arXiv subjects
Publications and source records attributed to Thanh Vu.
Let $I(G_{\mathbf{w}})$ be the edge ideal of an edge-weighted graph $(G,\mathbf{w})$. We prove that $I(G_{\mathbf{w}})$ is sequentially Cohen-Macaulay for all weight functions $w$ if and only if $G$ is a Woodroofe graph.
Let $I$ be the edge ideal of a cycle of length $n \ge 5$ over a polynomial ring $S = \mathrm{k}[x_1,\ldots,x_n]$. We prove that for $2 \le t < \lceil (n+1)/2 \rceil$, $$\operatorname{depth} (S/I^t) = \lceil \frac{n -t + 1}{3} \rceil.$$ When $G = T_{\mathbf{a}}$ is a starlike tree which is the join of $k$ paths of length $a_1, \ldots, a_k$ at a common root $1$, we give a formula for the depth of powers of $I(T_{\mathbf{a}})$.
Let $H = \langle n_1, n_2, n_3\rangle$ be a numerical semigroup. Let $\tilde H$ be the interval completion of $H$, namely the semigroup generated by the interval $\langle n_1, n_1+1, \ldots, n_3\rangle$. Let $K$ be a field and $K[H]$ the semigroup ring generated by $H$. Let $I_H^*$ be the defining ideal of the tangent cone of $K[H]$. In this paper, we describe the defining equations of $I_H^*$. From that, we establish the Herzog-Stamate conjecture for monomial space curves stating that $β_i(I_H^*) \le β_i(I_{\tilde H}^*)$ for all $i$, where $β_i(I_H^*)$ and $β_i(I_{\tilde H}^*)$ are the $i$th Betti numbers of $I_H^*$ and $I_{\tilde H}^*$ respectively.
Let $I(G)$ be the edge ideal of a simple graph $G$. We prove that $I(G)^2$ has a linear free resolution if and only if $G$ is gap-free and reg$I(G) \le 3$. Similarly, we show that $I(G)^3$ has a linear free resolution if and only if $G$ is gap-free and reg$I(G) \le 4$. We deduce these characterizations from a general formula for the regularity of powers of edge ideals of gap-free graphs $${\rm reg}(I(G)^s) = \max({\rm reg} I(G) + s-1,2s),$$ for $s =2,3$.
In this work, we propose a novel and scalable solution to address the challenges of developing efficient dense predictions on edge platforms. Our first key insight is that MultiTask Learning (MTL) and hardware-aware Neural Architecture Search (NAS) can work in synergy to greatly benefit on-device Dense Predictions (DP). Empirical results reveal that the joint learning of the two paradigms is surprisingly effective at improving DP accuracy, achieving superior performance over both the transfer learning of single-task NAS and prior state-of-the-art approaches in MTL, all with just 1/10th of the computation. To the best of our knowledge, our framework, named EDNAS, is the first to successfully leverage the synergistic relationship of NAS and MTL for DP. Our second key insight is that the standard depth training for multi-task DP can cause significant instability and noise to MTL evaluation. Instead, we propose JAReD, an improved, easy-to-adopt Joint Absolute-Relative Depth loss, that reduces up to 88% of the undesired noise while simultaneously boosting accuracy. We conduct extensive evaluations on standard datasets, benchmark against strong baselines and state-of-the-art approaches, as well as provide an analysis of the discovered optimal architectures.
We propose a simple yet effective embedding model to learn quaternion embeddings for entities and relations in knowledge graphs. Our model aims to enhance correlations between head and tail entities given a relation within the Quaternion space with Hamilton product. The model achieves this goal by further associating each relation with two relation-aware rotations, which are used to rotate quaternion embeddings of the head and tail entities, respectively. Experimental results show that our proposed model produces state-of-the-art performances on well-known benchmark datasets for knowledge graph completion. Our code is available at: \url{https://github.com/daiquocnguyen/QuatRE}.
Automatic post-editing (APE) is an important remedy for reducing errors of raw translated texts that are produced by machine translation (MT) systems or software-aided translation. In this paper, we present a systematic approach to tackle the APE task for Vietnamese. Specifically, we construct the first large-scale dataset of 5M Vietnamese translated and corrected sentence pairs. We then apply strong neural MT models to handle the APE task, using our constructed dataset. Experimental results from both automatic and human evaluations show the effectiveness of the neural MT models in handling the Vietnamese APE task.
