arXiv subjects
Publications and source records attributed to Boyan Xu.
A family of paths strongly separates the edges of a graph if every two distinct edges are separated in both directions by paths in the family. Bonamy, Botler, Dross, Naia, and Skokan proved that every $n$-vertex graph admits such a family of at most $19n$ paths. We improve this bound to $10n-o(n)$.
Whether $\mathsf{QAC}^0$ can compute $\mathtt{PARITY}_n$ remains open. Computing $\mathtt{PARITY}_n$ is equivalent to implementing $\mathtt{FANOUT}_n$ under $\mathsf{QAC}^0$ reductions. This raises a more general question: for an arbitrary symmetric Boolean function $f:\{0,1\}^n\to\{0,1\}$, what fanout size is necessary and sufficient for computing $f$ in $\mathsf{QAC}^0$? We show that the answer is exactly the transition radius $\rho(f)$: computing $f$ and implementing $\mathtt{FANOUT}_{\rho(f)}$ are equivalent under $\mathsf{QAC}^0$ reductions. In particular, if $\rho(f)\ge n^\delta$ for some constant $\delta>0$, then computing $f$ is $\mathsf{QAC}^0_{\mathrm{f}}$-complete. Combined with Paturi's theorem, our characterization implies that if $\mathtt{PARITY}_n \notin \mathsf{QAC}^0$, then any Boolean function in $\mathsf{QAC}^0$ of approximate degree $n^{1/2+\Omega(1)}$ must be nonsymmetric.
A $(1^j,2^k)$-packing edge-coloring of a graph $G$ is a partition of the edge set $E(G)$ into $j$ matchings and $k$ induced matchings. Hocquard, Lajou, and Lu\v zar found a subcubic planar graph of girth $3$ that has no $(1,2^5)$-packing edge-coloring and also conjectured that every subcubic planar graph has a $(1,2^6)$-packing edge-coloring. We also notice that for every fixed positive integer $k$ there exists a subcubic planar graph with girth $k$ that is not $(1,2^3)$-packing edge-colorable. It is natural to consider what is the minimum positive integer $k_1$ such that every subcubic planar graph with girth at least $k_1$ is $(1,2^5)$-packing edge-colorable. Furthermore, we also consider what is the minimum positive integer $k_2$ such that every subcubic planar graph with girth at least $k_2$ is $(1,2^4)$-packing edge-colorable. In this paper, we show both $k_1$ and $k_2$ are finite, and in fact $5 \le k_1 \le 12$ and $6 \le k_2 \le 16$.
Delta-Rule recurrent models maintain a fixed-size state, enabling $O(1)$ inference memory but potentially becoming unstable under extreme-context extrapolation. By tracking RWKV-7 over sequences of up to 100M tokens, we empirically identify a distinct failure pattern: \textbf{localized norm explosion atop a relatively sparse substrate}, rather than global state saturation. Analysis of the recurrent update suggests that persistent decay keeps weakly updated entries small, whereas uneven injections allow a few channels to accumulate extreme values. Motivated by this diagnosis, we propose \textbf{State Anomaly Neutralization (SANE)}, which applies adaptive $\tanh$ compression at chunk boundaries while preserving the intra-chunk parallel structure. Within a safe threshold range ($3 \le \alpha \le 5$), SANE matches the baseline on 11 short-context reasoning benchmarks with no statistically significant degradation. After a 100M-token prefix, which exceeds the training length by over $24{,}000\times$, SANE retains functional reasoning ($33.46$--$35.56$) while the baseline encounters numerical overflow. In contrast, overly permissive thresholds ($\alpha \ge 8$) remain numerically stable but lose reasoning capability entirely, showing that numerical stabilization alone does not guarantee functional reasoning and revealing a capacity--stability trade-off in state compression.
