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A dynamic graph algorithm is a data structure that supports edge insertions, deletions, and specific problem queries. While extensive research exists on dynamic algorithms for graph problems solvable in polynomial time, most of these algorithms have not been implemented or empirically evaluated. This work addresses the NP-complete maximum weight and cardinality independent set problems in a dynamic setting, applicable to areas like dynamic map-labeling and vehicle routing. Real-world instances can be vast, with millions of vertices and edges, making it challenging to find near-optimal solutions quickly. Exact solvers can find optimal solutions but have exponential worst-case runtimes. Conversely, heuristic algorithms use local search techniques to improve solutions by optimizing vertices. In this work, we introduce a novel local search technique called optimal neighborhood exploration. This technique creates independent subproblems that are solved to optimality, leading to improved overall solutions. Through numerous experiments, we assess the effectiveness of our approach and compare it with other state-of-the-art dynamic solvers. Our algorithm features a parameter, the subproblem size, that balances running time and solution quality. With this parameter, our configuration matches state-of-the-art performance for the cardinality independent set problem. By increasing the parameter, we significantly enhance solution quality.

Linear arrangements of graphs are a well-known type of graph labeling and are found in many important computational problems, such as the Minimum Linear Arrangement Problem ($\texttt{minLA}$). A linear arrangement is usually defined as a permutation of the $n$ vertices of a graph. An intuitive geometric setting is that of vertices lying on consecutive integer positions in the real line, starting at 1; edges are often drawn as semicircles above the real line. In this paper we study the Maximum Linear Arrangement problem ($\texttt{MaxLA}$), the maximization variant of $\texttt{minLA}$. We devise a new characterization of maximum arrangements of general graphs, and prove that $\texttt{MaxLA}$ can be solved for cycle graphs in constant time, and for $k$-linear trees ($k\le2$) in time $O(n)$. We present two constrained variants of $\texttt{MaxLA}$ we call $\texttt{bipartite MaxLA}$ and $\texttt{1-thistle MaxLA}$. We prove that the former can be solved in time $O(n)$ for any bipartite graph; the latter, by an algorithm that typically runs in time $O(n^4)$ on unlabelled trees. The combination of the two variants has two promising characteristics. First, it solves $\texttt{MaxLA}$ for almost all trees consisting of a few tenths of nodes. Second, we prove that it constitutes a $3/2$-approximation algorithm for $\texttt{MaxLA}$ for trees. Furthermore, we conjecture that $\texttt{bipartite MaxLA}$ solves $\texttt{MaxLA}$ for at least $50\%$ of all free trees.

In this paper, we define the quantum analogues of the {\em probabilistic pushdown systems} and {\em Markov chains}, and further investigate whether it is necessary to define a quantum analogue of {\em probabilistic computational tree logic} to describe the branching-time properties of the {\em quantum Markov chain} defined in this paper. We study its model-checking question and show that the model-checking of {\em stateless quantum pushdown systems (qBPA)} against {\em probabilistic computational tree logic (PCTL)} is generally undecidable, with the immediate corollaries summarized. We define the notion of {\em probabilistic $\omega$-pushdown automaton} for the first time and study the model-checking question of {\em stateless probabilistic $\omega$-pushdown system ($\omega$-pBPA)} against $\omega$-PCTL (defined by Chatterjee et al. in \cite{CSH08}) and show that the model-checking of {\em stateless probabilistic $\omega$-pushdown systems ($\omega$-pBPA)} against $\omega$-PCTL is generally undecidable, with immediate consequences summarized. Our approach is to construct formulas of $\omega$-PCTL encoding the {\em Post Correspondence Problem} indirectly.

In this paper, we propose Conceptual Codebook Learning (CoCoLe), a novel fine-tuning method for vision-language models (VLMs) to address the challenge of improving the generalization capability of VLMs while fine-tuning them on downstream tasks in a few-shot setting. We recognize that visual concepts, such as textures, shapes, and colors are naturally transferable across domains and play a crucial role in generalization tasks. Motivated by this interesting finding, we learn a conceptual codebook consisting of visual concepts as keys and conceptual prompts as values, which serves as a link between the image encoder's outputs and the text encoder's inputs. Specifically, for a given image, we leverage the codebook to identify the most relevant conceptual prompts associated with the class embeddings to perform the classification. Additionally, we incorporate a handcrafted concept cache as a regularization to alleviate the overfitting issues in low-shot scenarios. We observe that this conceptual codebook learning method is able to achieve enhanced alignment between visual and linguistic modalities. Extensive experimental results demonstrate that our CoCoLe method remarkably outperforms the existing state-of-the-art methods across various evaluation settings, including base-to-new generalization, cross-dataset evaluation, and domain generalization tasks. Detailed ablation studies further confirm the efficacy of each component in CoCoLe.

