We investigate how efficiently a well-studied family of domination-type problems can be solved on bounded-treewidth graphs. For sets $\sigma,\rho$ of non-negative integers, a $(\sigma,\rho)$-set of a graph $G$ is a set $S$ of vertices such that $|N(u)\cap S|\in \sigma$ for every $u\in S$, and $|N(v)\cap S|\in \rho$ for every $v\not\in S$. The problem of finding a $(\sigma,\rho)$-set (of a certain size) unifies standard problems such as Independent Set, Dominating Set, Independent Dominating Set, and many others. For all pairs of finite or cofinite sets $(\sigma,\rho)$, we determine (under standard complexity assumptions) the best possible value $c_{\sigma,\rho}$ such that there is an algorithm that counts $(\sigma,\rho)$-sets in time $c_{\sigma,\rho}^{\sf tw}\cdot n^{O(1)}$ (if a tree decomposition of width ${\sf tw}$ is given in the input). For example, for the Exact Independent Dominating Set problem (also known as Perfect Code) corresponding to $\sigma=\{0\}$ and $\rho=\{1\}$, we improve the $3^{\sf tw}\cdot n^{O(1)}$ algorithm of [van Rooij, 2020] to $2^{\sf tw}\cdot n^{O(1)}$. Despite the unusually delicate definition of $c_{\sigma,\rho}$, an accompanying paper shows that our algorithms are most likely optimal, that is, for any pair $(\sigma, \rho)$ of finite or cofinite sets where the problem is non-trivial, and any $\varepsilon>0$, a $(c_{\sigma,\rho}-\varepsilon)^{\sf tw}\cdot n^{O(1)}$-algorithm counting the number of $(\sigma,\rho)$-sets would violate the Counting Strong Exponential-Time Hypothesis (#SETH). For finite sets $\sigma$ and $\rho$, these lower bounds also extend to the decision version, and hence, our algorithms are optimal in this setting as well. In contrast, for many cofinite sets, we show that further significant improvements for the decision and optimization versions are possible using the technique of representative sets.
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Stochastic gradient methods have been a popular and powerful choice of optimization methods, aimed at minimizing functions. Their advantage lies in the fact that that one approximates the gradient as opposed to using the full Jacobian matrix. One research direction, related to this, has been on the application to infinite-dimensional problems, where one may naturally have a Hilbert space framework. However, there has been limited work done on considering this in a more general setup, such as where the natural framework is that of a Banach space. This article aims to address this by the introduction of a novel stochastic method, the stochastic steepest descent method (SSD). The SSD will follow the spirit of stochastic gradient descent, which utilizes Riesz representation to identify gradients and derivatives. Our choice for using such a method is that it naturally allows one to adopt a Banach space setting, for which recent applications have exploited the benefit of this, such as in PDE-constrained shape optimization. We provide a convergence theory related to this under mild assumptions. Furthermore, we demonstrate the performance of this method on a couple of numerical applications, namely a $p$-Laplacian and an optimal control problem. Our assumptions are verified in these applications.
We investigate the problem of compound estimation of normal means while accounting for the presence of side information. Leveraging the empirical Bayes framework, we develop a nonparametric integrative Tweedie (NIT) approach that incorporates structural knowledge encoded in multivariate auxiliary data to enhance the precision of compound estimation. Our approach employs convex optimization tools to estimate the gradient of the log-density directly, enabling the incorporation of structural constraints. We conduct theoretical analyses of the asymptotic risk of NIT and establish the rate at which NIT converges to the oracle estimator. As the dimension of the auxiliary data increases, we accurately quantify the improvements in estimation risk and the associated deterioration in convergence rate. The numerical performance of NIT is illustrated through the analysis of both simulated and real data, demonstrating its superiority over existing methods.
Social media platforms, despite their value in promoting open discourse, are often exploited to spread harmful content. Current deep learning and natural language processing models used for detecting this harmful content overly rely on domain-specific terms affecting their capabilities to adapt to generalizable hate speech detection. This is because they tend to focus too narrowly on particular linguistic signals or the use of certain categories of words. Another significant challenge arises when platforms lack high-quality annotated data for training, leading to a need for cross-platform models that can adapt to different distribution shifts. Our research introduces a cross-platform hate speech detection model capable of being trained on one platform's data and generalizing to multiple unseen platforms. To achieve good generalizability across platforms, one way is to disentangle the input representations into invariant and platform-dependent features. We also argue that learning causal relationships, which remain constant across diverse environments, can significantly aid in understanding invariant representations in hate speech. By disentangling input into platform-dependent features (useful for predicting hate targets) and platform-independent features (used to predict the presence of hate), we learn invariant representations resistant to distribution shifts. These features are then used to predict hate speech across unseen platforms. Our extensive experiments across four platforms highlight our model's enhanced efficacy compared to existing state-of-the-art methods in detecting generalized hate speech.
