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Peng Cui

Publications and source records attributed to Peng Cui.

At least 19 recordsLinked to original sources
arXiv2026

Learning a Prior-Data Fitted Network for Graph Foundation Models via Structural Causal Model Priors

Graph Foundation Models (GFMs) have recently emerged as a promising paradigm for learning transferable representations across different graphs and domains. However, existing GFMs face notable limitations, including limited pre-training scale or reliance on aligning with textual information in Large Language Models (LLMs). To overcome these limitations, recent studies have drawn inspiration from prior-data fitted networks (PFNs), which learn from large synthetic datasets and support multi-domain prediction backed by causal learning. However, existing graph PFNs encounter severe difficulties in modeling causal relationships within and across node and edge sets, generating diverse graph structures, and designing suitable architectures that can learn from complex synthetic datasets. To address these challenges, we propose **GSCM-PFN** (Graph SCM-based Prior-Data Fitted Network), a graph PFN pre-trained on synthetic data generated from an SCM-based prior that jointly models nodes and graph topology. Specifically, we (1) design a joint feature-edge-label structural causal model (SCM) to guide synthetic graph generation and capture causal relationships within and across node and edge sets; (2) introduce prior-guided node-edge dependency modeling to instantiate diverse graph generation strategies, and prove that our SCM-based generation prior is more expressive than existing priors; and (3) propose a feature-permutation-invariant dual-path graph network with theoretical guarantees for learning from diverse synthetic graphs. Experiments on 23 real-world benchmarks show that GSCM-PFN outperforms both conventional GFMs and PFN-based GFMs, without utilizing real-world graph data for pre-training. Code: https://anonymous.4open.science/r/GSCM-PFN-A3A3/

cs.LG↗
arXiv2026

PPA-Game: Characterizing and Learning Competitive Dynamics Among Online Content Creators

In this paper, we present the Proportional Payoff Allocation Game (PPA-Game), which characterizes situations where agents compete for divisible resources. In the PPA-game, agents select from available resources, and their payoffs are proportionately determined based on heterogeneous weights attributed to them. Such dynamics simulate content creators on online recommender systems like YouTube and TikTok, who compete for finite consumer attention, with content exposure reliant on inherent and distinct quality. We first conduct a game-theoretical analysis of the PPA-Game. While the PPA-Game does not always guarantee the existence of a pure Nash equilibrium (PNE), we identify prevalent scenarios ensuring its existence. Simulated experiments further prove that the cases where PNE does not exist rarely happen. Beyond analyzing static payoffs, we further discuss the agents' online learning about resource payoffs by integrating a multi-player multi-armed bandit framework. We propose an online algorithm facilitating each agent's maximization of cumulative payoffs over $T$ rounds. Theoretically, we establish that the regret of any agent is bounded by $O(\log^{1 + η} T)$ for any $η> 0$. Empirical results further validate the effectiveness of our online learning approach.

cs.GT↗
arXiv2026

SkillEval: Learning Interpretable Ability Profiles of LLMs via Cognitive Diagnosis Models

Current evaluation of LLMs on benchmarks typically aggregates performance over individual examples into a single scalar score. This approach is overly coarse and ignores the diverse scope of skills covered by benchmark datasets. To address this limitation and better exploit benchmark data, we propose SkillEval, a new evaluation framework that performs cross-model, skill-level analysis. The framework integrates advances from two areas: (1) it leverages the meta-cognitive capabilities of LLMs to automatically discover interpretable skills from questions, and (2) it applies cognitive diagnosis models (CDMs) from psychometrics to estimate per-skill abilities of LLMs. We conduct experiments on 3,811 LLMs evaluated on 9,523 items across five benchmarks spanning diverse domains (MATH, BBH, GPQA, MuSR, IFEval). Compared to the traditional average-based evaluation paradigm, SkillEval produces reliable, more calibrated and informative yet concise model profiles that more accurately predict model behavior on unseen items. We also demonstrate the utility of SkillEval in two downstream tasks: (1) LLM routing, which dynamically assigns each query to a capable but efficient model, reducing inference cost by over 60% while achieving improved performance, and (2) Computerized Adaptive Testing (CAT), where an unseen model can be efficiently evaluated using a trained CDM. Furthermore, we show that these skill profiles provide useful insights, for example, how benchmarks share skills and how instruction-tuned models differ from their base models.

