Large Language Models (LLMs) have demonstrated remarkable performance in code completion. However, the training data used to develop these models often contain a significant amount of buggy code. Yet, it remains unclear to what extent these buggy instances influence LLMs' performance when tackling bug-prone code completion tasks. To fill this gap, this paper presents the first empirical study evaluating the performance of LLMs in completing bug-prone code. Through extensive experiments on 7 LLMs and the Defects4J dataset, we analyze LLMs' accuracy, robustness, and limitations in this challenging context. Our experimental results show that completing bug-prone code is significantly more challenging for LLMs than completing normal code. Notably, in bug-prone tasks, the likelihood of LLMs generating correct code is nearly the same as generating buggy code, and it is substantially lower than in normal code completion tasks (e.g., 12.27% vs. 29.85% for GPT-4). To our surprise, 44.44% of the bugs LLMs make are completely identical to the pre-fix version, indicating that LLMs have been seriously biased by historical bugs when completing code. Additionally, we investigate the effectiveness
Point cloud completion is crucial for 3D computer vision tasks in autonomous driving, augmented reality, and robotics. However, obtaining clean and complete point clouds from real-world environments is challenging due to noise and occlusions. Consequently, most existing completion networks -- trained on synthetic data -- struggle with real-world degradations. In this work, we tackle the problem of completing and denoising highly corrupted partial point clouds affected by multiple simultaneous degradations. To benchmark robustness, we introduce the Corrupted Point Cloud Completion Dataset (CPCCD), which highlights the limitations of current methods under diverse corruptions. Building on these insights, we propose DWCNet (Denoising-While-Completing Network), a completion framework enhanced with a Noise Management Module (NMM) that leverages contrastive learning and self-attention to suppress noise and model structural relationships. DWCNet achieves state-of-the-art performance on both clean and corrupted, synthetic and real-world datasets. The dataset and code will be publicly available at https://github.com/keneniwt/DWCNET-Robust-Point-Cloud-Completion-against-Corruptions
3D point clouds directly collected from objects through sensors are often incomplete due to self-occlusion. Conventional methods for completing these partial point clouds rely on manually organized training sets and are usually limited to object categories seen during training. In this work, we propose a test-time framework for completing partial point clouds across unseen categories without any requirement for training. Leveraging point rendering via Gaussian Splatting, we develop techniques of Partial Gaussian Initialization, Zero-shot Fractal Completion, and Point Cloud Extraction that utilize priors from pre-trained 2D diffusion models to infer missing regions and extract uniform completed point clouds. Experimental results on both synthetic and real-world scanned point clouds demonstrate that our approach outperforms existing methods in completing a variety of objects. Our project page is at \url{https://tianxinhuang.github.io/projects/ComPC/}.
High dynamic range (HDR) video rendering from low dynamic range (LDR) videos where frames are of alternate exposure encounters significant challenges, due to the exposure change and absence at each time stamp. The exposure change and absence make existing methods generate flickering HDR results. In this paper, we propose a novel paradigm to render HDR frames via completing the absent exposure information, hence the exposure information is complete and consistent. Our approach involves interpolating neighbor LDR frames in the time dimension to reconstruct LDR frames for the absent exposures. Combining the interpolated and given LDR frames, the complete set of exposure information is available at each time stamp. This benefits the fusing process for HDR results, reducing noise and ghosting artifacts therefore improving temporal consistency. Extensive experimental evaluations on standard benchmarks demonstrate that our method achieves state-of-the-art performance, highlighting the importance of absent exposure completing in HDR video rendering. The code is available at https://github.com/cuijiahao666/NECHDR.
A $k$-star is a complete bipartite graph $K_{1,k}$. A partial $k$-star design of order $n$ is a pair $(V,\mathcal{A})$ where $V$ is a set of $n$ vertices and $\mathcal{A}$ is a set of edge-disjoint $k$-stars whose vertex sets are subsets of $V$. If each edge of the complete graph with vertex set $V$ is in some star in $\mathcal{A}$, then $(V,\mathcal{A})$ is a (complete) $k$-star design. We say that $(V,\mathcal{A})$ is completable if there is a $k$-star design $(V,\mathcal{B})$ such that $\mathcal{A} \subseteq \mathcal{B}$. In this paper we determine, for all $k$ and $n$, the minimum number of stars in an uncompletable partial $k$-star design of order $n$.
We derive the Cardano formula of cubic equations by completing the cube, and provide radical solutions to some algebraic equations of higher degree by completing powers. The main idea of completing powers arises from Harrison's center theory of higher degree forms. A very simple criterion for such algebraic equations is presented, and the computation amounts to solving linear equations and quadratic equations.
