arXiv subjects

Xiao Han

Publications and source records attributed to Xiao Han.

At least 37 records · Page 2Linked to original sources

arXiv2026

Didactic knowledge or Clinical Cases? How Data Types Shape Medical Large Language Models

Medical large language models are commonly trained on mixtures of didactic data (e.g., textbooks) and clinical data (e.g., patient records), yet how these data types differentially shape model capabilities remains unclear. We address this issue with token-matched experiments that vary the didactic-to-clinical ratio and analyze how data composition affects performance, capability profiles, and error patterns across knowledge-intensive and clinic-oriented tasks. We uncover an asymmetric transfer across task types: clinical data improves clinic-oriented tasks while remaining competitive on knowledge-intensive ones, whereas didactic data mainly improves knowledge-intensive tasks. Error analysis suggests a knowing-doing gap, where improvements in knowledge recall do not reliably generalize to clinical reasoning. We further observe that modest amounts of clinical data yield most of the gains on EHR-grounded tasks, while the optimal mixture ratio varies with the knowledge and clinical reasoning demands of downstream tasks. These findings suggest that medical LLM data curation should be application-driven, with higher proportions of clinical data preferred for reasoning-intensive use cases.

cs.AI↗

arXiv2026

Hopf Galois extensions of Hopf algebroids

We study Hopf Galois extensions of Hopf algebroids as a generalization of the theory for Hopf algebras. More precisely, we introduce (skew-)regular comodules and generalize the structure theorem for relative Hopf modules. Also, we show that if $N\subseteq P$ is a left $\mathcal{L}$-Galois extension and $Γ$ is a 2-cocycle of $\mathcal{L}$, then for the twisted comodule algebra ${}_ΓP$, $N\subseteq{}_ΓP$ is a left Hopf Galois extension of the twisted Hopf algebroid $\mathcal{L}^Γ$. We study twisted Drinfeld doubles of Hopf algebroids as examples for the Drinfeld twist theory. Finally, we introduce cleft extension and $σ$-twisted crossed products of Hopf algebroids. Moreover, we show the equivalence of cleft extensions, $σ$-twisted crossed products, and Hopf Galois extensions with normal basis properties, which generalize the theory of cleft extensions of Hopf algebras.

math.QA↗

arXiv2026

From the Square-Energy Conjecture to Signed Graphs: Sharp Bounds for Positive Square Energy

Let $Σ=(G,σ)$ be a connected signed graph of order $n$ and size $m$, and let $s^{+}(Σ)$ and $s^{-}(Σ)$ denote the sums of the squares of its positive and negative adjacency eigenvalues, respectively. The square-energy conjecture of Elphick, Farber, Goldberg, and Wocjan states that every connected graph $G$ of order $n$ satisfies \[ \min\{s^{+}(G),s^{-}(G)\}\ge n-1. \] Liu and Ning~\cite{LiuNing2023} published a wide-ranging paper entitled ``Unsolved Problems in spectral graph theory", and this conjectures were placed first in their list of such problems. We prove that every signature $σ$ of a connected graph $G$ satisfies the sharp bound \[ s^{+}(Σ)\le 2m-n+1. \] For the all-positive signing this gives $s^{+}(G)\le 2m-n+1$, whereas for the all-negative signing it gives $s^{-}(G)\le 2m-n+1$. Since $s^{+}(G)+s^{-}(G)=2m$, these two special cases imply the square-energy conjecture; the present theorem is stronger in scope because the same bound holds for every signing of $G$. Applying the theorem to the negation $-Σ$ also yields \[ s^{+}(Σ)\ge n-1. \] Both bounds are sharp. The proof is based on a doubly nonnegative matrix inequality. We also shorten the proof of that inequality by replacing its final case distinction with a fixed convex combination.

math.CO↗

arXiv2026

Cleft Extensions for Hopf Algebroids without Antipodes

We introduce cleft extensions for Hopf algebroids. We prove the equivalence between cleft extensions, $σ$-twisted crossed products, and Hopf-Galois extensions with the normal basis property, thereby generalizing the theory of cleft extensions for Hopf algebroids developed by B{ö}hm and Brzezi{ń}ski, and fitting in with the general theory of Galois and biGalois extensions over Hopf algebroids developed by the authors. We investigate the Ehresmann Hopf algebroid associated with a cleft extension and show that it is isomorphic to a generalized version of the Connes-Moscovici Hopf algebroid. A special case of the Connes-Moscovici Hopf algebroid, namely the case where the coinvariants of the cleft extension coincide with the base of the Hopf algebroid, is a Drinfeld twist of a Hopf algebroid by a two-cocycle, generalizing work of B{ö}hm, Han and Majid.

