arXiv subjects

Zhenhao Li

Publications and source records attributed to Zhenhao Li.

63 records · Page 4Linked to original sources

arXiv2023

2D internal waves in an ergodic setting

We study a model of internal waves under periodic forcing in an effectively 2-dimensional aquarium. When the underlying classical dynamics has sufficiently irrational rotation number, we prove that the solution to the internal waves equation remains bounded in energy space in time. This result is in contrast with the works by Colin de Verdière--Saint-Raymond and Dyatlov--Wang--Zworski, which gave a description of singular profiles when the underlying dynamics has periodic attractors. Our result is proved by showing the spectral measure near the forcing frequency is very small.

math.AP↗

arXiv2022

On the Smoothness and Regularity of the Chess Billiard Flow and the Poincaré Problem

The Poincaré problem is a model of two-dimensional internal waves in stable-stratified fluid. The chess billiard flow, a variation of a typical billiard flow, drives the formation behind and describes the evolution of these internal waves, and its trajectories can be represented as rotations around the boundary of a given domain. We find that for sufficiently irrational rotation in the square, or when the rotation number $r(λ)$ is Diophantine, the regularity of the solution $u(t)$ of the evolution problem correlates directly to the regularity of the forcing function $f(x)$. Additionally, we show that when $f$ is smooth, then $u$ is also smooth. These results extend studies that have examined singularity points, or the lack of regularity, in rational rotations of the chess billiard flow. We also present numerical simulations in various geometries that analyze plateau formation and fractal dimension in $r(λ)$ and conjecture an extension of our results. Our results can be applied in modeling two dimensional oceanic waves, and they also relate the classical quantum correspondence to fluid study.

math.AP↗

arXiv2022

NL-Augmenter: A Framework for Task-Sensitive Natural Language Augmentation

Data augmentation is an important component in the robustness evaluation of models in natural language processing (NLP) and in enhancing the diversity of the data they are trained on. In this paper, we present NL-Augmenter, a new participatory Python-based natural language augmentation framework which supports the creation of both transformations (modifications to the data) and filters (data splits according to specific features). We describe the framework and an initial set of 117 transformations and 23 filters for a variety of natural language tasks. We demonstrate the efficacy of NL-Augmenter by using several of its transformations to analyze the robustness of popular natural language models. The infrastructure, datacards and robustness analysis results are available publicly on the NL-Augmenter repository (https://github.com/GEM-benchmark/NL-Augmenter).

cs.CL↗

arXiv2022

Ensemble Multi-Relational Graph Neural Networks

It is well established that graph neural networks (GNNs) can be interpreted and designed from the perspective of optimization objective. With this clear optimization objective, the deduced GNNs architecture has sound theoretical foundation, which is able to flexibly remedy the weakness of GNNs. However, this optimization objective is only proved for GNNs with single-relational graph. Can we infer a new type of GNNs for multi-relational graphs by extending this optimization objective, so as to simultaneously solve the issues in previous multi-relational GNNs, e.g., over-parameterization? In this paper, we propose a novel ensemble multi-relational GNNs by designing an ensemble multi-relational (EMR) optimization objective. This EMR optimization objective is able to derive an iterative updating rule, which can be formalized as an ensemble message passing (EnMP) layer with multi-relations. We further analyze the nice properties of EnMP layer, e.g., the relationship with multi-relational personalized PageRank. Finally, a new multi-relational GNNs which well alleviate the over-smoothing and over-parameterization issues are proposed. Extensive experiments conducted on four benchmark datasets well demonstrate the effectiveness of the proposed model.

cs.LG↗

arXiv2022

Visual Cues and Error Correction for Translation Robustness

Neural Machine Translation models are sensitive to noise in the input texts, such as misspelled words and ungrammatical constructions. Existing robustness techniques generally fail when faced with unseen types of noise and their performance degrades on clean texts. In this paper, we focus on three types of realistic noise that are commonly generated by humans and introduce the idea of visual context to improve translation robustness for noisy texts. In addition, we describe a novel error correction training regime that can be used as an auxiliary task to further improve translation robustness. Experiments on English-French and English-German translation show that both multimodal and error correction components improve model robustness to noisy texts, while still retaining translation quality on clean texts.

