Qian Chen, Jingcheng Liu, Minglong Qin, Leonard J. Schulman, Fang Song, Penghui Yao, Mingnan Zhao
We reveal an unexpected connection between two interacting particle systems: Kac's walk and the Kipnis-Marchioro-Presutti (KMP) process. We first establish a mixing-time analogue of Aldous's conjecture for the KMP process on general graphs: the mixing time of the $t$-particle process on any connected $d$-vertex graph is at most $O(\log d)$ times the corresponding single-particle mixing time, uniformly in $t$. As an application, we improve the mixing-time bound for coordinate hit-and-run on the $n$-dimensional standard simplex from $\widetilde{O}(n^3)$ [KV26] to $O(n\log n)$, while removing the dependence on the initial distribution. We then show that the twirling channel induced by the parallel Kac's walk on the symmetric subspace can be exactly encoded by a Markov chain on partitions, which naturally lifts to a parallel KMP chain on the complete graph. We prove that $O(\log d+\log(1/\varepsilon))$ repetitions of the parallel Kac's walk suffice to approximate Haar twirling on the symmetric subspace of $(\mathbb{C}^d)^{\otimes t}$ to error $\varepsilon$, uniformly in all $t$. Our main technical contribution is a new structural property of KMP-type dynamics: conditional product structure, which holds for both the standard KMP processes on general graphs and the parallel KMP processes on complete graphs. Conditioned on suitable auxiliary randomness, the evolution of the labeled KMP process factorizes into independent single-particle updates. Combining this structure with an exact coupling, we remove the dependence on the number of particles from the mixing bounds for both unlabeled KMP models. This bypasses the $\log(π_{\min}^{-1})$ dependency from spectral-gap arguments, which is often prohibitively large for many-particle systems. Using this framework, we prove mixing bounds that are sharp up to logarithmic factors for both unlabeled KMP models.
Social media translation requires preserving meaning while capturing the cultural nuances of user-generated content (UGC). However, gaps in the cultural knowledge of LLM-based evaluators can lead to inaccurate assessments and unreliable training rewards. To improve these signals, we use retrieval-enhanced cultural evaluation to train CUE-MT, a family of social media translation models. A calibrated, domain-specific Judger guides supervised data refinement and is augmented by an Agent for hard-example mining and reinforcement learning. The Agent retrieves relevant external evidence as needed and distills it into concise hints that the Judger uses to score translations and assign rewards. Across 9B, 27B, and 35B-A3B backbones, CUE-MT outperforms the evaluated open-source baselines of comparable size on CUE-MT-Bench and three public benchmarks. Human evaluation on CUE-MT-Bench shows cultural effectiveness gains of 7.44-15.12 percentage points over the strongest external baseline in each size group. Retrieval improves the Judger's four-way classification accuracy by 8.07 percentage points over a matched no-retrieval baseline that uses LLM-generated hints alone. Training ablations further support the combination of hard-example mining and Agent-enhanced rewards.
Xiaokang Yuan, Binhui Yao, Luwei Yang, Ruimin Chen, Zeng Wang
Leading GUI grounders score 93 to 96% on ScreenSpot-v2, and reported gaps between new and prior models are about a point. At this level the useful question is what the remaining errors are. Benchmarks count a click as correct only inside one annotated box, but interfaces often expose one action through several elements: a duplicated link, the label of a checkbox, the title next to a logo. The box is not wrong. The rule is incomplete. We call a click correct when executing it produces the same outcome as clicking the annotated target. A probe that executes and fingerprints about a thousand clicks per page turns this definition into outcome maps and an execution judge for live web applications, with no new annotation. We execute the predictions of three strong 7--8B grounders on a code forge and an online shop. About one in five and one in three of the clicks that box scoring rejects reach the intended outcome, and the shares remain one in seven and one in three when the instructions are rewritten as natural tasks. A blind audit of 11 models on ScreenSpot-v2 (three 7--8B grounders and eight 3B variants) finds the same effect on web screenshots, with two independent reviewers on a 60-unit subset. The share is highest for the strongest grounders. Training seeds and test-set sampling add noise that more runs and paired intervals control. Box scoring instead under-counts correct clicks, which repetition does not remove, and the audit-based correction of 0.2 to 1.8 points on ScreenSpot-v2 is as large as the gaps the field reports. The correction is needed in evaluation. In our 3B GRPO study, crediting equivalent clicks in the reward gives no stable gain over box rewards across three seeds and four test sets. We release the probe, the outcome maps, the audit and every prediction.