math.CT↗

arXiv2026

TAGR: Task-Adaptive Geo-Semantic Retrieval across Heterogeneous Urban Delivery Tasks

As urban residents demand higher-quality instant delivery services, demand forecasting, estimated time of arrival prediction, and next-stop prediction have become critical tasks in urban delivery systems. However, the three tasks rely on historical evidence with substantially different structures and granularities. Meanwhile, their prediction targets differ in output form, making it difficult to integrate retrieved evidence through a single fusion mechanism without causing mismatch or negative transfer. These issues can increase prediction errors and subsequently lead to imbalanced resource allocation, where some regions experience unmet demand. In contrast, others suffer from underutilization, ultimately degrading overall efficiency and service quality. To address these challenges, we propose TAGR, a Task-Adaptive Geo-Semantic Retrieval framework across heterogeneous urban delivery tasks. TAGR constructs an LLM-based geo-semantic shared prior and task-specific retrieval banks to share regional knowledge while preserving heterogeneous task-specific evidence. The LLM-derived regional representations encode geographic context and semantic relations among regions, providing transferable knowledge for all three tasks without requiring online LLM inference. It further introduces a task-adaptive retrieval augmentation module to accommodate heterogeneous output structures, thereby mitigating information mismatch and negative transfer caused by a uniform retrieval-fusion strategy. Experiments on three city datasets demonstrate that TAGR consistently outperforms state-of-the-art baselines across multiple tasks.

cs.IR↗

arXiv2026

Towards Trustworthy Hypergraph Neural Networks under Label Noise

Hypergraph neural networks (HGNNs) have demonstrated remarkable capabilities in processing complex higher-order relationships. However, their performance is highly dependent on labeled data, making them vulnerable to label noise. Despite advances in learning with label noise (LLN) and graph learning with label noise (GLN), noisy-label learning on hypergraphs remains underexplored. In this paper, we present a systematic study of hypergraph node classification under label noise. First, we adapt representative LLN and GLN methods to hypergraphs and evaluate them under a unified benchmark, revealing the limitations of existing robust learning strategies for hypergraphs. Building on this, we propose a new hypergraph robust framework, HyperTrust, which first estimates hyperedge trustworthiness through a pretraining-based, entropy-aware strategy, and then incorporates the HyperedgeBoost module to enhance reliable supervision by connecting unlabeled nodes to trustworthy hyperedges, as well as the HyperedgePrune module to suppress noisy propagation by removing untrustworthy node-hyperedge incidences. Finally, two modules work collaboratively to adjust the hypergraph structure and generate final predictions. Extensive experiments and theoretical analysis demonstrate the effectiveness and robustness of HyperTrust on multiple hypergraph datasets under various noisy settings. Our work provides a unified benchmark and an effective solution for hypergraph learning with label noise and lays a foundation for future research in this direction.

cs.LG↗

arXiv2026

Safety, or Just Capability? A Validity Audit of Agent-Safety Benchmarks

Agent-safety benchmarks measure different behaviors, and their scores get quoted interchangeably as an agent's safety. We treat four of them (R-Judge, InjecAgent, AgentHarm, AgentDojo) as measurements to be validated, running each under its official implementation and author-provided scorer on up to 22 models, with MMLU and GPQA measured by us under one protocol as a capability composite. The metric is the first problem. On any binary trace-judgment benchmark scored by $F_1$, an ``always positive'' policy attains $F_1 = 2π/(1+π)$; on R-Judge that is $0.690$, above five of the 21 models that actually discriminate. The three broad-coverage benchmarks then rank the same 18 models differently, and the trade-off behind that disagreement is a small-panel artifact: R-Judge specificity against AgentHarm safety correlates $-0.64$ at $n{=}7$ and $+0.02$ at $n{=}18$, and a quarter of random size-7 subsets reach $|ρ| \geq 0.5$ around that near-zero value. Held-out validity turns on which outcome you pick. Capability predicts task success ($ρ{=}{+}0.60$) but correlates negatively with misalignment safety ($ρ{=}{-}0.44$, $n{=}21$). On their paired $n{=}20$ panel, the corresponding contrast is $Δ{=}{-}1.00$ (95% CI $[-1.48, -0.49]$, $p<0.001$), and it survives leave-one-organization-out and organization-clustered bootstrap analyses. On an expanded 41-model panel, the misalignment correlation weakens to $-0.16$ (95% CI $[-0.54, +0.22]$) and jailbreak strengthens to $+0.34$, though neither change is significant. \mbox{AgentHarm} shows the strongest held-out association, $ρ{=}{+}0.72$ with three-template jailbreak safety after controlling capability. But both instruments score harmful compliance, so this is evidence of convergent validity rather than general safety. Naming the benchmark, metric, target behavior, and model panel is the minimum a safety claim needs.

