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Large Language Models (LLMs) have demonstrated considerable cross-lingual alignment and generalization ability. Current research primarily focuses on improving LLMs' cross-lingual generalization capabilities. However, there is still a lack of research on the intrinsic mechanisms of how LLMs achieve cross-lingual alignment. From the perspective of region partitioning, this paper conducts several investigations on the linguistic competence of LLMs. We discover a core region in LLMs that corresponds to linguistic competence, accounting for approximately 1% of the total model parameters. Removing this core region by setting parameters to zero results in a significant performance decrease across 30 different languages. Furthermore, this core region exhibits significant dimensional dependency, perturbations to even a single parameter on specific dimensions leading to a loss of linguistic competence. Moreover, we discover that distinct regions exist for different monolingual families, and disruption to these specific regions substantially reduces the LLMs' proficiency in those corresponding languages. Our research also indicates that freezing the core linguistic region during further pre-training can mitigate the issue of catastrophic forgetting (CF), a common occurrence observed during further pre-training of LLMs. Overall, exploring the LLMs' functional regions provides insights into the foundation of their intelligence.

The web contains large-scale, diverse, and abundant information to satisfy the information-seeking needs of humans. Through meticulous data collection, preprocessing, and curation, webpages can be used as a fundamental data resource for language model pretraining. However, when confronted with the progressively revolutionized and intricate nature of webpages, rule-based/feature-based web scrapers are becoming increasingly inadequate. This paper presents a simple, fast, and effective Neural web Scraper (NeuScraper) to help extract primary and clean text contents from webpages. Experimental results show that NeuScraper surpasses the baseline scrapers by achieving more than a 20% improvement, demonstrating its potential in extracting higher-quality data to facilitate the language model pretraining. All of the code is available at //github.com/OpenMatch/NeuScraper.

Finding a Hamiltonian cycle in a given graph is computationally challenging, and in general remains so even when one is further given one Hamiltonian cycle in the graph and asked to find another. In fact, no significantly faster algorithms are known for finding another Hamiltonian cycle than for finding a first one even in the setting where another Hamiltonian cycle is structurally guaranteed to exist, such as for odd-degree graphs. We identify a graph class -- the bipartite Pfaffian graphs of minimum degree three -- where it is NP-complete to decide whether a given graph in the class is Hamiltonian, but when presented with a Hamiltonian cycle as part of the input, another Hamiltonian cycle can be found efficiently. We prove that Thomason's lollipop method~[Ann.~Discrete Math.,~1978], a well-known algorithm for finding another Hamiltonian cycle, runs in a linear number of steps in cubic bipartite Pfaffian graphs. This was conjectured for cubic bipartite planar graphs by Haddadan [MSc~thesis,~Waterloo,~2015]; in contrast, examples are known of both cubic bipartite graphs and cubic planar graphs where the lollipop method takes exponential time. Beyond the lollipop method, we address a slightly more general graph class and present two algorithms, one running in linear-time and one operating in logarithmic space, that take as input (i) a bipartite Pfaffian graph $G$ of minimum degree three, (ii) a Hamiltonian cycle $H$ in $G$, and (iii) an edge $e$ in $H$, and output at least three other Hamiltonian cycles through the edge $e$ in $G$. We also present further improved algorithms for finding optimal traveling salesperson tours and counting Hamiltonian cycles in bipartite planar graphs with running times that are not known to hold in general planar graphs.

The process of drawing electoral district boundaries is known as political redistricting. Within this context, gerrymandering is the practice of drawing these boundaries such that they unfairly favor a particular political party, often leading to unequal representation and skewed electoral outcomes. One of the few ways to detect gerrymandering is by algorithmically sampling redistricting plans. Previous methods mainly focus on sampling from some neighborhood of ``realistic' districting plans, rather than a uniform sample of the entire space. We present a deterministic subexponential time algorithm to uniformly sample from the space of all possible $ k $-partitions of a bounded degree planar graph, and with this construct a sample of the entire space of redistricting plans. We also give a way to restrict this sample space to plans that match certain compactness and population constraints at the cost of added complexity. The algorithm runs in $ 2^{O(\sqrt{n}\log n)} $ time, although we only give a heuristic implementation. Our method generalizes an algorithm to count self-avoiding walks on a square to count paths that split general planar graphs into $ k $ regions, and uses this to sample from the space of all $ k $-partitions of a planar graph.

Classic symmetry-breaking problems on graphs have gained a lot of attention in models of modern parallel computation. The Adaptive Massively Parallel Computation (AMPC) is a model that captures central challenges in data center computations. Chang et al. [PODC'2019] gave an extremely fast, constant time, algorithm for the $(\Delta + 1)$-coloring problem, where $\Delta$ is the maximum degree of an input graph of $n$ nodes. The algorithm works in the most restrictive low-space setting, where each machine has $n^{\delta}$ local space for a constant $0 < \delta < 1$. In this work, we study the vertex-coloring problem in sparse graphs parameterized by their arboricity $\alpha$, a standard measure for sparsity. We give deterministic algorithms that in constant, or almost constant, time give $\text{poly}(\alpha)$ and $O(\alpha)$-colorings, where $\alpha$ can be arbitrarily smaller than $\Delta$. A strong and standard approach to compute arboricity-dependent colorings is through the Nash-Williams forest decomposition, which gives rise to an (acyclic) orientation of the edges such that each node has a small outdegree. Our main technical contribution is giving efficient deterministic algorithms to compute these orientations and showing how to leverage them to find colorings in low-space AMPC. A key technical challenge is that the color of a node may depend on almost all of the other nodes in the graph and these dependencies cannot be stored on a single machine. Nevertheless, our novel and careful exploration technique yields the orientation, and the arboricity-dependent coloring, with a sublinear number of adaptive queries per node.