Let $k\geq2$ be an integer. A $1\bmod k$ edge-coloring of a graph $G$ is an edge-coloring in which every nonzero degree in each color class is congruent to $1$ modulo $k$. Let $\chi'_k(G)$ denote the minimum number of colors required, and let $\chi'_k$ be the supremum of $\chi'_k(G)$ over all finite simple graphs $G$. Botler, Colucci, and Kohayakawa conjectured that there exists an absolute constant $C$ such that $\chi'_k(G)\leq k+C$ for every $k$ and every $G$. We disprove this conjecture, even within the class of bipartite graphs. More precisely, for all integers $c\geq0$ and $k\geq3c+2$, we construct a finite simple bipartite graph $G_{k,c}$ satisfying $\chi'_k(G_{k,c})=k+c+1$. Consequently, $\chi'_k\geq k+\lfloor(k+1)/3\rfloor$ for every $k\geq2$. For $k_m=2\cdot3^{m-1}$, we give an affine-hyperplane construction of a finite simple bipartite graph $G_m$ satisfying $\Delta(G_m)=\chi'_{k_m}(G_m)=3^m=3k_m/2$. More generally, for every sufficiently large $k$, we construct a finite simple bipartite graph $G_k$ such that $\Delta(G_k)=\chi'_k(G_k)\geq3k/2-10(k\log k)^{1/3}$. Our proofs combine a codegree obstruction with explicit cyclic and affine-geometric constructions and a structured random perturbation.
Learning a classical description of a quantum state is a fundamental task in quantum computation. Among the most important classes of quantum states are stabilizer states, which play a central role in quantum error correction and fault-tolerant computation. To mitigate the effects of realistic noise, agnostic learning of stabilizer states has emerged as a natural and well-motivated problem. Recently, Chen \textit{et al.} [STOC'25, p. 429-438] resolved this problem for qubit systems by using a stabilizer bootstrapping framework. However, the agnostic learning of qudit stabilizer states remains largely unexplored, since the qudit setting introduces fundamental structural differences that prevent a direct generalization of existing qubit techniques. In this paper, we successfully generalize the stabilizer bootstrapping framework to qudit systems and present the first efficient quantum algorithm for agnostic learning of qudit stabilizer states. Specifically, given copies of an unknown $n$-qudit pure state $|\psi\rangle$ that has fidelity $\tau$ with some stabilizer state, our algorithm outputs a stabilizer state $|\phi\rangle$ such that $\left| \braket{\phi|\psi} \right|^2 \geq \tau - \varepsilon$ with high probability. The algorithm uses only single-copy and four-copy measurements, and its sample and time complexity scale as $(d/\tau)^{O(d^2 \log(1/\tau))} \cdot \mathrm{poly}(n, 1/\varepsilon)$, where the dimension $d$ is an odd prime. As a direct corollary, our algorithm enables efficient estimation of the magic of a quantum state, as quantified by its stabilizer fidelity. Completing the picture, we also present a streamlined algorithm for the high-fidelity regime $\tau > \cos^2(\pi/8)$, establishing a qudit analogue of the threshold-based approach in prior qubit work.
Causal discovery, the process of recovering underlying causal structures from observational data, is a fundamental pursuit across scientific disciplines. Over the past decades, numerous algorithms have been developed to tackle this challenge through workflows tailored to the specific causal mechanisms underlying each type of dataset, demonstrating effectiveness across a wide range of applications. However, as the volume and heterogeneity of real-world data continue to grow, this dataset-specific approach inevitably leads to a fragmented, test-driven paradigm that struggles to scale to the demands of modern scientific discovery. To address this, we formulate the Causal Discovery Foundation Model (CDFM) as a unified, general-purpose framework for zero-shot structural inference. To ensure reliable generalization across unknown domains, we first investigate the theoretical boundaries of causal identifiability, revealing the indispensable role of causal prior mechanisms in this process. Building on these insights, we formulate a principled variational framework that treats unknown causal mechanisms as latent variables and mathematically decomposes the intractable marginal likelihood into distinct, tractable learning modules. The variational decomposition provides a conceptual design principle for the architecture design of CDFM, while comprehensive causal knowledge guides the large-scale synthesis of our pretraining data. By pretraining on a massive, highly diverse space of synthetic structural causal models, CDFM successfully internalizes complex statistical asymmetries. Extensive experiments demonstrate that CDFM consistently outperforms traditional algorithms, driving a paradigm shift toward a general-purpose causal discovery foundation model.
