\le\frac{2\mathrm{KL}(\widehat\mu_0\Vert\pi)}{Nh}+6\beta^2dh\]
lower · Normalized SampleWiki statement
One-dimensional first-order Fisher lower bound
Primary theorem audit pending — this is not presented as a verbatim paper theorem
Guarantee / accuracy
\[\operatorname{FI}\le\varepsilon^2\]
Complexity / rate
\[\Omega\bigl(\varepsilon^{-1}\sqrt{\log(1/\varepsilon)}\bigr)\]
lower · Normalized SampleWiki statement
Large-initial-gap query complexity
Primary theorem audit pending — this is not presented as a verbatim paper theorem
Guarantee / accuracy
\[\operatorname{FI}\le\varepsilon^2\]
Complexity / rate
\[\Theta(\beta K_0/\varepsilon^2)\]