cs.AI↗

arXiv2026

Hopf BiGalois Theory for Hopf Algebroids

We develop a theory of Hopf BiGalois extensions for Hopf algebroids. We understand these to be left bialgebroids (whose left module categories are monoidal categories) fulfilling a condition that is equivalent to being Hopf in the case of ordinary bialgebras, but does not entail the existence of an antipode map. The immediate obstacle to developing a full biGalois theory for such Hopf algebroids is simple: The condition to be a left Hopf Galois extension can be defined in complete analogy to the Hopf case, but the Galois map for a right comodule algebra is not a well defined map. We find that this obstacle can be circumvented using bialgebroids fulfilling a condition that still does not entail the existence of an antipode, but is equivalent, for ordinary bialgebras, to being Hopf with bijective antipode. The key technical tool is a result of Chemla allowing to switch left and right comodule structures under flatness conditions much like one would do using an antipode. Using this, we arrive at a left-right symmetric theory of biGalois extensions, including the construction of an Ehresmann Hopf algebroid making a one-sided Hopf-Galois extension into a biGalois one. Moreover, we apply a more general 2-cocycle twist theory to Ehresmann Hopf algebroids. As the 2-cocycle is only left linear over the base, the base algebra is also twisted. We also study the Ehresmann Hopf algebroids of quantum Hopf fibrations and quantum homogeneous space as examples.

math.CT↗

arXiv2026

MobiWave: Dispatch-Oriented Graph Wavelets and Drift-Guided Selective Optimization for Autonomous Fleet Rebalancing

Autonomous fleets enable mobility platforms to coordinate idle vehicles directly, making fleet-wide rebalancing possible. However, two obstacles limit reliable deployment: overlapping regional and local traffic patterns can hide roads that remain useful for dispatch, and mobility drift can make a trained policy unreliable. Existing spatial aggregation mixes these patterns, while updating all parameters from limited recent data is costly and can damage stable knowledge. We propose \name, a framework that connects a dispatch-oriented multi-scale graph wavelet module with Drift-Guided Layer-Selective Optimization (DGLS). The first module addresses the representation challenge by separating graph-frequency patterns and weighting each scale according to its value for demand prediction and feasible rebalancing. DGLS addresses the adaptation challenge by measuring Dispatch-weighted Spectral Drift, selecting affected layers within a resource budget, and separating short shocks from persistent changes through a drift-aware fast--slow update. Candidate validation further rejects updates that fail to improve held-out dispatch reward without worsening monitored service or safety constraints. Experiments on both real-world datasets and simluated environments demonstrate the effectiveness of \name\ in comparing with state-of-the-art methods. The source code and datasets are available at https://anonymous.4open.science/r/MobiWave-40F8/.

cs.LG↗

arXiv2026

Support Thresholds, Not Algorithms, Limit Rare-Association Recovery in Co-Purchase Networks

The support threshold of the Apriori algorithm involves a trade-off in conducting market basket analysis: the associations that occur frequently are noted with high threshold; however, the low ones lead to generating the large amount of rules. The paper compares five methods for co-purchase edge filtration on two grocery datasets: i.e., Instacart (3.2 million baskets) and Dunnhumby (208 thousand baskets), including Apriori, Apriori + lift post-filtering, top-$K$ ranking based on lift, and two methods based on networks, noise-corrected (NC) and disparity filter (DF). The top-$K$ method ensures the maximum average lift, while the NC achieves similar lift level by means of a single value of the significance parameter ($α$). These two methods recover substantially more rare high-lift associations than Apriori (80-100% against 22-28%). NC and top-$K$ select meaningfully different edges (18-29% non-overlapping): NC retains statistically validated pairs, while top-$K$ retains rare pairs with high lift but low statistical significance. A rolling-origin holdout evaluation shows that top-$K$ edges recur at higher rates at every split, but NC edges are ~12 pp more likely to remain statistically significant in the held-out network.

cs.LG↗

arXiv2026

Interpretable Factor Decomposition for Decision Intelligence in Large-Scale Financial Markets: Evidence from China's A-Share Market

