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Yifeng Zhang

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math.CO math.RT Artificial Intelligence Computer Vision Data Structures and Algorithms math.GR

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preprint2026arXiv

Learning to Solve Compositional Geometry Routing Problems

We study the Compositional Geometry Routing Problem (CGRP), a unified superclass of traditional routing problems that covers point-only, line-only, area-only, and arbitrary hybrid task geometries, providing a broad abstraction for real-world routing scenarios. Beyond standard point-based routing, CGRP with non-point tasks can be inherently asymmetric, tightly coupled travel routes with the intrinsic path, and enlarges the action space with numerous feasible yet often irrelevant options, thereby posing significant challenges for both representation learning and decision-making. To address these challenges, we propose DiCon, a differential attention-assisted solver with contrastive learning, as a plug-and-play framework that tackles the problem from two complementary angles. First, we introduce a differential attention mechanism that actively suppresses the probability mass on less competitive candidate actions. Second, we design a double-level contrastive learning objective to promote robust global instance representations and regularize geometry-aware task representations. Extensive experiments demonstrate that DiCon achieves strong performance, broad versatility, and superior generalization across diverse CGRP instances with different compositions.

preprint2024arXiv

Insertion algorithms for Type $\mathrm{B}$ and $\mathrm{D}$ Gelfand $W$-graphs

Like the RSK correspondence for symmetric groups, Garfinkle defined a domino correspondence for type $\mathrm{B}$ and $\mathrm{D}$ Coxeter groups. Similar to the Knuth relations, Taskin and Pietraho give the plactic relations for the domino correspondence and Bonnafé use them to classify the cells for type $\mathrm{B}$ Coxeter groups. We give some further properties of the plactic relations and use these relations to describe the bidirected edges and the molecules of Gelfand $W$-graphs for type $\mathrm{B}$ and $\mathrm{D}$ Coxeter groups.

preprint2022arXiv

Perfect models for finite Coxeter groups

A model for a finite group is a set of linear characters of subgroups that can be induced to obtain every irreducible character exactly once. A perfect model for a finite Coxeter group is a model in which the relevant subgroups are the quasiparabolic centralizers of perfect involutions. In prior work, we showed that perfect models give rise to interesting examples of $W$-graphs. Here, we classify which finite Coxeter groups have perfect models. Specifically, we prove that the irreducible finite Coxeter groups with perfect models are those of types $\mathsf{A}_{n}$, $\mathsf{B}_n$, $\mathsf{D}_{2n+1}$, $\mathsf{H}_3$, or $\mathsf{I}_2(n)$. We also show that up to a natural form of equivalence, outside types $\mathsf{A}_3$, $\mathsf{B}_n$, and $\mathsf{H}_3$, each irreducible finite Coxeter group has at most one perfect model. Along the way, we also prove a technical result about representations of finite Coxeter groups, namely, that induction from standard parabolic subgroups of corank at least two is never multiplicity-free.

preprint2021arXiv

Affine transitions for involution Stanley symmetric functions

We study a family of symmetric functions $\hat F_z$ indexed by involutions $z$ in the affine symmetric group. These power series are analogues of Lam's affine Stanley symmetric functions and generalizations of the involution Stanley symmetric functions introduced by Hamaker, Pawlowski, and the first author. Our main result is to prove a transition formula for $\hat F_z$ which can be used to define an affine involution analogue of the Lascoux-Schützenberger tree. Our proof of this formula relies on Lam and Shimozono's transition formula for affine Stanley symmetric functions and some new technical properties of the strong Bruhat order on affine permutations.

preprint2020arXiv

Saliency Prediction with External Knowledge

The last decades have seen great progress in saliency prediction, with the success of deep neural networks that are able to encode high-level semantics. Yet, while humans have the innate capability in leveraging their knowledge to decide where to look (e.g. people pay more attention to familiar faces such as celebrities), saliency prediction models have only been trained with large eye-tracking datasets. This work proposes to bridge this gap by explicitly incorporating external knowledge for saliency models as humans do. We develop networks that learn to highlight regions by incorporating prior knowledge of semantic relationships, be it general or domain-specific, depending on the task of interest. At the core of the method is a new Graph Semantic Saliency Network (GraSSNet) that constructs a graph that encodes semantic relationships learned from external knowledge. A Spatial Graph Attention Network is then developed to update saliency features based on the learned graph. Experiments show that the proposed model learns to predict saliency from the external knowledge and outperforms the state-of-the-art on four saliency benchmarks.

preprint2016arXiv

Tight Analysis of a Multiple-Swap Heuristic for Budgeted Red-Blue Median

Budgeted Red-Blue Median is a generalization of classic $k$-Median in that there are two sets of facilities, say $\mathcal{R}$ and $\mathcal{B}$, that can be used to serve clients located in some metric space. The goal is to open $k_r$ facilities in $\mathcal{R}$ and $k_b$ facilities in $\mathcal{B}$ for some given bounds $k_r, k_b$ and connect each client to their nearest open facility in a way that minimizes the total connection cost. We extend work by Hajiaghayi, Khandekar, and Kortsarz [2012] and show that a multiple-swap local search heuristic can be used to obtain a $(5+ε)$-approximation for Budgeted Red-Blue Median for any constant $ε> 0$. This is an improvement over their single swap analysis and beats the previous best approximation guarantee of 8 by Swamy [2014]. We also present a matching lower bound showing that for every $p \geq 1$, there are instances of Budgeted Red-Blue Median with local optimum solutions for the $p$-swap heuristic whose cost is $5 + Ω\left(\frac{1}{p}\right)$ times the optimum solution cost. Thus, our analysis is tight up to the lower order terms. In particular, for any $ε> 0$ we show the single-swap heuristic admits local optima whose cost can be as bad as $7-ε$ times the optimum solution cost.