cs.CL↗

arXiv2022

Weyl Laws for Open Quantum Maps

We find Weyl upper bounds for the quantum open baker's map in the semiclassical limit. For the number of eigenvalues in an annulus, we derive the asymptotic upper bound $\mathcal O(N^δ)$ where $δ$ is the dimension of the trapped set of the baker's map and $(2 πN)^{-1}$ is the semiclassical parameter, which improves upon the previous result of $\mathcal O(N^{δ+ ε})$. Furthermore, we derive a Weyl upper bound with explicit dependence on the inner radius of the annulus for quantum open baker's maps with Gevrey cutoffs.

math.SP↗

arXiv2021

Design and Performance Evaluation of Joint Sensing and Communication Integrated System for 5G MmWave Enabled CAVs

The safety of connected automated vehicles (CAVs) relies on the reliable and efficient raw data sharing from multiple types of sensors. The 5G millimeter wave (mmWave) communication technology can enhance the environment sensing ability of different isolated vehicles. In this paper, a joint sensing and communication integrated system (JSCIS) is designed to support the dynamic frame structure configuration for sensing and communication dual functions based on the 5G New Radio protocol in the mmWave frequency band, which can solve the low latency and high data rate problems of raw sensing data sharing among CAVs. To evaluate the timeliness of raw sensing data transmission, the best time duration allocation ratio of sensing and communication dual functions for one vehicle is achieved by modeling the M/M/1 queuing problem using the age of information (AoI) in this paper. Furthermore, the resource allocation optimization problem among multiple CAVs is formulated as a non-cooperative game using the radar mutual information as a key indicator. And the feasibility and existence of pure strategy Nash equilibrium (NE) are proved theoretically, and a centralized time resource allocation (CTRA) algorithm is proposed to achieve the best feasible pure strategy NE. Finally, both simulation and hardware testbed are designed, and the results show that the proposed CTRA algorithm can improve the radar total mutual information by 26%, and the feasibility of the proposed JSCIS is achieved with an acceptable radar ranging accuracy within 0.25 m, as well as a stable data rate of 2.8 Gbps using the 28 GHz mmWave frequency band.

eess.SY↗

arXiv2021

Studying Duplicate Logging Statements and Their Relationships with Code Clones

In this paper, we focus on studying duplicate logging statements, which are logging statements that have the same static text message. We manually studied over 4K duplicate logging statements and their surrounding code in five large-scale open source systems. We uncovered five patterns of duplicate logging code smells. For each instance of the duplicate logging code smell, we further manually identify the potentially problematic and justifiable cases. Then, we contact developers to verify our manual study result. We integrated our manual study result and the feedback of developers into our automated static analysis tool, DLFinder, which automatically detects problematic duplicate logging code smells. We evaluated DLFinder on the five manually studied systems and three additional systems. In total, combining the results of DLFinder and our manual analysis, we reported 91 problematic duplicate logging code smell instances to developers and all of them have been fixed. We further study the relationship between duplicate logging statements, including the problematic instances of duplicate logging code smells, and code clones. We find that 83% of the duplicate logging code smell instances reside in cloned code, but 17% of them reside in micro-clones that are difficult to detect using automated clone detection tools. We also find that more than half of the duplicate logging statements reside in cloned code snippets, and a large portion of them reside in very short code blocks which may not be effectively detected by existing code clone detection tools. Our study shows that, in addition to general source code that implements the business logic, code clones may also result in bad logging practices that could increase maintenance difficulties.

cs.SE↗

arXiv2019

Improving Neural Machine Translation Robustness via Data Augmentation: Beyond Back Translation

Neural Machine Translation (NMT) models have been proved strong when translating clean texts, but they are very sensitive to noise in the input. Improving NMT models robustness can be seen as a form of "domain" adaption to noise. The recently created Machine Translation on Noisy Text task corpus provides noisy-clean parallel data for a few language pairs, but this data is very limited in size and diversity. The state-of-the-art approaches are heavily dependent on large volumes of back-translated data. This paper has two main contributions: Firstly, we propose new data augmentation methods to extend limited noisy data and further improve NMT robustness to noise while keeping the models small. Secondly, we explore the effect of utilizing noise from external data in the form of speech transcripts and show that it could help robustness.

cs.CL↗