We introduce the Concept Bottleneck Large Language Model (CB-LLM), a pioneering approach to creating inherently interpretable Large Language Models (LLMs). Unlike traditional black-box LLMs that rely on post-hoc interpretation methods with limited neuron function insights, CB-LLM sets a new standard with its built-in interpretability, scalability, and ability to provide clear, accurate explanations. This innovation not only advances transparency in language models but also enhances their effectiveness. Our unique Automatic Concept Correction (ACC) strategy successfully narrows the performance gap with conventional black-box LLMs, positioning CB-LLM as a model that combines the high accuracy of traditional LLMs with the added benefit of clear interpretability -- a feature markedly absent in existing LLMs.

In this paper, we explore a novel framework, EGIInet (Explicitly Guided Information Interaction Network), a model for View-guided Point cloud Completion (ViPC) task, which aims to restore a complete point cloud from a partial one with a single view image. In comparison with previous methods that relied on the global semantics of input images, EGIInet efficiently combines the information from two modalities by leveraging the geometric nature of the completion task. Specifically, we propose an explicitly guided information interaction strategy supported by modal alignment for point cloud completion. First, in contrast to previous methods which simply use 2D and 3D backbones to encode features respectively, we unified the encoding process to promote modal alignment. Second, we propose a novel explicitly guided information interaction strategy that could help the network identify critical information within images, thus achieving better guidance for completion. Extensive experiments demonstrate the effectiveness of our framework, and we achieved a new state-of-the-art (+16% CD over XMFnet) in benchmark datasets despite using fewer parameters than the previous methods. The pre-trained model and code and are available at //github.com/WHU-USI3DV/EGIInet.

In this paper, we propose a novel Feature Decomposition and Reconstruction Learning (FDRL) method for effective facial expression recognition. We view the expression information as the combination of the shared information (expression similarities) across different expressions and the unique information (expression-specific variations) for each expression. More specifically, FDRL mainly consists of two crucial networks: a Feature Decomposition Network (FDN) and a Feature Reconstruction Network (FRN). In particular, FDN first decomposes the basic features extracted from a backbone network into a set of facial action-aware latent features to model expression similarities. Then, FRN captures the intra-feature and inter-feature relationships for latent features to characterize expression-specific variations, and reconstructs the expression feature. To this end, two modules including an intra-feature relation modeling module and an inter-feature relation modeling module are developed in FRN. Experimental results on both the in-the-lab databases (including CK+, MMI, and Oulu-CASIA) and the in-the-wild databases (including RAF-DB and SFEW) show that the proposed FDRL method consistently achieves higher recognition accuracy than several state-of-the-art methods. This clearly highlights the benefit of feature decomposition and reconstruction for classifying expressions.

Data augmentation has been widely used to improve generalizability of machine learning models. However, comparatively little work studies data augmentation for graphs. This is largely due to the complex, non-Euclidean structure of graphs, which limits possible manipulation operations. Augmentation operations commonly used in vision and language have no analogs for graphs. Our work studies graph data augmentation for graph neural networks (GNNs) in the context of improving semi-supervised node-classification. We discuss practical and theoretical motivations, considerations and strategies for graph data augmentation. Our work shows that neural edge predictors can effectively encode class-homophilic structure to promote intra-class edges and demote inter-class edges in given graph structure, and our main contribution introduces the GAug graph data augmentation framework, which leverages these insights to improve performance in GNN-based node classification via edge prediction. Extensive experiments on multiple benchmarks show that augmentation via GAug improves performance across GNN architectures and datasets.

In this paper, we introduce the Reinforced Mnemonic Reader for machine reading comprehension tasks, which enhances previous attentive readers in two aspects. First, a reattention mechanism is proposed to refine current attentions by directly accessing to past attentions that are temporally memorized in a multi-round alignment architecture, so as to avoid the problems of attention redundancy and attention deficiency. Second, a new optimization approach, called dynamic-critical reinforcement learning, is introduced to extend the standard supervised method. It always encourages to predict a more acceptable answer so as to address the convergence suppression problem occurred in traditional reinforcement learning algorithms. Extensive experiments on the Stanford Question Answering Dataset (SQuAD) show that our model achieves state-of-the-art results. Meanwhile, our model outperforms previous systems by over 6% in terms of both Exact Match and F1 metrics on two adversarial SQuAD datasets.

In this paper, we propose a conceptually simple and geometrically interpretable objective function, i.e. additive margin Softmax (AM-Softmax), for deep face verification. In general, the face verification task can be viewed as a metric learning problem, so learning large-margin face features whose intra-class variation is small and inter-class difference is large is of great importance in order to achieve good performance. Recently, Large-margin Softmax and Angular Softmax have been proposed to incorporate the angular margin in a multiplicative manner. In this work, we introduce a novel additive angular margin for the Softmax loss, which is intuitively appealing and more interpretable than the existing works. We also emphasize and discuss the importance of feature normalization in the paper. Most importantly, our experiments on LFW BLUFR and MegaFace show that our additive margin softmax loss consistently performs better than the current state-of-the-art methods using the same network architecture and training dataset. Our code has also been made available at //github.com/happynear/AMSoftmax