Recent years have witnessed great advances in object segmentation research. In addition to generic objects, aquatic animals have attracted research attention. Deep learning-based methods are widely used for aquatic animal segmentation and have achieved promising performance. However, there is a lack of challenging datasets for benchmarking. In this work, we build a new dataset dubbed Aquatic Animal Species. We also devise a novel GUided mixup augmeNtatioN and multi-modEl fusion for aquatic animaL segmentation (GUNNEL) that leverages the advantages of multiple segmentation models to effectively segment aquatic animals and improves the training performance by synthesizing hard samples. Extensive experiments demonstrated the superiority of our proposed framework over existing state-of-the-art instance segmentation methods. The code is available at //github.com/lmquan2000/mask-mixup. The dataset is available at //doi.org/10.5281/zenodo.8208877 .
Inspired by the recent success of large language models (LLMs) like ChatGPT, researchers start to explore the adoption of LLMs for agile hardware design, such as generating design RTL based on natural-language instructions. However, in existing works, their target designs are all relatively simple and in a small scale, and proposed by the authors themselves, making a fair comparison among different LLM solutions challenging. In addition, many prior works only focus on the design correctness, without evaluating the design qualities of generated design RTL. In this work, we propose an open-source benchmark named RTLLM, for generating design RTL with natural language instructions. To systematically evaluate the auto-generated design RTL, we summarized three progressive goals, named syntax goal, functionality goal, and design quality goal. This benchmark can automatically provide a quantitative evaluation of any given LLM-based solution. Furthermore, we propose an easy-to-use yet surprisingly effective prompt engineering technique named self-planning, which proves to significantly boost the performance of GPT-3.5 in our proposed benchmark.
As an effective strategy, data augmentation (DA) alleviates data scarcity scenarios where deep learning techniques may fail. It is widely applied in computer vision then introduced to natural language processing and achieves improvements in many tasks. One of the main focuses of the DA methods is to improve the diversity of training data, thereby helping the model to better generalize to unseen testing data. In this survey, we frame DA methods into three categories based on the diversity of augmented data, including paraphrasing, noising, and sampling. Our paper sets out to analyze DA methods in detail according to the above categories. Further, we also introduce their applications in NLP tasks as well as the challenges.
Graph Neural Networks (GNNs) are widely used for analyzing graph-structured data. Most GNN methods are highly sensitive to the quality of graph structures and usually require a perfect graph structure for learning informative embeddings. However, the pervasiveness of noise in graphs necessitates learning robust representations for real-world problems. To improve the robustness of GNN models, many studies have been proposed around the central concept of Graph Structure Learning (GSL), which aims to jointly learn an optimized graph structure and corresponding representations. Towards this end, in the presented survey, we broadly review recent progress of GSL methods for learning robust representations. Specifically, we first formulate a general paradigm of GSL, and then review state-of-the-art methods classified by how they model graph structures, followed by applications that incorporate the idea of GSL in other graph tasks. Finally, we point out some issues in current studies and discuss future directions.
Deep neural networks have been able to outperform humans in some cases like image recognition and image classification. However, with the emergence of various novel categories, the ability to continuously widen the learning capability of such networks from limited samples, still remains a challenge. Techniques like Meta-Learning and/or few-shot learning showed promising results, where they can learn or generalize to a novel category/task based on prior knowledge. In this paper, we perform a study of the existing few-shot meta-learning techniques in the computer vision domain based on their method and evaluation metrics. We provide a taxonomy for the techniques and categorize them as data-augmentation, embedding, optimization and semantics based learning for few-shot, one-shot and zero-shot settings. We then describe the seminal work done in each category and discuss their approach towards solving the predicament of learning from few samples. Lastly we provide a comparison of these techniques on the commonly used benchmark datasets: Omniglot, and MiniImagenet, along with a discussion towards the future direction of improving the performance of these techniques towards the final goal of outperforming humans.
Translational distance-based knowledge graph embedding has shown progressive improvements on the link prediction task, from TransE to the latest state-of-the-art RotatE. However, N-1, 1-N and N-N predictions still remain challenging. In this work, we propose a novel translational distance-based approach for knowledge graph link prediction. The proposed method includes two-folds, first we extend the RotatE from 2D complex domain to high dimension space with orthogonal transforms to model relations for better modeling capacity. Second, the graph context is explicitly modeled via two directed context representations. These context representations are used as part of the distance scoring function to measure the plausibility of the triples during training and inference. The proposed approach effectively improves prediction accuracy on the difficult N-1, 1-N and N-N cases for knowledge graph link prediction task. The experimental results show that it achieves better performance on two benchmark data sets compared to the baseline RotatE, especially on data set (FB15k-237) with many high in-degree connection nodes.
Visual Question Answering (VQA) models have struggled with counting objects in natural images so far. We identify a fundamental problem due to soft attention in these models as a cause. To circumvent this problem, we propose a neural network component that allows robust counting from object proposals. Experiments on a toy task show the effectiveness of this component and we obtain state-of-the-art accuracy on the number category of the VQA v2 dataset without negatively affecting other categories, even outperforming ensemble models with our single model. On a difficult balanced pair metric, the component gives a substantial improvement in counting over a strong baseline by 6.6%.
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