arXiv subjects

Tian Bai

Publications and source records attributed to Tian Bai.

At least 19 recordsLinked to original sources

arXiv2026

Scaling Representation Diversity: Modulated Attention and Reconstructive Regularization for Visual Grounding

Referring Expression Comprehension (REC) is commonly studied under dataset-specific fine-tuning, resulting in specialist models with limited cross-dataset generalization. In this work, we revisit REC from the perspective of unified open-vocabulary grounding and identify representation degeneration as a key obstacle to scaling a single generalist model. To preserve representation diversity, we propose a holistic data-model co-design framework. Architecturally, we introduce the Modulated Attention-Contrastive Head (mACH) for efficient token-level vision-language alignment and a text-conditioned JEPA auxiliary stream that provides complementary gradient support to preserve alignment-active representations without inference overhead. On the data side, we introduce Objects365-Caption, enriching Objects365 with context-aware referring expressions for large-scale language supervision. We further provide a theoretical analysis showing that complementary gradient subspaces preserve alignment capacity and thereby scale representation diversity. Extensive experiments demonstrate that our single-checkpoint framework achieves highly competitive performance on standard REC benchmarks while exhibiting strong generalization across heterogeneous grounding datasets without benchmark-specific adaptation.

cs.CV↗

arXiv2026

Feedback Set Problems on Bounded-Degree (Planar) Graphs

The feedback set problems are about removing the minimum number of vertices or edges from a graph to break all its cycles. Much effort has gone into understanding their complexity on planar graphs as well as on graphs of bounded degree. We obtain a complete complexity classification for these problems on bounded-degree digraphs, including the planar case. In particular, we show that both problems are $\NP$-complete on digraphs of maximum degree three, while on planar digraphs the feedback vertex set problem is polynomial-time solvable when each vertex has either indegree at most one or outdegree at most one, and $\NP$-complete otherwise. We also give tight degree bounds for the connected feedback vertex set problem on undirected graphs, both planar and non-planar. We close the paper with a historical account of results for feedback vertex set on undirected graphs of bounded degree.

cs.CC↗

arXiv2026

Clustering Permutations under the Ulam Metric: A Parameterized Complexity Study

Rank aggregation seeks a representative permutation for a collection of rankings and plays a central role in areas such as social choice, information retrieval, and computational biology. Two fundamental aggregation tasks are the center and median problems, which minimize the maximum and the total distance to the input permutations, respectively. While these problems are well understood under Kendall's tau and related distances, their parameterized complexity under the Ulam metric, an edit-distance-based metric on permutations, has remained largely unexplored. In this work, we initiate a systematic study of the parameterized complexity of rank aggregation under the Ulam metric. We consider both the center and median problems, as well as their generalizations to the $k$-center and $k$-median clustering settings, parameterized by the number of centers $k$ and the distance budget $d$ (corresponding to the maximum distance for center variants and the total distance for median variants). Both problems are known to be NP-hard already for $k=1$. We show that the Ulam $k$-center problem remains NP-hard when $d=1$, but is fixed-parameter tractable when parameterized by $k + d$. Our algorithm is based on a novel local-search framework tailored to the non-local nature of Ulam distances. We complement this by proving that no polynomial kernel exists for the $k+d$ parameterization unless NP $\subseteq$ coNP/poly. For the Ulam $k$-median problem parameterized by the total distance $d$, we establish W[1]-hardness and provide an XP algorithm. We also provide a polynomial kernel for the parameter $k + d$, which in turn yields a fixed-parameter tractable algorithm.

cs.DS↗

arXiv2026

Conformal Selective Prediction with General Risk Control

In deploying artificial intelligence (AI) models, selective prediction offers the option to abstain from making a prediction when uncertain about model quality. To fulfill its promise, it is crucial to enforce strict and precise error control over cases where the model is trusted. We propose Selective Conformal Risk control with E-values (SCoRE), a new framework for deriving such decisions for any trained model and any user-defined, bounded and continuously-valued risk. SCoRE offers two types of guarantees on the risk among ``positive'' cases in which the system opts to trust the model. Built upon conformal inference and hypothesis testing ideas, SCoRE first constructs a class of (generalized) e-values, which are non-negative random variables whose product with the unknown risk has expectation no greater than one. Such a property is ensured by data exchangeability without requiring any modeling assumptions. Passing these e-values on to hypothesis testing procedures, we yield the binary trust decisions with finite-sample error control. SCoRE avoids the need of uniform concentration, and can be readily extended to settings with distribution shifts. We evaluate the proposed methods with simulations and demonstrate their efficacy through applications to error management in drug discovery, health risk prediction, and large language models.