cs.CL↗
arXiv2026

What Makes Something Hard(er)? Explaining Question Difficulty in Natural Language

Difficulty is one of the most fundamental properties of a question: it determines whether the question can meaningfully discriminate between models of differing ability. Although a variety of methods can now estimate or predict difficulty automatically, they yield only a single descriptive number, with no account of the underlying factors that make a question difficult in the first place. In this work, we propose a data-driven approach that automatically generates and validates natural-language hypotheses explaining what makes one question harder than another. We first estimate each item's difficulty from the responses of a large pool of LLMs using Item Response Theory. We then sample contrasting sets of easy and hard questions and prompt an LLM to propose candidate explanations of the difference, which are subsequently validated and selected on held-out questions. Experimental results across three datasets spanning mathematical, logical, and commonsense reasoning show that our method produces interpretable and predictive hypotheses. On their own, they predict the difficulty of unseen questions competitively with, or better than, advanced black-box difficulty regressors; used as additional features, they further improve those regressors, implying that they discover difficulty signals that existing models fail to capture. Moreover, we demonstrate that editing questions according to a hypothesis can shift their measured difficulty in the expected direction, indicating that the discovered hypotheses are causally valid difficulty factors rather than post-hoc descriptions. Our approach thus turns a purely descriptive difficulty score into actionable statements.

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arXiv2026

RareDx: Controlled Knowledge Integration and Graph-Grounded Policy Optimization for Rare-Disease Diagnosis

Rare-disease diagnosis is a long-tail reasoning problem: phenotypes are incomplete, individual disorders are sparsely documented, and relevant evidence is distributed across ontologies, gene annotations, and biomedical text. Language models consequently favor common conditions, miss rare candidates, or produce plausible but invalid names. We introduce RareDx, which couples controlled evidence use with knowledge-graph-grounded policy optimization. RareDx-Harness normalizes heterogeneous records into one ranked-diagnosis task and compares direct inference, static retrieval, adaptive tools, and structured phenotype-gene-disease reasoning over a shared knowledge layer. The training pipeline combines Top-10 post-training with RareDx-KGPO, our knowledge-graph-grounded policy optimization method. Its reward projects predictions into a canonical disease graph and integrates curated graded relevance, ontology proximity, biomedical similarity, and phenotype consistency. Vocabulary and output-budget constraints prevent dense partial credit from rewarding fabricated or overlong differentials. Across eight benchmarks, the complete RareDx system centered on Qwen3.5-9B reaches 38.34 macro Hit@10, 1.60 points above GPT-5.5 under the archived protocol; a disjoint validation-selection audit retains a 6.80-point routing gain over Direct on held-out cases. The 27B system reaches 23.53/36.56/40.76 at Hit@1/5/10. Controlled ablations show that retrieval is not uniformly helpful and that controlled routing is central to the gain. These results indicate that structured medical knowledge can turn a compact model into a competitive diagnostic ranker across heterogeneous long-tail settings in clinical practice.