Event Causality Identification (ECI) requires models to determine whether a given pair of events in a context exhibits a causal relationship. While Large Language Models (LLMs) have demonstrated strong performance across various NLP tasks, their effectiveness in ECI remains limited due to biases in causal reasoning, often leading to overprediction of causal relationships (causal hallucination). To mitigate these issues and enhance LLM performance in ECI, we propose SERE, a structural example retrieval framework that leverages LLMs' few-shot learning capabilities. SERE introduces an innovative retrieval mechanism based on three structural concepts: (i) Conceptual Path Metric, which measures the conceptual relationship between events using edit distance in ConceptNet; (ii) Syntactic Metric, which quantifies structural similarity through tree edit distance on syntactic trees; and (iii) Causal Pattern Filtering, which filters examples based on predefined causal structures using LLMs. By integrating these structural retrieval strategies, SERE selects more relevant examples to guide LLMs in causal reasoning, mitigating bias and improving accuracy in ECI tasks. Extensive experiments on multiple ECI datasets validate the effectiveness of SERE. The source code is publicly available at https://github.com/DMIRLAB-Group/SERE.
Zero-shot Named Entity Recognition (ZS-NER) remains brittle under domain and schema shifts, where unseen label definitions often misalign with a large language model's (LLM's) intrinsic semantic organization. As a result, directly mapping entity mentions to fine-grained target labels can induce systematic semantic drift, especially when target schemas are novel or semantically overlapping. We propose \textbf{SAM-NER}, a three-stage framework based on \emph{Semantic Archetype Mediation} that stabilizes cross-domain transfer through an intermediate, domain-invariant archetype space. SAM-NER: (i) performs \emph{Entity Discovery} via cooperative extraction and consensus-based denoising to obtain high-coverage, high-fidelity entity spans; (ii) conducts \emph{Abstract Mediation} by projecting entities into a compact set of universal semantic archetypes distilled from high-level ontological abstractions; and (iii) applies \emph{Semantic Calibration} to resolve archetype-level predictions into target-domain types through constrained, definition-aligned inference with a frozen LLM. Experiments on the CrossNER benchmark show that SAM-NER consistently outperforms strong prior ZS-NER baselines in cross-domain settings. Our implementation will be open-sourced at https://github.com/DMIRLAB-Group/SAM-NER.
Recent advances in Large Reasoning Models (LRMs) trained with Long Chain-of-Thought have demonstrated remarkable capabilities in code generation and mathematical reasoning. However, their potential in multi-turn Text-to-SQL tasks remains largely underexplored. Existing approaches typically rely on unstable API-based inference or require expensive fine-tuning on small-scale models. In this work, we present Rose-SQL, a training-free framework that leverages small-scale LRMs through in-context learning to enable accurate context-dependent parsing. We introduce the Role-State, a fine-grained representation that bridges the structural gap between schema linking and SQL generation by serving as a structural blueprint. To handle conversational dependencies, Rose-SQL traces the evolution of Role-State through historical context via structural isomorphism checks, guiding the model to infer the possible SQL composition for the current question through verified interaction trajectories. Experiments on the SParC and CoSQL benchmarks show that, within the Qwen3 series, Rose-SQL outperforms in-context learning baselines at the 4B scale and substantially surpasses state-of-the-art fine-tuned models at the 8B and 14B scales, while showing consistent gains on additional reasoning backbones.
