arXiv subjects

Yujia Zhai

Publications and source records attributed to Yujia Zhai.

27 records · Page 2Linked to original sources

arXiv2021

Multi-parameter flag Leibniz rules of arbitrary complexity in mixed-norm spaces

We prove multi-parameter Leibniz rules corresponding to flag paraproducts of arbitrary complexity in mixed-norm spaces, including endpoint estimates. The proof relies on multi-linear harmonic analysis techniques and a quantitative treatment of the commutators introduced by Bourgain and Li. The argument is robust and applicable to a generic class of multipliers, including (symmetric) Mikhlin multipliers of positive order and asymmetric variants of partial differential operators and Mikhlin multipliers of positive order.

math.CA↗

arXiv2021

FT-BLAS: A High Performance BLAS Implementation With Online Fault Tolerance

Basic Linear Algebra Subprograms (BLAS) is a core library in scientific computing and machine learning. This paper presents FT-BLAS, a new implementation of BLAS routines that not only tolerates soft errors on the fly, but also provides comparable performance to modern state-of-the-art BLAS libraries on widely-used processors such as Intel Skylake and Cascade Lake. To accommodate the features of BLAS, which contains both memory-bound and computing-bound routines, we propose a hybrid strategy to incorporate fault tolerance into our brand-new BLAS implementation: duplicating computing instructions for memory-bound Level-1 and Level-2 BLAS routines and incorporating an Algorithm-Based Fault Tolerance mechanism for computing-bound Level-3 BLAS routines. Our high performance and low overhead are obtained from delicate assembly-level optimization and a kernel-fusion approach to the computing kernels. Experimental results demonstrate that FT-BLAS offers high reliability and high performance -- faster than Intel MKL, OpenBLAS, and BLIS by up to 3.50%, 22.14% and 21.70%, respectively, for routines spanning all three levels of BLAS we benchmarked, even under hundreds of errors injected per minute.

cs.DC↗

arXiv2021

Innovation adoption: Broadcasting vs. Virality

Diffusion channels are critical to determining the adoption scale which leads to the ultimate impact of an innovation. The aim of this study is to develop an integrative understanding of the impact of two diffusion channels (i.e., broadcasting vs virality) on innovation adoption. Using citations of a series of classic algorithms and the time series of co-authorship as the footprints of their diffusion trajectories, we propose a novel method to analyze the intertwining relationships between broadcasting and virality in the innovation diffusion process. Our findings show that broadcasting and virality have similar diffusion power, but play different roles across diffusion stages. Broadcasting is more powerful in the early stages but may be gradually caught up or even surpassed by virality in the later period. Meanwhile, diffusion speed in virality is significantly faster than broadcasting and members from virality channels tend to adopt the same innovation repetitively.

cs.SI↗

arXiv2021

Five-Linear Singular Integral Estimates of Brascamp-Lieb Type

We prove the full range of estimates for a five-linear singular integral of Brascamp-Lieb type. The study is methodology-oriented with the goal to develop a sufficiently general technique to estimate singular integral variants of Brascamp-Lieb inequalities that do not obey Hölder scaling. The invented methodology constructs localized analysis on the entire space from local information on its subspaces of lower dimensions and combines such tensor-type arguments with the generic localized analysis. A direct consequence of the boundedness of the five-linear singular integral is a Leibniz rule which captures nonlinear interactions of waves from transversal directions.

math.CA↗

arXiv2020

Biparameter $\text{BMO}$ under the action of a rotation

In this work, we aim to study the action of composing by a rotation on the biparameter $\text{BMO}$ space in $\mathbb{R}^2$. This $\text{BMO}$ space is not preserved by a rotation since it relies on the structure of axis-parallel rectangles. We will quantify this fact by interpolation inequalities. One straightforward application of the interpolation inequalities is a boundedness property of directional Hilbert transforms.