cs.AI↗
arXiv2026

From Objectives to What Models Learn: A Landau Theory of Invariant Learning

Invariant-learning objectives pursue similar goals yet produce qualitatively different regularization paths, leaving unclear when shortcuts can be suppressed without damaging stable modes. Our starting point is simple: in the desired shortcut-suppressed regime, shortcut loading is small, so the objective's low-order expansion governs local stability and residual amplitude. This brings the problem into the domain of Landau phase-transition theory. We establish a mathematical isomorphism between the near-critical normal form of predictive-mode learning and Landau theory, identifying the learning objective as an effective free energy and critical-mode amplitude as an order parameter. The resulting low-order objective signatures predict distinct regularization phenotypes: quadratic $R_2$ terms shift phase boundaries and enable finite-strength elimination, whereas quartic $R_4$ terms continuously attenuate acquired modes while leaving nonzero residual loading at finite strengths. Higher-order terms may further shape nonlinear tails. In a canonical bilinear model, we derive exact phase boundaries and equilibrium loadings, identifying conditions for a selective-retention window in which shortcut suppression preserves stable structure. Controlled bilinear and ReLU experiments, including an MNIST construction, support the predicted signature-phenotype relation, while coupled-feature experiments validate its extension to collective modes. The framework connects the mathematical structure of invariant-learning objectives to what models learn as regularization varies.

cs.LG↗
arXiv2026

CAFE: Counterfactual Prediction via Fast Posterior Estimation

Counterfactual prediction estimates an individual's outcome under an alternative intervention given their factual observations. Such outcomes are generally not identifiable from observational data without additional assumptions. Even within the class of fully observed additive noise models (ANMs), different causal graphs can generate the same observational distribution yet imply different individual counterfactual outcomes. Predictions based on a single estimated graph ignore this structural uncertainty. We therefore target a Bayesian counterfactual posterior predictive distribution that combines predictions from plausible SCMs. We introduce CAFE (\textbf{C}ounterf\textbf{A}ctual Prediction via \textbf{F}ast Posterior \textbf{E}stimation), an amortized inference framework that directly approximates the Bayesian counterfactual posterior predictive distribution. We pretrain a transformer-based model on synthetic counterfactual tasks generated from a diverse prior over ANMs. Given an observational dataset, an individual's factual observations, and an intervention, CAFE approximates the corresponding posterior predictive distribution in a single forward pass. Experiments show that CAFE accurately predicts individual counterfactual outcomes in identifiable settings and approximates the posterior predictive distribution when structural uncertainty induced by observationally indistinguishable causal graphs exists. Strong performance in realistic manufacturing and viticulture settings further demonstrates its empirical robustness beyond the assumptions of the training prior.

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arXiv2026

LimiX-2: A Contextual Mechanism Network Towards General Structured-Data Intelligence

We introduce LimiX-2, a new model in the LimiX family, developed through model and data scaling guided by our previously established scaling laws. LimiX-2 adopts the Contextual Mechanism Networks (CMNs) paradigm and is pretrained with Context-Conditional Masked Modeling (CCMM). CMNs shifts the organizing principle of in-context learning from target-centric prediction to mechanism-oriented joint modeling. Rather than centering the network on the $p(y \mid x, D_{\mathrm{context}})$ objective of conventional tabular PFNs, it is designed around learning $p(x, y \mid D_{\mathrm{context}})$, a context-dependent representation of the joint structure underlying data generation. Pretraining uses synthetic datasets generated by structural causal models (SCMs) spanning diverse graph structures, functional mechanisms, and observation processes. Evaluations on TabArena, TALENT, and BCCO show that LimiX-2 outperforms current dataset-specific models and tabular foundation models. Beyond predictive performance, the CMN paradigm also promotes causal awareness in LimiX-2: its feature attention encodes direct causal relationships, enabling accurate causal skeleton recovery.

cs.AI↗
arXiv2026

Do LLMs Exhibit Coherent Knowledge Structures in Mathematical Reasoning? A Perspective from Knowledge Space Theory

Human knowledge is inherently structured and interdependent: mastery of a concept requires prior mastery of its prerequisites, a principle formalized by Knowledge Space Theory (KST). While LLMs achieve strong performance on complex reasoning tasks, it remains unclear whether they exhibit coherent, human-like knowledge structure. We introduce a KST-grounded framework for evaluating LLM knowledge structure in mathematical reasoning, using it as a normative framework to analyze whether LLM behavior adheres to principled knowledge dependencies. Evaluating eight open- and closed-source LLMs against real human learners, we find that (1) LLMs do not adhere to human knowledge structure -- they frequently violate knowledge dependencies and fail to leverage related knowledge provided in context to improve performance on dependent questions; (2) LLMs do not share a consistent knowledge structure among themselves, as reflected by low overlap in their knowledge distributions. Furthermore, these structural deficiencies remain largely invisible to accuracy-based and LLM-as-judge evaluations. Together, our results provide behavioral evidence that current LLMs knowledge does not follow a human-like structure.