Purpose: Ultrasound (US) imaging, while advantageous for its radiation-free nature, is challenging to interpret due to only partially visible organs and a lack of complete 3D information. While performing US-based diagnosis or investigation, medical professionals therefore create a mental map of the 3D anatomy. In this work, we aim to replicate this process and enhance the visual representation of anatomical structures. Methods: We introduce a point-cloud-based probabilistic DL method to complete occluded anatomical structures through 3D shape completion and choose US-based spine examinations as our application. To enable training, we generate synthetic 3D representations of partially occluded spinal views by mimicking US physics and accounting for inherent artifacts. Results: The proposed model performs consistently on synthetic and patient data, with mean and median differences of 2.02 and 0.03 in CD, respectively. Our ablation study demonstrates the importance of US physics-based data generation, reflected in the large mean and median difference of 11.8 CD and 9.55 CD, respectively. Additionally, we demonstrate that anatomic landmarks, such as the spinous process (with reconstru
Motivated by problems in the study of Anosov and pseudo-Anosov flows on 3-manifolds, we characterize when a pair $(L^+, L^-)$ of subsets of transverse laminations of the circle can be completed to a pair of transverse foliations of the plane or, separately, realized as the endpoints of such a bifoliation of the plane. (We allow also singular bifoliations with simple prongs, such as arise in pseudo-Anosov flows). This program is carried out at a level of generality applicable to bifoliations coming from pseudo-Anosov flows with and without perfect fits, as well as many other examples, and is natural with respect to group actions preserving these structures.
The quality of ontologies in terms of their correctness and completeness is crucial for developing high-quality ontology-based applications. Traditional debugging techniques repair ontologies by removing unwanted axioms, but may thereby remove consequences that are correct in the domain of the ontology. In this paper we propose an interactive approach to mitigate this for $\mathcal{EL}$ ontologies by axiom weakening and completing. We present algorithms for weakening and completing and present the first approach for repairing that takes into account removing, weakening and completing. We show different combination strategies, discuss the influence on the final ontologies and show experimental results. We show that previous work has only considered special cases and that there is a trade-off between the amount of validation work for a domain expert and the quality of the ontology in terms of correctness and completeness.
This paper presents the Sierpinski Gasket ($\mathbb{S}$) as a final coalgebra obtained by Cauchy completing the initial algebra for an endofunctor on the category of tri-pointed one bounded metric spaces with continuous maps. It has been previously observed that $\mathbb{S}$ is bi-Lipschitz equivalent to the coalgebra obtained by completing the initial algebra, where the latter was observed to be final when morphisms are restricted to short maps. This raised the question "Is $\mathbb{S}$ the final coalgebra in the Lipschitz setting?". The results of this paper show that the natural setup is to consider all continuous functions. The description of the final coalgebra as the Cauchy completion of the initial algebra has been explicitly used to determine the mediating morphism from a given coalgebra to the the final coalgebra. This has been used to show that if the structure map of a coalgebra is continuous, then so is the mediating morphism. The description of $\mathbb{S}$ given here not only generalizes previous observations, but also unifies classical descriptions of $\mathbb{S}$. We also show, by means of an example, that $\mathbb{S}$ is not the final coalgebra if we consider only
Recently, many authors have embraced the study of certain properties of modules such as projectivity, injectivity and flatness from an alternative point of view. Rather than saying a module has a certain property or not, each module is assigned a relative domain which, somehow, measures to which extent it has this particular property. In this work, we introduce a new and fresh perspective on flatness of modules. However, we will first investigate a more general context by introducing domains relative to a precovering class $\x$. We call these domains $\x$-precover completing domains. In particular, when $\x$ is the class of flat modules, we call them flat-precover completing domains. This approach allows us to provide a common frame for a number of classical notions. Moreover, some known results are generalized and some classical rings are characterized in terms of these domains.
We examine the relationship between homework completion and exam performance for students having different physics aptitudes for five different semesters of an introductory electricity and magnetism course. In our analysis, we plot exam scores versus homework completion scores and calculate the slopes of the line fits and the Pearson correlations. On average, completing many homework problems correlated to better exam scores only for students with high physics aptitude. Low aptitude physics students had a negative correlation between exam performance and completing homework; the more homework problems they did, the worse their performance was on exams. One explanation for this effect is that the assigned homework problems placed an excessive cognitive load on low aptitude students. As a result, no learning or even negative learning might have taken place when low aptitude students attempted to do assigned homework. Another explanation is based on the fact that the negative benefit effects first appeared when magnetism concepts were introduced. According to this explanation, low aptitude students had difficulty consolidating knowledge of magnetic fields with previously-learned knowl
The $c_2$-invariant is an arithmetic graph invariant useful for understanding Feynman periods. Brown and Schnetz conjectured that the $c_2$-invariant has a particular symmetry known as completion invariance. This paper will prove completion invariance of the $c_2$-invariant in the $p=2$ case, extending previous work of one of us. The methods are combinatorial and enumerative involving counting certain partitions of the edges of the graph.
