arXiv subjects

Qilin Ye

Publications and source records attributed to Qilin Ye.

6 recordsLinked to original sources

arXiv2026

Stable Voting Rules on the Edge of Optimal Metric Distortion

We prove the existence of a randomized voting rule with metric distortion at most $2.13713$, within $0.025$ of the lower bound of $2.11264$. Our rule comes from a generalization of stable $k$-lotteries developed in the context of committee selection. In contrast to prior work, our rule samples from a single distribution derived from a zero-sum game, without mixing between voting rules. Our result also gives sharp distortion bounds for stable $k$-lotteries, and in particular shows that stable $2$-lotteries have distortion $7/3$, despite only relying on aggregate preferences over triples of candidates.

cs.GT↗

arXiv2026

Cutting Down the Tower: Single-Exponential Envy-Free Cake Cutting

Envy-free cake cutting is a central problem in fair division with a striking divide between existence and computation. Classical topology guarantees that envy-free allocations exist, yet finding one efficiently turned out to be much harder, and this problem has resisted decades of work. A well-known result by Aziz and Mackenzie established the existence of a bounded protocol for every $n$, but its query bound is $n^{n^{n^{n^{n^n}}}}$. A tighter analysis by Sokolov subsequently reduced this upper bound to $n^{8n^2(1+o(1))}$, the best known prior to this work. In contrast, the general lower bound, due to Procaccia, is merely $\Omega(n^2)$. We close much of this massive gap with a protocol using at most $n^{O(1)}2^n$ queries. At a high level, our protocol repeatedly allocates some cake without creating envy until the remaining problem involves fewer agents. The main difficulty is to ensure that, when we later put these allocations together, we neither assign any cake twice nor create envy. To overcome this difficulty, we develop a new construction using only polynomially many partial allocations, replacing the $n^{n^{n^n}}$ partial allocations used in previous work. Overall, our protocol gives the first single-exponential query bound for finding a complete envy-free allocation with arbitrary nonatomic, additive valuations.

cs.GT↗

arXiv2026

Half Veto, Half Maximal Lottery, Five-halves Distortion

We give a randomized voting rule with expected metric distortion $5/2$, improving the previous best upper bound of $2.753$. Our rule is the equal mixture of a Maximal Lottery [CRWW24] and a lottery obtained by averaging scores in Simultaneous Plurality Veto [KK23] over time. We further show that $5/2$ is optimal within a broader family that allows profile-dependent mixing weights and arbitrary, possibly adaptive, weights over the veto process.

cs.GT↗

arXiv2026

HydraCollab: Adaptive Collaborative-Perception for Distributed Autonomous Systems

Collaborative-perception enables multi-robot systems to enhance situational awareness by sharing perceptual information. Existing collaborative-perception systems face an inherent trade-off between communication bandwidth requirements and perception accuracy, where methods that exchange more information achieve better perception results at the cost of increased communication overhead. However, real-world communication networks impose bandwidth constraints that require minimizing communication overhead without sacrificing perception performance. To address this challenge, we propose HydraCollab, an adaptive collaborative-perception framework that (i) selectively transmits the most informative sensor features and (ii) dynamically employs collaboration strategies (intermediate or late) based on spatial confidence maps. Extensive evaluations on the V2X-R, V2X-Radar and UAV3D-mini datasets demonstrate that HydraCollab achieves the best overall trade-off between accuracy and communication cost among existing collaborative-perception methods. Relative to SOTA Where2comm, HydraCollab uses only 41% of the bandwidth on V2X-R and 26% on V2X-Radar while improving performance by 0.78% and 0.75% respectively. Our code and models are available at https://github.com/AICPS/HydraCollab.

cs.RO↗

arXiv2025

Deliberation via Matching

We study deliberative social choice, where voters engage in small-group discussions to output collective preferences that are then aggregated by a social choice rule. We introduce a simple deliberation-via-matching protocol. In this protocol, for each pair of candidates, we form a maximum matching among voters who disagree on that pair, and have each matched pair deliberate. We then aggregate the resulting individual and deliberative preferences using the weighted uncovered set tournament rule. We show that this protocol has a tight distortion bound of $3$ within the metric distortion framework. In the absence of deliberation, general deterministic social choice rules can achieve this distortion, whereas deterministic tournament rules face a strictly larger lower bound of $3.11$. Our result closes this gap: Pairwise deliberation allows a tournament-based rule to attain distortion $3$. Conceptually, this shows that tournament rules can match the power of general deterministic social choice rules once they are given the minimal added power of pairwise deliberations. We prove this bound via a novel bilinear relaxation of the non-linear program capturing optimal distortion, whose vertices we can explicitly enumerate, leading to an analytic proof. Loosely speaking, our key technical insight is that the distortion objective, as a function of metric distances to any three alternatives, is both supermodular and convex. This characterization therefore provides a new analytical tool for studying the distortion of deliberative protocols, and may be of independent interest. Finally, although our analysis is for the full protocol, we show that this mechanism also admits a lightweight sampling-based implementation, yielding a high-probability approximation to the deterministic guarantee with arbitrary accuracy and low per-voter complexity.

cs.GT↗

arXiv2025

Transformers Provably Learn Algorithmic Solutions for Graph Connectivity, But Only with the Right Data

Transformers often fail to learn generalizable algorithms, instead relying on brittle heuristics. Using graph connectivity as a testbed, we explain this phenomenon both theoretically and empirically. We consider a simplified Transformer architecture, the Disentangled Transformer, and prove that an $L$-layer model can compute connectivity in graphs with diameters up to $3^L$, implementing an algorithm equivalent to computing powers of the adjacency matrix. By analyzing training dynamics, we prove that whether the model learns this strategy hinges on whether most training instances are within this model capacity. Within-capacity graphs (diameter $\leq 3^L$) drive the learning of the algorithmic solution while beyond-capacity graphs drive the learning of a simple heuristic based on node degrees. Finally, we empirically show that restricting training data to stay within a model's capacity makes both standard and Disentangled Transformers learn the exact algorithm.

cs.LG↗