Claims Browser

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 $\mathrm{MAX}_8$."

Recent work by Ruess et al. (2026) obtained two-hidden-layer representations of MAX_N for all N≤10

"Very recently, two-hidden-layer representations of $\mathrm{MAX}_N$ of the above form were obtained for all $N\leq 10$ in [Ruess et al., 2026]."

The best lower bound for representing MAX_N is 2 hidden layers while the current upper bound is logarithmic in N

"The best lower bound is 2, while the current upper bound is logarithmic in $N$."

Anthropic has asked prospective employees whether they are comfortable with the possibility that company stock could crash to zero

"Anthropic has sometimes asked prospective employees whether they are comfortable with the possibility that the price of the company stock could potentially crash to zero"

Thomson Reuters has pulled back on its Claude usage

"Thomson Reuters has become the latest company to pull back on its Claude usage"

The regularized Lee-Sidford walk achieves warm-start mixing in Õ((d²+dL²R²)log(w/δ)) steps for polytopes given by n inequalities and a convex L-Lipschitz potential

"For a polytope given by $n$ inequalities and a convex $L$-Lipschitz potential, this yields warm-start mixing in $\widetilde O((d^{2}+dL^{2}R^{2})\log(w/δ))$ steps for the regularized Lee--Sidford walk."

The log-det walk for spectrahedra with n×n blocks achieves mixing in Õ((ψ*nd+dL²R²)log(w/δ)) steps, where ψ* measures matrix leverage

"For a spectrahedron with $n\times n$ blocks, the log-det walk mixes in $\widetilde O((ψ^\star nd+dL^{2}R^{2})\log(w/δ))$ steps, where $ψ^\star$ measures matrix leverage."

Exact-metric Metropolis-adjusted Dikin walks can be analyzed by keeping the proposal determinant and reverse quadratic form together, with their leading uncentered terms canceling in the logarithmic acceptance ratio

"We analyze exact-metric, Metropolis-adjusted Dikin walks by keeping the proposal determinant and reverse quadratic form together. Their leading uncentered terms cancel in the complete logarithmic acceptance ratio, leaving centered fluctuations that can be controlled with second-order tools."

OBABO and BAOAB schemes cannot achieve square-root of condition number acceleration for sampling with any fixed choice of step size and friction based only on curvature bounds and dimension

"We prove that no fixed choice of step size and friction, based only on the curvature bounds and the dimension, achieves this acceleration: total variation mixing time lower bounds for OBABO show that ballistic cold-start mixing fails uniformly over the smooth strongly convex class"

The optimal condition-number dependence of cold-start total variation mixing for fixed-parameter OBABO tunings is linear (not square-root) up to logarithmic factors

"among fixed-parameter OBABO tunings, the optimal condition-number dependence of cold-start total variation mixing over this class is linear, up to logarithmic factors"

A complementary upper bound of O(κ) steps exists for a fixed-parameter OBABO tuning, up to logarithmic factors

"we prove a complementary upper bound of $O(κ)$ steps, up to logarithmic factors, for a fixed-parameter OBABO tuning"

Fixed-parameter acceleration is impossible for the left-endpoint exponential integrator, as demonstrated by direct Gaussian calculation

"A direct Gaussian calculation also rules out fixed-parameter acceleration for the left-endpoint exponential integrator"

Interactions alone may not suffice to bring bio-inspired swarms to a desired aggregate configuration within a prescribed time horizon

"In bio-inspired swarms, however, interactions alone may not suffice to bring the population to a desired aggregate configuration within a prescribed time horizon"

The Schrödinger bridges framework can be applied to finite-horizon minimum-energy collective steering for inertial swarms subject to stochastic disturbances

"Our formalism is rooted in the theory of Schrödinger bridges, which has inspired contemporary developments spanning statistical inference, biological modeling, stochastic control, and generative learning."