Most existing point cloud completion methods are only applicable to partial point clouds without any noises and outliers, which does not always hold in practice. We propose in this paper an end-to-end network, named CS-Net, to complete the point clouds contaminated by noises or containing outliers. In our CS-Net, the completion and segmentation modules work collaboratively to promote each other, benefited from our specifically designed cascaded structure. With the help of segmentation, more clean point cloud is fed into the completion module. We design a novel completion decoder which harnesses the labels obtained by segmentation together with FPS to purify the point cloud and leverages KNN-grouping for better generation. The completion and segmentation modules work alternately share the useful information from each other to gradually improve the quality of prediction. To train our network, we build a dataset to simulate the real case where incomplete point clouds contain outliers. Our comprehensive experiments and comparisons against state-of-the-art completion methods demonstrate our superiority. We also compare with the scheme of segmentation followed by completion and their end
We study the structure and enumeration of the final two 2x4 permutation classes, completing a research program that has spanned almost two decades. For both classes, careful structural analysis produces a complicated functional equation. One of these equations is solved with the guess-and-check paradigm, while the other is solved with kernel method-like techniques and Gröbner basis calculations.
This paper studies the rank-1 tensor completion problem for cubic tensors when there are noises for observed tensor entries. First, we propose a robust biquadratic optimization model for obtaining rank-1 completing tensors. When the observed tensor is sufficiently close to be rank-1, we show that this biquadratic optimization produces an accurate rank-$1$ tensor completion. Second, we give an efficient convex relaxation for solving the biquadratic optimization. When the optimizer matrix is separable, we show how to get optimizers for the biquadratic optimization and how to compute the rank-$1$ completing tensor. When that matrix is not separable, we apply its spectral decomposition to obtain an approximate rank-1 completing tensor. The software SDPNAL+ is applied to solve the resulting large size semidefinite programs. Numerical experiments are given to explore the efficiency of this biquadratic optimization model and the proposed convex relaxation.
Recent point-based object completion methods have demonstrated the ability to accurately recover the missing geometry of partially observed objects. However, these approaches are not well-suited for completing objects within a scene, as they do not consider known scene constraints (e.g., other observed surfaces) in their completions and further expect the partial input to be in a canonical coordinate system, which does not hold for objects within scenes. While instance scene completion methods have been proposed for completing objects within a scene, they lag behind point-based object completion methods in terms of object completion quality and still do not consider known scene constraints during completion. To overcome these limitations, we propose a point cloud-based instance completion model that can robustly complete objects at arbitrary scales and pose in the scene. To enable reasoning at the scene level, we introduce a sparse set of scene constraints represented as point clouds and integrate them into our completion model via a cross-attention mechanism. To evaluate the instance scene completion task on indoor scenes, we further build a new dataset called ScanWCF, which conta
Recently, Abbadini and Guffanti gave an algebraic proof of Herbrand's theorem using a completion for Lawvere doctrines that freely adds existential and universal quantifiers. A more direct argument can be given by only completing with respect to existential quantifiers. We construct the free existential completion on a presheaf of distributive lattices, and deduce Herbrand's theorem for coherent logic from the explicit description. We also discuss the cases involving presheaves of meet-semilattices, due to Trotta, and presheaves of frames.
Bilingual Lexicon Induction is the task of learning word translations without bilingual parallel corpora. We model this task as a matrix completion problem, and present an effective and extendable framework for completing the matrix. This method harnesses diverse bilingual and monolingual signals, each of which may be incomplete or noisy. Our model achieves state-of-the-art performance for both high and low resource languages.
This paper considers the problem of completing a rating matrix based on sub-sampled matrix entries as well as observed social graphs and hypergraphs. We show that there exists a \emph{sharp threshold} on the sample probability for the task of exactly completing the rating matrix -- the task is achievable when the sample probability is above the threshold, and is impossible otherwise -- demonstrating a phase transition phenomenon. The threshold can be expressed as a function of the ``quality'' of hypergraphs, enabling us to \emph{quantify} the amount of reduction in sample probability due to the exploitation of hypergraphs. This also highlights the usefulness of hypergraphs in the matrix completion problem. En route to discovering the sharp threshold, we develop a computationally efficient matrix completion algorithm that effectively exploits the observed graphs and hypergraphs. Theoretical analyses show that our algorithm succeeds with high probability as long as the sample probability exceeds the aforementioned threshold, and this theoretical result is further validated by synthetic experiments. Moreover, our experiments on a real social network dataset (with both graphs and hyper