We present an interpretable machine learning pipeline to decompose cross-sectional equity return predictability into auditable factor contributions. We apply an XGBoost model with TreeSHAP attribution and conduct stress testing on 3,632 Chinese A-share stocks from 2009 until 2019. On prediction, using 60-month rolling windows over 55 months of out-of-sample data, XGBoost obtains a mean AUC of 0.547 (rank IC = 0.119) and +2.38%/month (Newey-West t = 5.94; annualized Sharpe 2.23) long-short spread for the top vs bottom quintiles. This alpha is persistent after adjusting for the Carhart four-factor model (+2.31%/month; t = 7.48). On interpretation, SHAP decomposition indicates that behavioral signals (turnover and momentum) account for 58.2% of predictive attribution compared to 10.7% for valuation ratios, on average, across 50 industry groups. Ablation analysis serves to cross-validate this ranking and provides evidence that SHAP and ablation diverge in a manner that highlights feature substitutability structure that is largely invisible to either method used in isolation.

cs.LG↗

arXiv2026

Local Information for Global Network Estimation in Latent Space Models

In many social networks, an individual observes only a restricted local view of the full network structure. We study such local views under a partial information framework that models an individual's observations as a subgraph based on path length, and address the problem of estimating a general latent space model from a single individual's local view. Compared to the full network, the partial information network contains many missing edges and depends on a random, potentially sparse neighborhood, posing significant challenges for estimation. We propose a projected gradient descent algorithm for maximum likelihood estimation and establish theoretical guarantees for its convergence under both conditional likelihood and full likelihood settings. To characterize the quality of a local view, we introduce an imbalance measure as a theoretical and diagnostic quantity for assessing bias in a local view and show that it plays a central role in determining convergence rates and estimation error bounds. Using simulated networks, we demonstrate that satisfactory estimation is possible from a single local view. In an application to U.S. Congress cosponsorship networks, we show how the estimated latent positions reveal nuanced structure in legislators' social relationships.

stat.ME↗

arXiv2026

Driving Like Yourself: A Benchmark for Closed-Loop Personalized End-to-End Autonomous Driving

Human driving behavior is inherently diverse, yet most end-to-end autonomous driving (E2E-AD) systems learn a single average driving style, neglecting individual differences. Achieving personalized E2E-AD faces challenges across three levels: limited real-world datasets with individual-level annotations, a lack of quantitative metrics for evaluating personal driving styles, and the absence of algorithms that can learn stylized representations from users' trajectories. To address these gaps, we propose Person2Drive, a comprehensive personalized E2E-AD platform and benchmark. It includes an open-source, flexible data collection system that simulates realistic scenarios to generate scalable, diverse personalized driving datasets; style vector-based evaluation metrics with Maximum Mean Discrepancy and KL divergence to comprehensively quantify individual driving behaviors; and a personalized E2E-AD framework with a style reward model that efficiently adapts E2E models for safe and individualized driving. Crucially, our framework enables plug-and-play personalization by fine-tuning only the trajectory prediction head, preserving the pretrained base model and ensuring safety. Extensive experiments demonstrate that Person2Drive enables fine-grained analysis and effective personalization, while preserving driving performance and success rate even in challenging scenarios.

cs.CV↗

arXiv2026

Label Hierarchy Transition: Delving into Class Hierarchies to Enhance Deep Classifiers

Hierarchical classification aims to sort the object into a hierarchical structure of categories. For example, a bird can be categorized according to a three-level hierarchy of order, family, and species. Existing methods commonly address hierarchical classification by decoupling it into a series of multi-class classification tasks. However, such a multi-task learning strategy fails to fully exploit the correlation among various categories across different levels of the hierarchy. In this paper, we propose Label Hierarchy Transition (LHT), a unified probabilistic framework based on deep learning, to address the challenges of hierarchical classification. The LHT framework consists of a transition network and a confusion loss. The transition network focuses on explicitly learning the label hierarchy transition matrices, which has the potential to effectively encode the underlying correlations embedded within class hierarchies. The confusion loss encourages the classification network to learn correlations across different label hierarchies during training. The proposed framework can be readily adapted to any existing deep network with only minor modifications. We experiment with a series of public benchmark datasets for hierarchical classification problems, and the results demonstrate the superiority of our approach beyond current state-of-the-art methods. Furthermore, we extend our proposed LHT framework to the skin lesion diagnosis task and validate its great potential in computer-aided diagnosis. The code of our method is available at \href{https://github.com/renzhenwang/label-hierarchy-transition}{https://github.com/renzhenwang/label-hierarchy-transition}.

