Claims Browser

GRAPE outperforms the second best method by 3.8 log-units reduction in final average regret on large language model prompt optimization tasks

"on large language model prompt optimization tasks, it outperforms the second best method by a reduction of 3.8 log-units in the final average regret"

Existing local Bayesian optimization techniques are overly conservative, wasting queries on directions that offer little decrease

"existing techniques often prioritize the probability of descent over the magnitude of progress. This leads to overly conservative steps that yield negligible improvement, wasting queries on directions that are nearly certain to descend but offer little decrease"

GRAPE's gradient refinement stage monotonically minimizes local uncertainty and the progress-aware direction converges to true steepest descent as the posterior sharpens

"Theoretical analysis proves that this gradient refinement stage monotonically minimizes local uncertainty and that the progress-aware direction converges to true steepest descent as the posterior sharpens"

GRAPE demonstrates superior query efficiency across high-dimensional tasks

"Empirically, GRAPE demonstrates superior query efficiency across high-dimensional tasks"

Machine learning formalizations typically focus on samples while leaving the persistent individual referent implicit

"Machine learning is usually formalized through samples, while the persistent individual to which multiple observed or possible events refer often remains implicit."

A sample-only conditional cannot distinguish whether the world is homogeneous or whether the observed law is merely the marginal of a heterogeneous family

"a sample-only conditional is silent as to whether the world is homogeneous or the observed law is only the marginal of a heterogeneous family"

Unlinked single-row observations cannot distinguish between a heterogeneous unit world and a homogeneous pooled world

"Unlinked single-row observations can fail to distinguish a heterogeneous unit world from a homogeneous pooled world"

Gromov-Wasserstein pointwise comparison can be too sensitive in one-to-many settings where several target outcomes refine one source state

"This pointwise comparison can be too sensitive in one-to-many settings, where several target outcomes refine one source state and their mean carries the geometry of interest."

The barycentric weak inner-product GW satisfies a specific mathematical relationship that allows searching for intermediate target geometries

"The resulting barycentric weak inner-product GW (wIGW) satisfies $\mathrm{wIGW}_{\mathrm{bar}}^2(μ,ν)=\inf_{η\preceq_{\mathrm{cx}}ν}\mathrm{IGW}^2(μ,η)$."

Under a quantitative ridge condition, the reduced problem is convex-concave and the projected outer iteration satisfies an explicit contraction bound for inexact inner solves

"Under a quantitative ridge condition, the reduced problem is convex--concave, and the projected outer iteration satisfies an explicit contraction bound for inexact inner solves."

Point cloud and graph feature refinement experiments demonstrate that mean-preserving target refinements can have zero cost

"Point cloud and graph feature refinement experiments illustrate how mean-preserving target refinements can have zero cost."

For the d-expert problem, the minimax alternating regret is Θ(log d), independent of the horizon T

"for the $d$-expert problem, we show that the minimax alternating regret is $Θ(\log d)$, independent of the horizon $T$"

The new result significantly improves upon the best-known O(T^(1/3) log^(2/3) d) bound established by Hait et al. (2025)

"This significantly improves upon the best-known $\mathcal{O}(T^{1/3}\log^{2/3} d)$ established by Hait et al. [2025]"

For general OCO over a d-dimensional compact convex set, the worst-case minimax alternating regret is Θ(d log(1 + T/d))

"We further extend our results to general OCO over a $d$-dimensional compact convex set and prove that the worst-case minimax alternating regret is $Θ\left(d\log \left(1+\frac{T}{d}\right)\right)$"

The new OCO bound resolves the open problem posed by Cevher et al. (2023) and Hait et al. (2025) and improves upon the best-known O((d log T)^(2/3) T^(1/3)) upper bound

"also significantly improving upon the best-known $\mathcal{O}((d\log T)^{2/3}T^{1/3})$ upper bound and resolving the open problem posed by Cevher et al. [2023], Hait et al. [2025]"

The upper bound for the expert problem is achieved by a corrected variant of Hedge with carefully designed correction terms that cancel the unfavorable curvature in alternating-regret analysis

"our upper bound for the expert problem is achieved by a corrected variant of Hedge, in which carefully designed correction terms cancel the unfavorable curvature arising in the alternating-regret analysis"

The exact number of hidden layers required to represent continuous piecewise linear functions remains open, with the answer potentially being a constant (possibly even 2) or higher

"It remains completely open if the right answer is a constant number of hidden layers (possibly even 2!) or not."

Two-hidden-layer ReLU representations have been obtained for MAX_5, MAX_6, MAX_7, and MAX_8 using computer-assisted search

"Using a careful computer assisted search, we obtain two-hidden-layer ReLU representations of $\mathrm{MAX}_5, \mathrm{MAX}_6, \mathrm{MAX}_7$, and $\mathrm{MAX}_8$."