cs.AI↗
arXiv2026

Grounding Large Language Models as Generalizable Policies in Network Control

Designing generalizable control policies that operate reliably under changing conditions is essential for robust network services in modern digital infrastructure. Yet network control remains dominated by specialized policies built from handcrafted rules or deep learning models, which struggle to generalize under real-world dynamics. Large language models (LLMs) offer a promising alternative because of their broad pretrained knowledge and emergent generalization abilities, but their practical adoption in network control is hindered by non-textual observations, constrained action spaces, complex optimization knowledge, and strict real-time requirements. Therefore, we introduce Trailblazer, a systematic framework that combines domain alignment to adapt LLMs for network control with adaptive policy collaboration to reduce inference overhead. Simulations across two heterogeneous network control tasks, adaptive bitrate streaming and cluster job scheduling, show that Trailblazer improves performance over conventional policies by 6.5%-36.6% and 3.5%-41.3%, respectively. Moreover, in a large-scale online A/B test of congestion control on Douyin, Trailblazer outperforms a highly optimized industrial policy, corresponding to a projected reduction of approximately 3,145 hours of platform-wide video stall time per day. Further analysis reveals that effective LLM-based control can be achieved by properly aligning compact LLMs and only invoking them for complex conditions, rather than model scaling or extensive invocation. Together, our results establish an LLM-driven paradigm for designing generalizable network policies and offer practical insights into grounding foundation models for real-world network control.

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arXiv2026

SkillTFM: Gated Skill Evolution for Training-Free Adaptation of Tabular Foundation Models

Tabular data are ubiquitous in real-world applications and are crucial for data-driven prediction and decision-making across science, industry, finance, healthcare, and public services. Tabular foundation models (TFMs) have emerged as a promising paradigm for general-purpose tabular learning, offering reusable predictors across diverse datasets and substantially reducing the need for task-specific training, tuning, and model development. However, their practical deployment remains constrained by distribution shifts, heterogeneous feature semantics, and task-specific patterns that are difficult to capture without costly fine-tuning or additional labeled data. To this end, we propose SkillTFM, a training-free system that shifts TFM adaptation from parameter updates to the gated evolution of agentic skills. The core of SkillTFM is a verifiable and extensible skill bank that couples boundary evidence identification with gated skill evolution: the former characterizes task structure and base-model failure patterns, whereas the latter retrieves and extends reusable skills subject to explicit validation. Across simulated boundary settings and real-world electricity-price forecasting, SkillTFM improves AUC by 0.128--0.142, raises nonlinear-boundary AUC from 0.699 to 0.898. Furthermore, experiments across TFM backbones demonstrate the effectiveness and generality of SkillTFM.

cs.LG↗
arXiv2026

DAG-FM: A Foundation Model for Causal Discovery under Heterogeneous Causal Mechanisms

Causal discovery from observational tabular data remains fundamentally challenging, primarily due to the heterogeneity of underlying causal mechanisms and the high-dimensional combinatorial search space of Directed Acyclic Graphs (DAGs). In this paper, we propose \textbf{DAG-FM}, a novel foundation model architecture that amortizes causal discovery. Unlike direct matrix prediction, DAG-FM decomposes the causal discovery process into two auto-regressive stages using two specialized Transformer-based sub-modules: a leaf-node predictor and a parent-node predictor. To effectively model complex row-column interactions, we adopt a robust tabular interaction block to output feature-wise representations. Crucially, to handle diverse and unknown Functional Causal Model (FCM) assumptions in real-world scenarios, we introduce Mixture-of-Leaf-Experts (MoLE), allowing the model to dynamically route and adapt to identifiable mechanism families. Through an iterative inference algorithm, DAG-FM seamlessly extracts causal orderings and constructs valid DAGs. Extensive experiments demonstrate that DAG-FM achieves state-of-the-art performance on both synthetic benchmarks and complex real-world datasets, significantly outperforming traditional classical algorithms and recent foundation models in both accuracy and scalability.