Let $I(G)$ be the edge ideal of a simple graph $G$ over a field k. We prove that $${\rm reg}(\overline {I(G)^s}) = {\rm reg}(I(G)^s),$$ for all $s \le 4$. Furthermore, we provide an example of a graph $G$ such that $${\rm reg} I(G)^s = {\rm reg} \overline{I(G)^s} = {\rm reg} I(G)^{(s)} = \begin{cases} 5 + 2s & \text{ if char k} = 2 \\ 4 + 2s & \text{ if char k} \neq 2, \end{cases}$$ for all $s \ge 1.$
Let $Δ$ be a one-dimensional simplicial complex. Let $I_Δ$ be the Stanley-Reisner ideal of $Δ$. We prove that for all $s \ge 1$ and all intermediate ideals $J$ generated by $I_Δ^s$ and some minimal generators of $I_Δ^{(s)}$, we have $${\rm reg} J = {\rm reg} I_Δ^s = {\rm reg} I_Δ^{(s)}.$$
Let $G$ be a simple graph and $I$ its edge ideal. We prove that $${\rm reg}(I^{(s)}) = {\rm reg}(I^s)$$ for $s = 2,3$, where $I^{(s)}$ is the $s$-th symbolic power of $I$. As a consequence, we prove the following bounds \begin{align*} {\rm reg} I^{s} & \le {\rm reg} I + 2s - 2, \text{ for } s = 2,3, {\rm reg} I^{(s)} & \le {\rm reg} I + 2s - 2,\text{ for } s = 2,3,4. \end{align*}
In this letter, we present an interactive probabilistic mapping framework for a mobile manipulator picking objects from a pile. The aim is to map the scene, actively decide where to go next and which object to pick, make changes to the scene by picking the chosen object, and then map these changes alongside. The proposed framework uses a novel dynamic Gaussian Process (GP) Implicit Surface method to incrementally build and update the scene map that reflects environment changes. Actively the framework provides the next-best-view, balancing the need for picking object reachability with map information gain (IG). To enforce a priority of visiting boundary segments over unknown regions, the IG formulation includes an uncertainty gradient-based frontier score by exploiting the GP kernel derivative. This leads to an efficient strategy that addresses the often conflicting requirement of unknown environment exploration and object picking exploitation given a limited execution horizon. We demonstrate the effectiveness of our framework with software simulation and real-life experiments.
Despite remarkable improvements in speed and accuracy, convolutional neural networks (CNNs) still typically operate as monolithic entities at inference time. This poses a challenge for resource-constrained practical applications, where both computational budgets and performance needs can vary with the situation. To address these constraints, we propose the Any-Width Network (AWN), an adjustable-width CNN architecture and associated training routine that allow for fine-grained control over speed and accuracy during inference. Our key innovation is the use of lower-triangular weight matrices which explicitly address width-varying batch statistics while being naturally suited for multi-width operations. We also show that this design facilitates an efficient training routine based on random width sampling. We empirically demonstrate that our proposed AWNs compare favorably to existing methods while providing maximally granular control during inference.
In this paper, we provide an overview of the WNUT-2020 shared task on the identification of informative COVID-19 English Tweets. We describe how we construct a corpus of 10K Tweets and organize the development and evaluation phases for this task. In addition, we also present a brief summary of results obtained from the final system evaluation submissions of 55 teams, finding that (i) many systems obtain very high performance, up to 0.91 F1 score, (ii) the majority of the submissions achieve substantially higher results than the baseline fastText (Joulin et al., 2017), and (iii) fine-tuning pre-trained language models on relevant language data followed by supervised training performs well in this task.
