arXiv subjects

Peng Cui

Publications and source records attributed to Peng Cui.

At least 19 recordsLinked to original sources

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

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

Invariant learning seeks representations that remain predictive across environments, yet the behavior of its objectives along the regularization path is often opaque. We address this objective-behavior gap by viewing representation learning as multimode magnetization and deriving, from concrete invariant-learning objectives, a Landau-type effective free energy whose low-order coefficients form objective signatures and induce distinct regularization phenotypes. Effective quadratic corrections move the phase boundary and enable finite-strength mode elimination; quartic corrections regulate post-onset amplitude and typically leave residual loading at finite strength; higher-order structure governs non-monotone tails, instability, and collapse at large regularization. In a canonical bilinear model, the theory yields closed-form phase boundaries and steady-state loadings, as well as distinct critical strengths for shortcut and stable modes that define a selective-retention window. Controlled experiments confirm the predicted phase boundaries, loadings, and regularization phenotypes. In one- and two-hidden-layer ReLU networks, the same signatures remain predictive of qualitative regularization-path behavior despite depth-dependent shifts in scale. A matrix extension generalizes the framework to coupled collective modes and yields a spectral phase-boundary criterion. Together, the framework turns low-order objective signatures into predictions of regularization phenotypes and, ultimately, of what models learn as regularization varies.

cs.LG↗

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.

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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.

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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

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.

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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

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%.

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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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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.

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arXiv2026

Bayesian Gated Non-Negative Contrastive Learning

While Contrastive Learning (CL) has revolutionized self-supervised representation learning, its latent representations remain highly entangled and opaque, limiting their interpretability in safety-critical applications. We identify that a fundamental cause of this entanglement is the reliance on deterministic similarity measures, which treat all feature dimensions equally. In compositional scenes, this creates an Optimization Conflict: common background features, such as, "blue sky", are encouraged to align in positive pairs but simultaneously repelled in negative pairs, causing gradient oscillations that hinder precise semantic disentanglement. To address this, we propose BayesNCL (Bayesian Gated Non-Negative Contrastive Learning). Unlike standard approaches, BayesNCL introduces a probabilistic gating mechanism that dynamically filters out task-irrelevant, high-frequency common features while selectively retaining discriminative semantics. By formalizing feature selection as a variational inference problem with a sparse Bernoulli prior, our method effectively resolves the optimization conflict. Empirical experimental results on Imagenet-100 demonstrate that BayesNCL achieves a remarkable 142.1% improvement in semantic consistency compared to state-of-the-art baselines, yielding highly interpretable representations without compromising downstream task performance. Code is available at https://github.com/Cui-Peng-624/BayesNCL.

cs.CV↗

arXiv2026

SARAD: LLM-Based Safety-Aware Hybrid Reinforcement Learning with Collision Prediction for Autonomous Driving

Ensuring both safety and efficiency in decision-making for autonomous driving systems remains a fundamental challenge. Traditional Deep Reinforcement Learning (DRL) suffers from unsafe random exploration and slow convergence, while Large Language Models (LLMs) demonstrate inherent latency in real-time inference operations. To address these limitations, this paper proposes SARAD, a novel safety-aware hybrid framework that synergizes LLMs and DRL for autonomous driving. SARAD substitutes the random exploration of DRL with Retrieval-Augmented Generation (RAG)-enhanced, LLM-guided decisions sourced from a dynamic expert knowledge repository. An attention discriminator is proposed to integrate the prior knowledge of LLMs into DRL policy optimization. A collision predictor module, fine-tuned with historical collision data, is further designed to improve vehicle safety. Extensive experiments show that SARAD achieves significant performance improvements in the Highway-Env simulator, validating the effectiveness of the proposed model in autonomous driving.

cs.RO↗

arXiv2026

Ranking-Aware Calibration for Reliable Multimodal Reinforcement Learning

Reinforcement learning post-training has substantially improved the reasoning accuracy of vision-language models, yet the resulting policies remain poorly calibrated. Terminal correctness rewards provide no gradient that penalizes confident errors more than uncertain ones and no signal that ties confidence to the quality of visual evidence, a gap that becomes especially severe under corrupted or ambiguous inputs where models continue to report high confidence on incorrect answers. We introduce Ranking-Aware Calibration (RAC), a training-time framework that supervises confidence using two comparison signals that group-based RL already produces at no additional labeling cost. The ranking-aware group loss enforces that a better rollout receives higher confidence than a worse one within the same prompt. The clean--corrupted pairwise loss enforces that confidence attenuates as visual evidence degrades. Because the ranking signal forces the policy to distinguish between correct and incorrect reasoning paths, it also reinforces task accuracy beyond what correctness rewards alone produce. Both losses require no external confidence annotations and integrate naturally with group-based RL post-training. We instantiate RAC on Qwen2.5-VL and InternVL-3.5 backbones and evaluate on six multimodal reasoning benchmarks under clean and corrupted inputs. Empirical results show that the ranking-aware loss substantially improves task accuracy by teaching the policy to discriminate between better and worse reasoning, while the pairwise corruption loss reduces calibration error under degraded inputs. Their combination achieves the best calibration across all tested backbones while improving accuracy in the majority of settings.