Aspect Sentiment Quad Prediction (ASQP) has seen significant advancements, largely driven by the powerful semantic understanding and generative capabilities of large language models (LLMs). However, while syntactic structure information has been proven effective in previous extractive paradigms, it remains underutilized in the generative paradigm of LLMs due to their limited reasoning capabilities. In this paper, we propose S^2IT, a novel Stepwise Syntax Integration Tuning framework that progressively integrates syntactic structure knowledge into LLMs through a multi-step tuning process. The training process is divided into three steps. S^2IT decomposes the quadruple generation task into two stages: 1) Global Syntax-guided Extraction and 2) Local Syntax-guided Classification, integrating both global and local syntactic structure information. Finally, Fine-grained Structural Tuning enhances the model's understanding of syntactic structures through the prediction of element links and node classification. Experiments demonstrate that S^2IT significantly improves state-of-the-art performance across multiple datasets. Our implementation will be open-sourced at https://github.com/DMIRLAB-Group/S2IT.
Generative language models have shown significant potential in single-turn Text-to-SQL. However, their performance does not extend equivalently to multi-turn Text-to-SQL. This is primarily due to generative language models' inadequacy in handling the complexities of context information and dynamic schema linking in multi-turn interactions. In this paper, we propose a framework named Track-SQL, which enhances generative language models with dual-extractive modules designed to track schema and contextual changes in multi-turn Text-to-SQL. Specifically, Track-SQL incorporates a \emph{Semantic-enhanced Schema Extractor} and a \emph{Schema-aware Context Extractor}. Experimental results demonstrate that Track-SQL achieves state-of-the-art performance on the SparC and CoSQL datasets. Furthermore, detailed ablation studies reveal that Track-SQL significantly improves execution accuracy in multi-turn interactions by 7.1\% and 9.55\% on these datasets, respectively. Our implementation will be open-sourced at https://github.com/DMIRLAB-Group/Track-SQL.
Humans perceive actions through key transitions that structure actions across multiple abstraction levels, whereas machines, relying on visual features, tend to over-segment. This highlights the difficulty of enabling hierarchical reasoning in video understanding. Interestingly, we observe that lower-level visual and high-level action latent variables evolve at different rates, with low-level visual variables changing rapidly, while high-level action variables evolve more slowly, making them easier to identify. Building on this insight, we propose the Hierarchical Action Learning (\textbf{HAL}) model for weakly-supervised action segmentation. Our approach introduces a hierarchical causal data generation process, where high-level latent action governs the dynamics of low-level visual features. To model these varying timescales effectively, we introduce deterministic processes to align these latent variables over time. The \textbf{HAL} model employs a hierarchical pyramid transformer to capture both visual features and latent variables, and a sparse transition constraint is applied to enforce the slower dynamics of high-level action variables. This mechanism enhances the identification of these latent variables over time. Under mild assumptions, we prove that these latent action variables are strictly identifiable. Experimental results on several benchmarks show that the \textbf{HAL} model significantly outperforms existing methods for weakly-supervised action segmentation, confirming its practical effectiveness in real-world applications.
Most interpretability work focuses on layer- or neuron-level mechanisms in Transformers, leaving expert-level behavior in MoE LLMs underexplored. Motivated by functional specialization in the human brain, we analyze expert activation by distinguishing domain and driver experts. In this work, we study expert activation in MoE models across three public domains and address two key questions: (1) which experts are activated, and whether certain expert types exhibit consistent activation patterns; and (2) how tokens are associated with and trigger the activation of specific experts. To answer these questions, we introduce entropy-based and causal-effect metrics to assess whether an expert is strongly favored for a particular domain, and how strongly expert activation contributes causally to the model's output, thus identify domain and driver experts, respectively. Furthermore, we explore how individual tokens are associated with the activation of specific experts. Our analysis reveals that (1) Among the activated experts, some show clear domain preferences, while others exert strong causal influence on model performance, underscoring their decisive roles. (2) tokens occurring earlier in a sentence are more likely to trigger the driver experts, and (3) adjusting the weights of domain and driver experts leads to significant performance gains across all three models and domains. These findings shed light on the internal mechanisms of MoE models and enhance their interpretability.