math.CA↗

arXiv2020

FT-CNN: Algorithm-Based Fault Tolerance for Convolutional Neural Networks

Convolutional neural networks (CNNs) are becoming more and more important for solving challenging and critical problems in many fields. CNN inference applications have been deployed in safety-critical systems, which may suffer from soft errors caused by high-energy particles, high temperature, or abnormal voltage. Of critical importance is ensuring the stability of the CNN inference process against soft errors. Traditional fault tolerance methods are not suitable for CNN inference because error-correcting code is unable to protect computational components, instruction duplication techniques incur high overhead, and existing algorithm-based fault tolerance (ABFT) techniques cannot protect all convolution implementations. In this paper, we focus on how to protect the CNN inference process against soft errors as efficiently as possible, with the following three contributions. (1) We propose several systematic ABFT schemes based on checksum techniques and analyze their fault protection ability and runtime thoroughly.Unlike traditional ABFT based on matrix-matrix multiplication, our schemes support any convolution implementations. (2) We design a novel workflow integrating all the proposed schemes to obtain a high detection/correction ability with limited total runtime overhead. (3) We perform our evaluation using ImageNet with well-known CNN models including AlexNet, VGG-19, ResNet-18, and YOLOv2. Experimental results demonstrate that our implementation can handle soft errors with very limited runtime overhead (4%~8% in both error-free and error-injected situations).

cs.DC↗

arXiv2020

Analysis of misinformation during the COVID-19 outbreak in China: cultural, social and political entanglements

COVID-19 resulted in an infodemic, which could erode public trust, impede virus containment, and outlive the pandemic itself. The evolving and fragmented media landscape is a key driver of the spread of misinformation. Using misinformation identified by the fact-checking platform by Tencent and posts on Weibo, our results showed that the evolution of misinformation follows an issue-attention cycle, pertaining to topics such as city lockdown, cures, and preventions, and school reopening. Sources of authority weigh in on these topics, but their influence is complicated by peoples' pre-existing beliefs and cultural practices. Finally, social media has a complicated relationship with established or legacy media systems. Sometimes they reinforce each other, but in general, social media may have a topic cycle of its own making. Our findings shed light on the distinct characteristics of misinformation during the COVID-19 and offer insights into combating misinformation in China and across the world at large.

cs.SI↗

arXiv2020

Normalization of Input-output Shared Embeddings in Text Generation Models

Neural Network based models have been state-of-the-art models for various Natural Language Processing tasks, however, the input and output dimension problem in the networks has still not been fully resolved, especially in text generation tasks (e.g. Machine Translation, Text Summarization), in which input and output both have huge sizes of vocabularies. Therefore, input-output embedding weight sharing has been introduced and adopted widely, which remains to be improved. Based on linear algebra and statistical theories, this paper locates the shortcoming of existed input-output embedding weight sharing method, then raises methods for improving input-output weight shared embedding, among which methods of normalization of embedding weight matrices show best performance. These methods are nearly computational cost-free, can get combined with other embedding techniques, and show good effectiveness when applied on state-of-the-art Neural Network models. For Transformer-big models, the normalization techniques can get at best 0.6 BLEU improvement compared to the original version of model on WMT'16 En-De dataset, and similar BLEU improvements on IWSLT 14' datasets. For DynamicConv models, 0.5 BLEU improvement can be attained on WMT'16 En-De dataset, and 0.41 BLEU improvement on IWSLT 14' De-En translation task is achieved.

cs.CL↗

arXiv2012

Areas of triangles and Beck's theorem in planes over finite fields

It is shown that any subset $E$ of a plane over a finite field $\F_q$, of cardinality $|E|>q$ determines not less than $\frac{q-1}{2}$ distinct areas of triangles, moreover once can find such triangles sharing a common base. It is also shown that if $|E|\geq 64q\log_2 q$, then there are more than $\frac{q}{2}$ distinct areas of triangles sharing a common vertex. The result follows from a finite field version of the Beck theorem for large subsets of $\F_q^2$ that we prove. If $|E|\geq 64q\log_2 q$, there exists a point $z\in E$, such that there are at least $\frac{q}{4}$ straight lines incident to $z$, each supporting the number of points of $E$ other than $z$ in the interval between $\frac{|E|}{2q}$ and $\frac{2|E|}{q}.$ This is proved by combining combinatorial and Fourier analytic techniques. We also discuss higher-dimensional implications of these results in light of recent developments.

math.CO↗