arXiv subjects

Senrong Xu

Publications and source records attributed to Senrong Xu.

8 recordsLinked to original sources

arXiv2026

Task Abstention for Large Language Models in Code Generation

Large language models (LLMs) have revolutionized automated code generation. One serious concern, however, is the so-called ``hallucination'', i.e., LLMs may generate seemingly plausible but functionally incorrect code. In this paper, we study the task abstention problem, i.e., determining whether a given LLM should abstain from performing a specific code generation task to avoid likely hallucination. Our approach features a calibrated abstention rule, grounded in the principles of multiple hypothesis testing. The rule assesses generation consistency through code execution outcomes, allowing it to handle syntactic diversity of semantically equivalent code without reliance on oracle test cases or external databases. We prove that our approach provides a rigorous, distribution-free theoretical guarantee on its abstention decisions. We evaluate our method on benchmark datasets using several open-source code LLMs. Results show that our method allows generative models to more accurately and efficiently identify and abstain from tasks that induce hallucination compared to existing techniques, providing a reliable mechanism for safer and more robust code generation.

cs.SE↗

arXiv2026

Fair Conformal Classification via Learning Representation-Based Groups

Conformal prediction methods provide statistically rigorous marginal coverage guarantees for machine learning models, but such guarantees fail to account for algorithmic biases, thereby undermining fairness and trust. This paper introduces a fair conformal inference framework for classification tasks. The proposed method constructs prediction sets that guarantee conditional coverage on adaptively identified subgroups, which can be implicitly defined through nonlinear feature combinations. By balancing effectiveness and efficiency in producing compact, informative prediction sets and ensuring adaptive equalized coverage across unfairly treated subgroups, our approach paves a practical pathway toward trustworthy machine learning. Extensive experiments on both synthetic and real-world datasets demonstrate the effectiveness of the framework.

cs.LG↗

arXiv2026

Uncertainty Quantification for LLM-based Code Generation

Prediction sets provide a theoretically grounded framework for quantifying uncertainty in machine learning models. Adapting them to structured generation tasks, in particular, large language model (LLM) based code generation, remains a challenging problem. An existing attempt proposes PAC prediction sets but is limited by its strong monotonicity assumption on risk and single-label classification framework, which severely limits the space of candidate programs and cannot accommodate the multiple valid outputs inherent to code generation. To address these limitations, we propose an approach RisCoSet that leverages multiple hypothesis testing to construct risk-controlling predictions for LLM-based code generation. Given a trained code generation model, we produce a prediction set represented by a partial program, which is guaranteed to contain a correct solution with high confidence. Extensive experiments on three LLMs demonstrate the effectiveness of the proposed method. For instance, compared with the state-of-the-art, our method can significantly reduce the code removal by up to 24.5%, at the same level of risk.

cs.SE↗

arXiv2025

Conformal Correction for Efficiency May be at Odds with Entropy

Conformal prediction (CP) provides a comprehensive framework to produce statistically rigorous uncertainty sets for black-box machine learning models. To further improve the efficiency of CP, conformal correction is proposed to fine-tune or wrap the base model with an extra module using a conformal-aware inefficiency loss. In this work, we empirically and theoretically identify a trade-off between the CP efficiency and the entropy of model prediction. We then propose an entropy-constrained conformal correction method, exploring a better Pareto optimum between efficiency and entropy. Extensive experimental results on both computer vision and graph datasets demonstrate the efficacy of the proposed method. For instance, it can significantly improve the efficiency of state-of-the-art CP methods by up to 34.4%, given an entropy threshold.

cs.LG↗

arXiv2023

Post Lie-Yamaguti algebras, relative Rota-Baxter operators of nonzero weights, and their deformations

In this paper, we introduce the notions of relative Rota-Baxter operators of weight $1$ on Lie-Yamaguti algebras, and post-\LYA s, which is an underlying algebraic structure of relative Rota-Baxter operators of weight $1$. We give the relationship between these two algebraic structures. Besides, we establish the cohomology theory of relative Rota-Baxter operators of weight $1$ via the Yamaguti cohomology. Consequently, we use this cohomology to characterize linear deformations of relative Rota-Baxter operators of weight $1$ on Lie-Yamaguti algebras. We show that if two linear deformations of a relative Rota-Baxter operator of weight $1$ are equivalent, then their infinitesimals are in the same cohomology class in the first cohomology group. Moreover, we show that an order $n$ deformation of a relative Rota-Baxter operator of weight $1$ can be extended to an order $n+1$ deformation if and only if the obstruction class in the second cohomology group is trivial.

math.RA↗

arXiv2023

Cohomology and deformations of crossed homomorphisms between Lie-Yamaguti algebras

In this paper, we introduce the notion of crossed homomorphisms between Lie-Yamaguti algebras and establish the cohomology theory of crossed homomorphisms via the Yamaguti cohomology. Consequently, we use this cohomology to characterize linear deformations of crossed homomorphisms between Lie-Yamaguti algebras. We show that if two linear or formal deformations of a crossed homomorphism are equivalent, then their infinitesimals are in the same cohomology class in the first cohomology group. Moreover, we show that an order $n$ deformation of a crossed homomorphism can be extended to an order $n+1$ deformation if and only if the obstruction class in the second cohomology group is trivial.

math.RA↗

arXiv2022

Detecting Topology Attacks against Graph Neural Networks

Graph neural networks (GNNs) have been widely used in many real applications, and recent studies have revealed their vulnerabilities against topology attacks. To address this issue, existing efforts have mainly been dedicated to improving the robustness of GNNs, while little attention has been paid to the detection of such attacks. In this work, we study the victim node detection problem under topology attacks against GNNs. Our approach is built upon the key observation rooted in the intrinsic message passing nature of GNNs. That is, the neighborhood of a victim node tends to have two competing group forces, pushing the node classification results towards the original label and the targeted label, respectively. Based on this observation, we propose to detect victim nodes by deliberately designing an effective measurement of the neighborhood variance for each node. Extensive experimental results on four real-world datasets and five existing topology attacks show the effectiveness and efficiency of the proposed detection approach.

cs.LG↗

arXiv2021

Cohomologies of 3-Lie algebras with derivations

In this paper, we consider a 3-Lie algebra with a derivation (called a 3-LieDer pair). We define cohomology for a 3-LieDer pair with coefficients in a representation. We use this cohomology to study deformations and abelian extensions of 3-LieDer pairs. We give the notion of a 3-Lie2Der pair, which can be viewed as the categorification of a 3-LieDer pair. We show that skeletal 3-Lie2Der pairs are classified by triples given by 3-LieDer pairs, representations and 3-cocycles. We define crossed modules of 3-LieDer pairs and show that there exists a one-to-one correspondence between strict 3-Lie2Der pairs and crossed modules of 3-LieDer pairs.

math.RA↗