stat.ME↗

arXiv2026

ExpAlign: Expectation-Guided Vision-Language Alignment for Open-Vocabulary Grounding

Open-vocabulary grounding requires accurate vision-language alignment under weak supervision, yet existing methods either rely on global sentence embeddings that lack fine-grained expressiveness or introduce token-level alignment with explicit supervision or heavy cross-attention designs. We propose ExpAlign, a theoretically grounded vision-language alignment framework built on a principled multiple instance learning formulation. ExpAlign introduces an Expectation Alignment Head that performs attention-based soft MIL pooling over token-region similarities, enabling implicit token and instance selection without additional annotations. To further stabilize alignment learning, we develop an energy-based multi-scale consistency regularization scheme, including a Top-K multi-positive contrastive objective and a Geometry-Aware Consistency Objective derived from a Lagrangian-constrained free-energy minimization. Extensive experiments show that ExpAlign consistently improves open-vocabulary detection and zero-shot instance segmentation, particularly on long-tail categories. Most notably, it achieves 36.2 AP$_r$ on the LVIS minival split, outperforming other state-of-the-art methods at comparable model scale, while remaining lightweight and inference-efficient.

cs.CV↗

arXiv2026

Multi-Stage Patient Role-Playing Framework for Realistic Clinical Interactions

The simulation of realistic clinical interactions plays a pivotal role in advancing clinical Large Language Models (LLMs) and supporting medical diagnostic education. Existing approaches and benchmarks rely on generic or LLM-generated dialogue data, which limits the authenticity and diversity of doctor-patient interactions. In this work, we propose the first Chinese patient simulation dataset (Ch-PatientSim), constructed from realistic clinical interaction scenarios to comprehensively evaluate the performance of models in emulating patient behavior. Patients are simulated based on a five-dimensional persona structure. To address issues of the persona class imbalance, a portion of the dataset is augmented using few-shot generation, followed by manual verification. We evaluate various state-of-the-art LLMs and find that most produce overly formal responses that lack individual personality. To address this limitation, we propose a training-free Multi-Stage Patient Role-Playing (MSPRP) framework, which decomposes interactions into three stages to ensure both personalization and realism in model responses. Experimental results demonstrate that our approach significantly improves model performance across multiple dimensions of patient simulation.

cs.CL↗

arXiv2026

On the Leaky Private Information Retrieval with Side Information

This paper investigates the problem of Leaky Private Information Retrieval with Side Information (L-PIR-SI), providing a fundamental characterization of the trade-off among leaky privacy, side information, and download cost. We propose a unified probabilistic framework to design L-PIR-SI schemes under $\varepsilon$-differential privacy variants of both $W$-privacy and $(W, S)$-privacy. Explicit upper bounds on the download cost are derived, which strictly generalize existing results: our bounds recover the capacity of perfect PIR-SI as $\varepsilon \to 0$, and reduce to the known $\varepsilon$-leaky PIR rate in the absence of side information. Furthermore, we conduct a refined analysis of the privacy--utility trade-off at the scaling-law level, demonstrating that the leakage ratio exponent scales as $\mathcal{O}(\log \frac{K}{M + 1})$ under leaky $W$-privacy, and as $\mathcal{O}(\log K)$ under leaky $(W, S)$-privacy in the minimal non-trivial setting $M = 1$, where $K$ and $M$ denote the number of messages and the side information size, respectively.

cs.IT↗

arXiv2026

VERHallu: Evaluating and Mitigating Event Relation Hallucination in Video Large Language Models