cs.LG↗

arXiv2026

Learning-Zone Energy: Online Data Selection for Efficient RL Post-Training

Reinforcement Learning (RL) post-training has emerged as the dominant paradigm for eliciting mathematical reasoning in Large Language Models (LLMs), yet prevailing techniques such as GRPO and DAPO distribute rollout and gradient budgets nearly uniformly across prompts, squandering compute on samples that are already mastered or remain far beyond the model's current capability. To address this fundamental inefficiency, we propose Learning-Zone Energy (LZE), a theoretically grounded, fully online data selection framework that concentrates computation on the model's active learning frontier. At its core, we define a closed-form Learning-Zone Energy Score that fuses three complementary signals, an initial-difficulty anchor, a normalized outcome-uncertainty term, and a pass-rate momentum, into a single scalar that is provably aligned with the expected magnitude of group-relative policy gradient updates. A forward pruner with replay further reduces wall-clock time cost by skipping rollout generation for persistently solved prompts while periodically checking for forgetting. Evaluated on Qwen-family models (1.5B-8B) across GSM8K, MATH and DAPO-MATH, our method retains only 40% of the training data per step yet matches or surpasses full-data baselines, with especially pronounced out-of-distribution gains on AIME25 (+45.9%) and AMC23 (+18.2%), alongside an estimated 36% reduction in training FLOPs. Our code is available at https://github.com/Stellaris167/LZE.

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arXiv2026

A Knowledge-Informed Pretrained Model for Causal Discovery

Causal discovery has been widely studied, yet many existing methods rely on strong assumptions or fall into two extremes: either depending on costly interventional signals or partial ground truth as strong priors, or adopting purely data driven paradigms with limited guidance, which hinders practical deployment. Motivated by real-world scenarios where only coarse domain knowledge is available, we propose a knowledge-informed pretrained model for causal discovery that integrates weak prior knowledge as a principled middle ground. Our model adopts a dual source encoder-decoder architecture to process observational data in a knowledge-informed way. We design a diverse pretraining dataset and a curriculum learning strategy that smoothly adapts the model to varying prior strengths across mechanisms, graph densities, and variable scales. Extensive experiments on in-distribution, out-of distribution, and real-world datasets demonstrate consistent improvements over existing baselines, with strong robustness and practical applicability.

cs.LG↗

arXiv2026

Guideline-Grounded Evidence Accumulation for High-Stakes Agent Verification

As LLM-powered agents have been used for high-stakes decision-making, such as clinical diagnosis, it becomes critical to develop reliable verification of their decisions to facilitate trustworthy deployment. Yet, existing verifiers usually underperform owing to a lack of domain knowledge and limited calibration. To address this, we establish GLEAN, an agent verification framework with Guideline-grounded Evidence Accumulation that compiles expert-curated protocols into trajectory-informed, well-calibrated correctness signals. GLEAN evaluates the step-wise alignment with domain guidelines and aggregates multi-guideline ratings into surrogate features, which are accumulated along the trajectory and calibrated into correctness probabilities using Bayesian logistic regression. Moreover, the estimated uncertainty triggers active verification, which selectively collects additional evidence for uncertain cases via expanding guideline coverage and performing differential checks. We empirically validate GLEAN with agentic clinical diagnosis across three diseases from the MIMIC-IV dataset, surpassing the best baseline by 12% in AUROC and 50% in Brier score reduction, which confirms the effectiveness in both discrimination and calibration. In addition, the expert study with clinicians recognizes GLEAN's utility in practice.

cs.AI↗

arXiv2026

TFMLinker: Universal Link Predictor by Graph In-Context Learning with Tabular Foundation Models

Link prediction is a fundamental task in graph machine learning with widespread applications such as recommendation systems, drug discovery, knowledge graphs, etc. In the foundation model era, how to develop universal link prediction methods across datasets and domains becomes a key problem, with some initial attempts adopting Graph Foundation Models utilizing Graph Neural Networks and Large Language Models. However, the existing methods face notable limitations, including limited pre-training scale or heavy reliance on textual information. Motivated by the success of tabular foundation models (TFMs) in achieving universal prediction across diverse tabular datasets, we explore an alternative approach by TFMs, which are pre-trained on diverse synthetic datasets sampled from structural causal models and support strong in-context learning independent of textual attributes. Nevertheless, adapting TFMs for link prediction faces severe technical challenges such as how to obtain the necessary context and capture link-centric topological information. To solve these challenges, we propose TFMLinker (Tabular Foundation Model for Link Predictor), aiming to leverage the in-context learning capabilities of TFMs to perform link prediction across diverse graphs without requiring dataset-specific fine-tuning. Specifically, we first develop a prototype-augmented local-global context module to construct context that captures both graph-specific and cross-graph transferable patterns. Next, we design a universal topology-aware link encoder to capture link-centric topological information and generate link representations as inputs for the TFM. Finally, we employ the TFM to predict link existence through in-context learning. Experiments on 6 graph benchmarks across diverse domains demonstrate the superiority of our method over state-of-the-art baselines without requiring dataset-specific finetuning.

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arXiv2025

Generating Risky Samples with Conformity Constraints via Diffusion Models

Although neural networks achieve promising performance in many tasks, they may still fail when encountering some examples and bring about risks to applications. To discover risky samples, previous literature attempts to search for patterns of risky samples within existing datasets or inject perturbation into them. Yet in this way the diversity of risky samples is limited by the coverage of existing datasets. To overcome this limitation, recent works adopt diffusion models to produce new risky samples beyond the coverage of existing datasets. However, these methods struggle in the conformity between generated samples and expected categories, which could introduce label noise and severely limit their effectiveness in applications. To address this issue, we propose RiskyDiff that incorporates the embeddings of both texts and images as implicit constraints of category conformity. We also design a conformity score to further explicitly strengthen the category conformity, as well as introduce the mechanisms of embedding screening and risky gradient guidance to boost the risk of generated samples. Extensive experiments reveal that RiskyDiff greatly outperforms existing methods in terms of the degree of risk, generation quality, and conformity with conditioned categories. We also empirically show the generalization ability of the models can be enhanced by augmenting training data with generated samples of high conformity.

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