cs.LG↗
arXiv2026

Surprisingly Simple and Effective Multi-Domain Graph Foundation Model through Graph-to-Table Alignment

Graph Foundation Models (GFMs) have emerged as a promising paradigm for learning transferable representations across diverse graph domains. Recent advancements in GFMs have been largely dominated by two paradigms: Graph Neural Network and Large Language Model (LLM) based methods. However, these methods often face a fundamental dilemma between training with limited data and a heavy reliance on textual attributes. Tabular foundation models (TFMs) offer a potential alternative, as node features and representations can be naturally organized in a tabular form. However, how to enable TFMs to effectively capture structural information of graphs remains largely unexplored. The key challenge is to learn a graph-to-table alignment mechanism that enables graph structural understanding for TFMs. To address this, we propose GTAlign, a surprisingly simple yet effective Graph-to-Table Alignment framework for text-free Graph Foundation Model. Specifically, we first pretrain a graph encoder that maps diverse graphs into a unified latent space to capture domain-agnostic graph representations. To further bridge the gap between graph topology and the tabular representation space, we propose community-guided continual pre-training, where pseudo-labels derived from graph community are used to construct few-shot prediction episodes. Lastly, we adapt the graph encoder for an unseen target domain and perform in-context inference. Extensive experiments on five benchmark datasets demonstrate that GTAlign significantly outperforms state-of-the-art baselines on both node and graph classification, offering a simple, effective, and text-free GFM model. Code will be released upon acceptance.

cs.LG↗
arXiv2026

CDFM: Towards a General-Purpose Causal Discovery Foundation Model

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.

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arXiv2026

Towards Precision Therapy in Hepatocellular Carcinoma: A Clinical-Reasoning LLM for Risk Stratification and Treatment Guidance

Hepatocellular carcinoma (HCC) is a common malignancy and a leading cause of cancer-related mortality. Current guidelines and staging systems provide coarse categories, but often miss within-stage heterogeneity and the clinical context in electronic medical records (EMRs). We present HCC-STAR (Hepatocellular Carcinoma Staging, Treatment And pRognosis), a clinically aligned large language model that reads routine EMR narratives and jointly outputs risk score-based staging, ranked guideline-consistent treatments with evidence-based rationales, and individualized survival estimates. We curated about 30,000 HCC cases from SEER and expanded them into EMR-style narrative training data using a clinician-validated, prompt-based augmentation workflow. On this corpus, we developed a knowledge-aligned reasoning framework optimized with a step-verifiable composite reward, moving beyond text-level memorization of clinical guidelines. In a multi-center cohort of 6,668 patients from 12 hospitals in China, HCC-STAR achieved state-of-the-art performance in treatment recommendation and risk stratification compared with clinical guidelines and competitive models, including GPT-5 and Gemini-2.5 Pro. Hypothetical overall-survival analysis showed a median survival of 51 months under adherence to HCC-STAR recommendations, compared with 29 and 32 months under BCLC and CNLC. In clinician-centric evaluations, blinded hepatobiliary specialists rated HCC-STAR's reasoning and evidence-based justifications as trustworthy. The model surpassed resident and attending physicians in treatment accuracy and helped physicians make more accurate decisions faster when used as an assistant. These findings support HCC-STAR as a reliable and verifiable decision-support system for risk stratification and precision therapy in HCC.

cs.AI↗
arXiv2026

Beyond Independent Manipulation: Individual Fairness-aware Strategic Classification with Peer Imitation