We present BERTweet, the first public large-scale pre-trained language model for English Tweets. Our BERTweet, having the same architecture as BERT-base (Devlin et al., 2019), is trained using the RoBERTa pre-training procedure (Liu et al., 2019). Experiments show that BERTweet outperforms strong baselines RoBERTa-base and XLM-R-base (Conneau et al., 2020), producing better performance results than the previous state-of-the-art models on three Tweet NLP tasks: Part-of-speech tagging, Named-entity recognition and text classification. We release BERTweet under the MIT License to facilitate future research and applications on Tweet data. Our BERTweet is available at https://github.com/VinAIResearch/BERTweet
The paper describes the organisation of the "HateSpeech Detection" (HSD) task at the VLSP workshop 2019 on detecting the fine-grained presence of hate speech in Vietnamese textual items (i.e., messages) extracted from Facebook, which is the most popular social network site (SNS) in Vietnam. The task is organised as a multi-class classification task and based on a large-scale dataset containing 25,431 Vietnamese textual items from Facebook. The task participants were challenged to build a classification model that is capable of classifying an item to one of 3 classes, i.e., "HATE", "OFFENSIVE" and "CLEAN". HSD attracted a large number of participants and was a popular task at VLSP 2019. In particular, there were 71 teams signed up for the task, 14 of them submitted results with 380 valid submissions from 20th September 2019 to 4th October 2019.
ICD coding is a process of assigning the International Classification of Disease diagnosis codes to clinical/medical notes documented by health professionals (e.g. clinicians). This process requires significant human resources, and thus is costly and prone to error. To handle the problem, machine learning has been utilized for automatic ICD coding. Previous state-of-the-art models were based on convolutional neural networks, using a single/several fixed window sizes. However, the lengths and interdependence between text fragments related to ICD codes in clinical text vary significantly, leading to the difficulty of deciding what the best window sizes are. In this paper, we propose a new label attention model for automatic ICD coding, which can handle both the various lengths and the interdependence of the ICD code related text fragments. Furthermore, as the majority of ICD codes are not frequently used, leading to the extremely imbalanced data issue, we additionally propose a hierarchical joint learning mechanism extending our label attention model to handle the issue, using the hierarchical relationships among the codes. Our label attention model achieves new state-of-the-art results on three benchmark MIMIC datasets, and the joint learning mechanism helps improve the performances for infrequent codes.
Given many recent advanced embedding models, selecting pre-trained word embedding (a.k.a., word representation) models best fit for a specific downstream task is non-trivial. In this paper, we propose a systematic approach, called ETNLP, for extracting, evaluating, and visualizing multiple sets of pre-trained word embeddings to determine which embeddings should be used in a downstream task. For extraction, we provide a method to extract subsets of the embeddings to be used in the downstream task. For evaluation, we analyse the quality of pre-trained embeddings using an input word analogy list. Finally, we visualize the word representations in the embedding space to explore the embedded words interactively. We demonstrate the effectiveness of the proposed approach on our pre-trained word embedding models in Vietnamese to select which models are suitable for a named entity recognition (NER) task. Specifically, we create a large Vietnamese word analogy list to evaluate and select the pre-trained embedding models for the task. We then utilize the selected embeddings for the NER task and achieve the new state-of-the-art results on the task benchmark dataset. We also apply the approach to another downstream task of privacy-guaranteed embedding selection, and show that it helps users quickly select the most suitable embeddings. In addition, we create an open-source system using the proposed systematic approach to facilitate similar studies on other NLP tasks. The source code and data are available at https://github.com/vietnlp/etnlp.
We present a versatile formulation of the convolution operation that we term a "mapped convolution." The standard convolution operation implicitly samples the pixel grid and computes a weighted sum. Our mapped convolution decouples these two components, freeing the operation from the confines of the image grid and allowing the kernel to process any type of structured data. As a test case, we demonstrate its use by applying it to dense inference on spherical data. We perform an in-depth study of existing spherical image convolution methods and propose an improved sampling method for equirectangular images. Then, we discuss the impact of data discretization when deriving a sampling function, highlighting drawbacks of the cube map representation for spherical data. Finally, we illustrate how mapped convolutions enable us to convolve directly on a mesh by projecting the spherical image onto a geodesic grid and training on the textured mesh. This method exceeds the state of the art for spherical depth estimation by nearly 17%. Our findings suggest that mapped convolutions can be instrumental in expanding the application scope of convolutional neural networks.