Video Large Language Models (VideoLLMs) exhibit various types of hallucinations. Existing research has primarily focused on hallucinations involving the presence of events, objects, and scenes in videos, while largely neglecting event relation hallucination. In this paper, we introduce a novel benchmark for evaluating the Video Event Relation Hallucination, named VERHallu. This benchmark focuses on causal, temporal, and subevent relations between events, encompassing three types of tasks: relation classification, question answering, and counterfactual question answering, for a comprehensive evaluation of event relation hallucination. Additionally, it features counterintuitive video scenarios that deviate from typical pretraining distributions, with each sample accompanied by human-annotated candidates covering both vision-language and pure language biases. Our analysis reveals that current state-of-the-art VideoLLMs struggle with dense-event relation reasoning, often relying on prior knowledge due to insufficient use of frame-level cues. Although these models demonstrate strong grounding capabilities for key events, they often overlook the surrounding subevents, leading to an incomplete and inaccurate understanding of event relations. To tackle this, we propose a Key-Frame Propagating (KFP) strategy, which reallocates frame-level attention within intermediate layers to enhance multi-event understanding. Experiments show it effectively mitigates the event relation hallucination without affecting inference speed.

cs.CV↗

arXiv2025

Optimal Stopping with a Predicted Prior

There are two major models of value uncertainty in the optimal stopping literature: the secretary model, which assumes no prior knowledge, and the prophet inequality model, which assumes full information about value distributions. In practice, decision makers often rely on machine-learned priors that may be erroneous. Motivated by this gap, we formulate the model of optimal stopping with a predicted prior to design algorithms that are both consistent, exploiting the prediction when accurate, and robust, retaining worst-case guarantees when it is not. Existing secretary and prophet inequality algorithms are either pessimistic in consistency or not robust to misprediction. A randomized combination only interpolates their guarantees linearly. We show that a family of bi-criteria algorithms achieves improved consistency-robustness trade-offs, both for maximizing the expected accepted value and for maximizing the probability of accepting the maximum value. We further prove that for the latter objective, no algorithm can simultaneously match the best prophet inequality algorithm in consistency, and the best secretary algorithm in robustness.

cs.DS↗

arXiv2025

Contracting with a Mechanism Designer

This paper explores the economic interactions within modern crowdsourcing markets. In these markets, employers issue requests for tasks, platforms facilitate the recruitment of crowd workers, and workers complete tasks for monetary rewards. Recognizing that these roles serve distinct functions within the ecosystem, we introduce a three-party model that distinguishes among the principal (the requester), the intermediary (the platform), and the pool of agents (the workers). The principal, unable to directly engage with agents, relies on the intermediary to recruit and incentivize them. This interaction unfolds in two stages: first, the principal designs a profit-sharing contract with the intermediary; second, the intermediary implements a mechanism to select an agent to complete the delegated task. We analyze the proposed model as an extensive-form Stackelberg game. Our contributions are threefold. First, we fully characterize the subgame perfect equilibrium of our model. In particular, the principal's contract design problem can be represented as virtual value pricing, a novel auction-theoretic formulation. We identify the optimality of linear contracts, even when the task has multiple outcomes and agents' cost distributions are asymmetric. Second, to quantify the principal's utility loss from delegation and information asymmetry, we introduce the price of double marginalization (PoDM) and the classical price of anarchy (PoA). We derive tight or nearly tight bounds on both ratios under regular and monotone hazard rate distributions. Finally, we extend our analysis to two natural variants of the base model: (i) the intermediary is restricted to anonymous pricing mechanisms, and (ii) the principal lacks precise information about the market size.

cs.GT↗

arXiv2025

Adaptive Grid Designs for Classifying Monotonic Binary Deterministic Computer Simulations

This research is motivated by the need for effective classification in ice-breaking dynamic simulations, aimed at determining the conditions under which an underwater vehicle will break through the ice. This simulation is extremely time-consuming and yields deterministic, binary, and monotonic outcomes. Detecting the critical edge between the negative-outcome and positive-outcome regions with minimal simulation runs necessitates an efficient experimental design for selecting input values. In this paper, we derive lower bounds on the number of functional evaluations needed to ensure a certain level of classification accuracy for arbitrary static and adaptive designs. We also propose a new class of adaptive designs called adaptive grid designs, which are sequences of grids with increasing resolution such that lower resolution grids are proper subsets of higher resolution grids. By prioritizing simulation runs at lower resolution points and skipping redundant runs, adaptive grid designs require the same order of magnitude of runs as the best possible adaptive design, which is an order of magnitude fewer than the best possible static design. Numerical results across test functions, the road crash simulation and the ice-breaking simulation validate the superiority of adaptive grid designs.