Context and motivation: Requirements engineering of complex IT systems needs to manage the many, and often vague and conflicting, organisational rules that exist in the context of a modern enterprise. At the same time, IT systems affect the organisation, essentially setting new rules on how the organisation should work. Question/problem: Gathering requirements for an IT system involves understanding the complex rules that govern an organisation. The research question is: How can the holistic properties of organisational rules be conceptualised? Principal ideas/results: This paper introduces the concept of organisational rule systems that may be used to describe complex organisational rules. The concept and its components are presented as a conceptual framework, which in turn is condensed into a conceptual framework diagram. The framework is grounded in a critical literature review. Contribution: The conceptual framework will, as a first step of a wider research agenda, help requirements engineers understand the influence of organisational rules.

Many real-world networks, like transportation networks and social networks, are dynamic in the sense that the edge set may change over time, but these changes are known in advance. This behavior is captured by the temporal graphs model, which has recently become a trending topic in theoretical computer science. A core open problem in the field is to prove the existence of linear-size temporal spanners in temporal cliques, i.e., sparse subgraphs of complete temporal graphs that ensure all-pairs reachability via temporal paths. So far, the best known result is the existence of temporal spanners with $\mathcal{O}(n\log n)$ many edges. We present significant progress towards proving that linear-size temporal spanners exist in all temporal cliques. We adapt techniques used in previous works and heavily expand and generalize them to provide a simpler and more intuitive proof of the $\mathcal{O}(n\log n)$ bound. Moreover, we use our novel approach to show that a large class of temporal cliques, called edge-pivot graphs, admit linear-size temporal spanners. To contrast this, we investigate other classes of temporal cliques that do not belong to the class of edge-pivot graphs. We introduce two such graph classes and we develop novel techniques for establishing the existence of linear temporal spanners in these graph classes as well.

Graphs are commonly used to model complex networks prevalent in modern social media and literacy applications. Our research investigates the vulnerability of these graphs through the application of feature based adversarial attacks, focusing on both decision-time attacks and poisoning attacks. In contrast to state-of-the-art models like Net Attack and Meta Attack, which target node attributes and graph structure, our study specifically targets node attributes. For our analysis, we utilized the text dataset Hellaswag and graph datasets Cora and CiteSeer, providing a diverse basis for evaluation. Our findings indicate that decision-time attacks using Projected Gradient Descent (PGD) are more potent compared to poisoning attacks that employ Mean Node Embeddings and Graph Contrastive Learning strategies. This provides insights for graph data security, pinpointing where graph-based models are most vulnerable and thereby informing the development of stronger defense mechanisms against such attacks.

The real-world data tends to be heavily imbalanced and severely skew the data-driven deep neural networks, which makes Long-Tailed Recognition (LTR) a massive challenging task. Existing LTR methods seldom train Vision Transformers (ViTs) with Long-Tailed (LT) data, while the off-the-shelf pretrain weight of ViTs always leads to unfair comparisons. In this paper, we systematically investigate the ViTs' performance in LTR and propose LiVT to train ViTs from scratch only with LT data. With the observation that ViTs suffer more severe LTR problems, we conduct Masked Generative Pretraining (MGP) to learn generalized features. With ample and solid evidence, we show that MGP is more robust than supervised manners. In addition, Binary Cross Entropy (BCE) loss, which shows conspicuous performance with ViTs, encounters predicaments in LTR. We further propose the balanced BCE to ameliorate it with strong theoretical groundings. Specially, we derive the unbiased extension of Sigmoid and compensate extra logit margins to deploy it. Our Bal-BCE contributes to the quick convergence of ViTs in just a few epochs. Extensive experiments demonstrate that with MGP and Bal-BCE, LiVT successfully trains ViTs well without any additional data and outperforms comparable state-of-the-art methods significantly, e.g., our ViT-B achieves 81.0% Top-1 accuracy in iNaturalist 2018 without bells and whistles. Code is available at //github.com/XuZhengzhuo/LiVT.

Graph neural networks (GNNs) is widely used to learn a powerful representation of graph-structured data. Recent work demonstrates that transferring knowledge from self-supervised tasks to downstream tasks could further improve graph representation. However, there is an inherent gap between self-supervised tasks and downstream tasks in terms of optimization objective and training data. Conventional pre-training methods may be not effective enough on knowledge transfer since they do not make any adaptation for downstream tasks. To solve such problems, we propose a new transfer learning paradigm on GNNs which could effectively leverage self-supervised tasks as auxiliary tasks to help the target task. Our methods would adaptively select and combine different auxiliary tasks with the target task in the fine-tuning stage. We design an adaptive auxiliary loss weighting model to learn the weights of auxiliary tasks by quantifying the consistency between auxiliary tasks and the target task. In addition, we learn the weighting model through meta-learning. Our methods can be applied to various transfer learning approaches, it performs well not only in multi-task learning but also in pre-training and fine-tuning. Comprehensive experiments on multiple downstream tasks demonstrate that the proposed methods can effectively combine auxiliary tasks with the target task and significantly improve the performance compared to state-of-the-art methods.