Large Reasoning Models (LRMs) often suffer from overthinking, generating unnecessarily long reasoning chains even for simple tasks. This leads to substantial computational overhead with limited performance gain, primarily due to redundant verification and repetitive generation. While prior work typically constrains output length or optimizes correctness, such coarse supervision fails to guide models toward concise yet accurate inference. In this paper, we propose ENTRA, an entropy-based training framework that suppresses redundant reasoning while preserving performance. ENTRA first estimates the token-level importance using a lightweight Bidirectional Importance Estimation (BIE) method, which accounts for both prediction confidence and forward influence. It then computes a redundancy reward based on the entropy of low-importance tokens, normalized by its theoretical upper bound, and optimizes this reward via reinforcement learning. Experiments on mathematical reasoning benchmarks demonstrate that ENTRA reduces output length by 37% to 53% with no loss-and in some cases, gains-in accuracy. Our approach offers a principled and efficient solution to reduce overthinking in LRMs, and provides a generalizable path toward redundancy-aware reasoning optimization.
Recent advances in Vision-Language Models (VLMs) have improved performance in multi-modal learning, raising the question of whether these models truly understand the content they process. Crucially, can VLMs detect when a reasoning process is wrong and identify its error type? To answer this, we present MMErroR, a multi-modal benchmark of 1997 samples, each embedding a single coherent reasoning error. These samples span 24 subdomains across six top-level domains, ensuring broad coverage and taxonomic richness. Unlike existing benchmarks that focus on answer correctness, MMErroR targets a process-level, error-centric evaluation that requires models to detect incorrect reasoning and classify the error type within both visual and linguistic contexts. We evaluate 12 representative VLMs, and even the best model, Gemini-3-Pro-Preview, classifies the error correctly in only 66.65\% of cases, underscoring the challenge of identifying erroneous reasoning. Furthermore, the ability to accurately identify errors offers valuable insights into the capabilities of multi-modal models. Project Page: https://mmerror-benchmark.github.io
Indonesian, spoken by over 200 million people, remains underserved in multimodal emotion recognition research despite its dominant presence on Southeast Asian social media platforms. We introduce IndoMER, the first multimodal emotion recognition benchmark for Indonesian, comprising 1,944 video segments from 203 speakers with temporally aligned text, audio, and visual annotations across seven emotion categories. The dataset exhibits realistic challenges including cross-modal inconsistency and long-tailed class distributions shaped by Indonesian cultural communication norms. To address these challenges, we propose OmniMER, a multimodal adaptation framework built upon Qwen2.5-Omni that enhances emotion recognition through three auxiliary modality-specific perception tasks: emotion keyword extraction for text, facial expression analysis for video, and prosody analysis for audio. These auxiliary tasks help the model identify emotion-relevant cues in each modality before fusion, reducing reliance on spurious correlations in low-resource settings. Experiments on IndoMER show that OmniMER achieves 0.582 Macro-F1 on sentiment classification and 0.454 on emotion recognition, outperforming the base model by 7.6 and 22.1 absolute points respectively. Cross-lingual evaluation on the Chinese CH-SIMS dataset further demonstrates the generalizability of the proposed framework. The dataset and code are publicly available. https://github.com/yanxm01/INDOMER
Recent divide-and-conquer reasoning approaches, particularly those based on Chain-of-Thought (CoT), have substantially improved the Text-to-SQL capabilities of Large Language Models (LLMs). However, when applied to complex enterprise databases, such methods struggle to maintain coherent reasoning due to limited context capacity, unreliable schema linking, and weak grounding in database semantics. To overcome these issues, we introduce DSR-SQL, a \textbf{D}ual-\textbf{S}tate \textbf{R}easoning framework that models Text-to-SQL as an interaction between an adaptive context state and a progressive generation state. The first constructs a compact, semantically faithful environment by refining large schemas and selecting relevant structures, while the second formalizes SQL synthesis as feedback-guided state transitions, enabling the model to self-correct and align with user intent. Without any post-training or in-context examples, DSR-SQL achieves competitive performance, reaching 35.28\% execution accuracy on Spider 2.0-Snow and 68.32\% on BIRD development set. Our implementation will be open-sourced at: https://github.com/DMIRLAB-Group/DSR-SQL.