stat.ME↗

arXiv2025

P$^2$HCT: Plug-and-Play Hierarchical C2F Transformer for Multi-Scale Feature Fusion

Feature fusion plays a pivotal role in achieving high performance in vision models, yet existing attention-based fusion techniques often suffer from substantial computational overhead and implementation complexity, particularly in resource-constrained settings. To address these limitations, we introduce the Plug-and-Play Hierarchical C2F Transformer (P$^2$HCT), a lightweight module that combines coarse-to-fine token selection with shared attention parameters to preserve spatial details while reducing inference cost. P$^2$HCT is trainable using coarse attention alone and can be seamlessly activated at inference to enhance accuracy without retraining. Integrated into real-time detectors such as YOLOv11-N/S/M, P$^2$HCT achieves mAP gains of 0.9\%, 0.5\%, and 0.4\% on MS COCO with minimal latency increase. Similarly, embedding P$^2$HCT into ResNet-18/50/101 backbones improves ImageNet top-1 accuracy by 6.5\%, 1.7\%, and 1.0\%, respectively. These results underscore P$^2$HCT's effectiveness as a hardware-friendly and general-purpose enhancement for both detection and classification tasks.

cs.CV↗

arXiv2025

Multivariate Conformal Selection

Selecting high-quality candidates from large datasets is critical in applications such as drug discovery, precision medicine, and alignment of large language models (LLMs). While Conformal Selection (CS) provides rigorous uncertainty quantification, it is limited to univariate responses and scalar criteria. To address this issue, we propose Multivariate Conformal Selection (mCS), a generalization of CS designed for multivariate response settings. Our method introduces regional monotonicity and employs multivariate nonconformity scores to construct conformal p-values, enabling finite-sample False Discovery Rate (FDR) control. We present two variants: mCS-dist, using distance-based scores, and mCS-learn, which learns optimal scores via differentiable optimization. Experiments on simulated and real-world datasets demonstrate that mCS significantly improves selection power while maintaining FDR control, establishing it as a robust framework for multivariate selection tasks.

stat.ME↗

arXiv2025

Text-to-TrajVis: Enabling Trajectory Data Visualizations from Natural Language Questions

This paper introduces the Text-to-TrajVis task, which aims to transform natural language questions into trajectory data visualizations, facilitating the development of natural language interfaces for trajectory visualization systems. As this is a novel task, there is currently no relevant dataset available in the community. To address this gap, we first devised a new visualization language called Trajectory Visualization Language (TVL) to facilitate querying trajectory data and generating visualizations. Building on this foundation, we further proposed a dataset construction method that integrates Large Language Models (LLMs) with human efforts to create high-quality data. Specifically, we first generate TVLs using a comprehensive and systematic process, and then label each TVL with corresponding natural language questions using LLMs. This process results in the creation of the first large-scale Text-to-TrajVis dataset, named TrajVL, which contains 18,140 (question, TVL) pairs. Based on this dataset, we systematically evaluated the performance of multiple LLMs (GPT, Qwen, Llama, etc.) on this task. The experimental results demonstrate that this task is both feasible and highly challenging and merits further exploration within the research community.

cs.CL↗

arXiv2025

An Almost Quadratic Vertex Kernel for Subset Feedback Arc Set in Tournaments

In the Feedback Arc Set in Tournaments (Subset-FAST) problem, we are given a tournament $D$ and a positive integer $k$, and the objective is to determine whether there exists an arc set $S \subseteq A(D)$ of size at most $k$ whose removal makes the graph acyclic. This problem is well-known to be equivalent to a natural tournament ranking problem, whose task is to rank players in a tournament such that the number of pairs in which the lower-ranked player defeats the higher-ranked player is no more than $k$. Using the PTAS for Subset-FAST [STOC 2007], Bessy et al. [JCSS 2011] present a $(2 + \varepsilon)k$-vertex kernel for this problem, given any fixed $\varepsilon > 0$. A generalization of Subset-FAST, called Subset-FAST, further includes an additional terminal subset $T \subseteq V(D)$ in the input. The goal of Subset-FAST is to determine whether there is an arc set $S \subseteq A(D)$ of size at most $k$ whose removal ensures that no directed cycle passes through any terminal in $T$. Prior to our work, no polynomial kernel for Subset-FAST was known. In our work, we show that Subset-FAST admits an $\mathcal{O}((\alpha k)^{2})$-vertex kernel, provided that Subset-FAST has an approximation algorithm with an approximation ratio $\alpha$. Consequently, based on the known $\mathcal{O}(\log k \log \log k)$-approximation algorithm, we obtain an almost quadratic kernel for Subset-FAST.