cs.CV↗

arXiv2026

Interpretable vs Learned Encoders for High-Cardinality Fraud Detection

A total of seven categorical encoding methods were tested on the IEEE-CIS fraud benchmark dataset (590,540 records, 3.5% positives, 8 high-cardinality columns). The encoders were evaluated using a stratified 5-fold cross-validation (CV) with three repetitions. Five of the encoders had identical frozen LightGBM learners in the downstream phase, allowing for controlled comparisons of their performance to each other. CatBoost and TabNet were included as comparisons across paradigms using different learners. The entity embeddings produced the highest AUC-ROC (0.9612), with a statistically significant tie with that of CatBoost (0.9602) and statistically superior to tier group encoding (0.9548), whereas target encoding was only 0.0023 worse than tier group encoding and the auditor-friendly tier boundaries were maintained. Off-the-shelf TabNet did not outperform tree-based pipelines and collapsed under data scarcity. On AUC-PR, CatBoost leads (0.822 vs. 0.793); no encoder dominated both metrics. Per-column analysis confirmed the embedding advantage arises from joint multi-column representation.

cs.LG↗

arXiv2026

Bisections and cocycles on Hopf algebroids

We introduce and study the group $\mathcal{B}(\mathcal{L})$ of bisections of a Hopf algebroid $\mathcal{L}$ and show that they form a group crossed module or 2-group with the group $\Aut(\mathcal{L})$ of automorphisms. Moreover, the group of vertical bisections turns out to be part of a certain non-Abelian cohomology of which $\mathcal{H}^2(\mathcal{L},B)$ governs cotwisting of a Hopf algebroid with base $B$. For the Ehresmann-Schauenburg Hopf algebroid $\mathcal{L}(P,H)$ of a quantum principal bundle or Hopf-Galois extension, $\mathcal{B}(\mathcal{L}(P,H))$ reduces to the group $\Aut_H(P)$ of bundle automorphisms and vertical bisections to the group of `gauge transformations' of the bundle. The general $\mathcal{H}^2(\mathcal{L}(P,H),B)$ reduces to a known non-Abelian cohomology in the case where $P$ is a trivial principal bundle or cleft extension. Parallel characterisations are obtained for the bisections and non-Abelian cohomology of the action Hopf algebroid $B\# H^{op}$ associated to a braided-commutative algebra $B$ in the category of Drinfeld-Yetter modules over a Hopf algebra $H$. Examples include the Heisenberg double or Weyl Hopf algebroid of a Hopf algebra and a canonical action Hopf algebroid $\underline H\# H^{op}$ when $H$ is coquasitriangular and $\underline{H}$ is its transmutation.

math.QA↗

arXiv2026

Coquasi-bialgebroids and cocycle twisting

We introduce coquasi-bialgebroids over a noncommutative base algebra. Using Takeuchi's $\times_B$-coalgebra formalism, we require the coproduct to remain an algebra map into the Takeuchi product, while the product is associative only up to an invertible normalized $3$-cocycle. This gives a bialgebroid analogue of coquasi-bialgebras and provides a natural framework for cocycle-twisted bialgebroid constructions. We develop the basic theory and prove a twisting theorem by convolution-invertible $2$-cochains. As a main class of examples, we construct coquasi Connes--Moscovici-type bialgebroids on $B\otimes H\otimes B$, where $H$ is a coquasi-bialgebra measuring an algebra $B$, with twisting data $γ:H\otimes H\to B$. We also give finite-group examples arising from a subgroup $G\subseteq X$ and a choice of transversal. Finally, under finite projectivity assumptions, we describe the dual quasi-bialgebroid construction and its relation to Drinfeld-type twisting.

math.QA↗

arXiv2026

Teach-to-Reason: Competition-Guided Reasoning with a Self-Improving Teacher

Chest X-ray visual question answering (CXR VQA) requires models not only to predict correct answers, but also to produce reliable medical reasoning. However, existing reinforcement-learning-based training typically relies on answer-level rewards, which are often too coarse to improve chain-of-thought (CoT) quality and can become ineffective when group-level advantages collapse to zero. We propose \textbf{Teach-to-Reason (T2R)}, a framework that introduces comparison-based supervision into CoT optimization through a self-improving \emph{Teacher} and a competition-guided \emph{Reasoner}. As the Teacher is iteratively strengthened via self-competition, the Reasoner is optimized against progressively stronger Teacher-generated references. We further introduce a case-wise reward design that preserves the original reward-induced positive/negative partition when it is informative, and restores supervision from competition scores when the original reward signal degenerates. Experiments on multiple CXR open-ended VQA benchmarks show that T2R consistently outperforms strong baselines, indicating that comparison-based supervision, when integrated in a controlled and principled manner, provides a more effective training signal for reasoning optimization.

cs.CV↗