Strategic classification (SC) investigates scenarios where agents manipulate their features to obtain favorable decisions from predictive models. Existing fairness-aware SC approaches primarily focus on group fairness and typically assume that agents respond independently. However, when individual fairness is required, ensuring similar individuals receive similar outcomes, agents' manipulation becomes interdependent: an agent's preferred manipulation depends on the neighborhoods' outcomes. This induces a mismatch between classical SC formulations and fairness-aware decision settings, where independent models no longer accurately characterize strategic manipulations. To address this issue, we introduce individual fairness-aware strategic classification (IFSC), a framework that models peer-driven manipulation arising from individual fairness, where agents imitate nearby positively decided peers to obtain favorable outcomes. IFSC characterizes strategic manipulation as similarity-based imitation toward visible accepted peers and learns classifiers under the resulting post-manipulation distributions. To account for uncertainty in peer observability, IFSC employs a robust learning process that introduces stochastic perturbations during manipulation simulation. Experiments on synthetic and real-world datasets demonstrate that IFSC improves individual-fairness consistency and mitigates imitation-induced distortions.

cs.LG↗
arXiv2026

Closed-Form Spectral Regularization for Multi-Task Model Merging

Model merging combines several independently fine-tuned experts into a single multi-task model without any training data, reducing the storage, serving, and decentralized-development costs of large foundation models. State-of-the-art merging methods formulate merging as a layer-wise quadratic interference minimization problem. Although this problem admits an exact closed-form pseudoinverse solution, that solution underperforms hundreds of iterations of gradient descent in practice. The iterative loop dominates the cost of the pipeline, yet its effectiveness has remained unexplained. We revisit this regime and show that the iterative solver does not primarily act as an optimizer; rather, it serves as an implicit spectral regularizer for an ill-posed normal equation, where small-eigenvalue directions of the per-layer interference operator amplify proxy noise. Building on this finding, we formalize multi-task model merging as a noisy linear inverse problem and propose a spectral filtering estimator parameterized by a per-direction filter. We instantiate this estimator with SWUDI, a closed-form method that combines a soft exponential filter, which matches the gradient-flow trajectory of iterative descent, with a hard top-K truncation that suppresses noise-amplifying small-eigenvalue directions. Furthermore, we propose SWUDI-A, an adaptive variant that replaces the global rank hyperparameter with per-layer rank rules, further improving robustness across architectures. Both variants share a single symmetric eigendecomposition per linear layer and require no training data or optimizer state. Across four general benchmarks and a multimodal merging benchmark spanning VQA, Geometry, Chart, OCR, Grounding, and modality merging, our proposed spectral solvers match or outperform state-of-the-art merging methods. Crucially, they reduce wall-clock time by 28-72x and peak GPU memory by up to 50%.

cs.LG↗
arXiv2026

LimiX-2M: Mitigating Low-Rank Collapse and Attention Bottlenecks in Tabular Foundation Models

Tabular foundation models (TFMs) increasingly rival tree ensembles, but their performance is often compute-inefficient: with standard affine scalar tokenization, each feature injects value variation through an essentially one-dimensional channel, and feature IDs/positional signals cannot increase within-feature value degrees of freedom, yielding weak early-layer value sensitivity and redundant hidden states. We present a unified tokenize-and-route framework for strong TFMs: RaBEL expands each scalar into compact localized RBF features (optionally exponent-gated) to improve conditioning and shallow-layer effective rank, while a reordered bidirectional block S->N->F aligns computation with the readout by aggregating cross-sample context before feature mixing and using attention pooling. Together, these changes yield LimiX-2M, a 2M-parameter model that outperforms larger TabPFN-v2 and TabICL baselines on widely used tabular benchmarks while reducing training and inference costs. These results highlight value-aware tokenization and readout-aligned routing as key levers for improving the accuracy--efficiency trade-off in TFMs. Model checkpoints and inference code are available at https://github.com/limix-ldm-ai/LimiX.

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