cs.DS↗

arXiv2024

Optimized Conformal Selection: Powerful Selective Inference After Conformity Score Optimization

Model selection/optimization in conformal inference is challenging, since it may break the exchangeability between labeled and unlabeled data. We study this problem in the context of conformal selection, which uses conformal p-values to select ``interesting'' instances with large unobserved labels from a pool of unlabeled data, while controlling the FDR in finite sample. For validity, existing solutions require the model choice to be independent of the data used to construct the p-values and calibrate the selection set. However, when presented with many model choices and limited labeled data, it is desirable to (i) select the best model in a data-driven manner, and (ii) mitigate power loss due to sample splitting. This paper presents OptCS, a general framework that allows valid statistical testing (selection) after flexible data-driven model optimization. We introduce general conditions under which OptCS constructs valid conformal p-values despite substantial data reuse and handles complex p-value dependencies to maintain finite-sample FDR control via a novel multiple testing procedure. We instantiate this general recipe to propose three FDR-controlling procedures, each optimizing the models differently: (i) selecting the most powerful one among multiple pre-trained candidate models, (ii) using all data for model fitting without sample splitting, and (iii) combining full-sample model fitting and selection. We demonstrate the efficacy of our methods via simulation studies and real applications in drug discovery and alignment of large language models in radiology report generation.

stat.ME↗

arXiv2024

Facility Location Games Beyond Single-Peakedness: the Entrance Fee Model

The facility location game has been studied extensively in mechanism design. In the classical model, each agent's cost is solely determined by her distance to the nearest facility. In this paper, we introduce a novel model where each facility charges an entrance fee. Thus, the cost of each agent is determined by both the distance to the facility and the entrance fee of the facility. In our model, the entrance fee function is allowed to be an arbitrary function, causing agents' preferences may no longer be single-peaked anymore: This departure from the classical model introduces additional challenges. We systematically delve into the intricacies of the model, designing strategyproof mechanisms with favorable approximation ratios. Additionally, we complement these ratios with nearly-tight impossibility results. Specifically, for one-facility and two-facility games, we provide upper and lower bounds for the approximation ratios given by deterministic and randomized mechanisms with respect to utilitarian and egalitarian objectives.

cs.GT↗

arXiv2024

Facility Assignment with Fair Cost Sharing: Equilibrium and Mechanism Design

In the one-dimensional facility assignment problem, m facilities and n agents are positioned along the real line. Each agent will be assigned to a single facility to receive service. Each facility incurs a building cost, which is shared equally among the agents utilizing it. Additionally, each agent independently bears a connection cost to access a facility. Thus, an agent's cost is the sum of the connection cost and her portion of the building cost. The social cost is the total cost of all agents. Notably, the optimal assignment that minimizes the social cost can be found in polynomial time. In this paper, we study the problem from two game-theoretical settings regarding the strategy space of agents and the rule the assignment. In both settings, agents act strategically to minimize their individual costs. In our first setting, the strategy space of agents is the set of facilities, granting agents the freedom to select any facility. Consequently, the self-formed assignment can exhibit instability, as agents may deviate to other facilities. We focus on the computation of an equilibrium assignment, where no agent has an incentive to unilaterally change her choice. We show that we can compute a pure Nash equilibrium in polynomial time. In our second setting, agents report their positions to a mechanism for assignment to facilities. The strategy space of agents becomes the set of all positions. Our interest lies in strategyproof mechanisms. It is essential to note that the preference induced by the agents' cost function is more complex as it depends on how other agents are assigned. We establish a strong lower bound against all strategyproof and anonymous mechanisms: none can achieve a bounded social cost approximation ratio. Nonetheless, we identify a class of non-trivial strategyproof mechanisms for any n and m that is unanimous and anonymous.

cs.GT↗