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Rong Chen

Publications and source records attributed to Rong Chen.

At least 73 records · Page 4Linked to original sources
arXiv2024

Congruences modulo powers of $5$ and $7$ for the crank and rank parity functions and related mock theta functions

It is well known that Ramanujan conjectured congruences modulo powers of $5$, $7$ and and $11$ for the partition function. These were subsequently proved by Watson (1938) and Atkin (1967). In 2009 Choi, Kang, and Lovejoy proved congruences modulo powers of $5$ for the crank parity function. The generating function for the analogous rank parity function is $f(q)$, the first example of a mock theta function that Ramanujan mentioned in his last letter to Hardy. Recently we proved congruences modulo powers of $5$ for the rank parity function, and here we extend these congruences for powers of $7$. We also show how these congruences imply congruences modulo powers of $5$ and $7$ for the coefficients of the related third order mock theta function $ω(q)$, using Atkin-Lehner involutions and transformation results of Zwegers. Finally we a prove a family of congruences modulo powers of $7$ for the crank parity function.

math.NT↗
arXiv2024

Characterizing the Dilemma of Performance and Index Size in Billion-Scale Vector Search and Breaking It with Second-Tier Memory

Vector searches on large-scale datasets are critical to modern online services like web search and RAG, which necessity storing the datasets and their index on the secondary storage like SSD. In this paper, we are the first to characterize the trade-off of performance and index size in existing SSD-based graph and cluster indexes: to improve throughput by 5.7$\times$ and 1.7$\times$, these indexes have to pay a 5.8$\times$ storage amplification and 7.7$\times$ with respect to the dataset size, respectively. The root cause is that the coarse-grained access of SSD mismatches the fine-grained random read required by vector indexes with small amplification. This paper argues that second-tier memory, such as remote DRAM/NVM connected via RDMA or CXL, is a powerful storage for addressing the problem from a system's perspective, thanks to its fine-grained access granularity. However, putting existing indexes -- primarily designed for SSD -- directly on second-tier memory cannot fully utilize its power. Meanwhile, second-tier memory still behaves more like storage, so using it as DRAM is also inefficient. To this end, we build a graph and cluster index that centers around the performance features of second-tier memory. With careful execution engine and index layout designs, we show that vector indexes can achieve optimal performance with orders of magnitude smaller index amplification, on a variety of second-tier memory devices. Based on our improved graph and vector indexes on second-tier memory, we further conduct a systematic study between them to facilitate developers choosing the right index for their workloads. Interestingly, the findings on the second-tier memory contradict the ones on SSDs.

cs.DC↗
arXiv2024

CP Factor Model for Dynamic Tensors

Observations in various applications are frequently represented as a time series of multidimensional arrays, called tensor time series, preserving the inherent multidimensional structure. In this paper, we present a factor model approach, in a form similar to tensor CP decomposition, to the analysis of high-dimensional dynamic tensor time series. As the loading vectors are uniquely defined but not necessarily orthogonal, it is significantly different from the existing tensor factor models based on Tucker-type tensor decomposition. The model structure allows for a set of uncorrelated one-dimensional latent dynamic factor processes, making it much more convenient to study the underlying dynamics of the time series. A new high order projection estimator is proposed for such a factor model, utilizing the special structure and the idea of the higher order orthogonal iteration procedures commonly used in Tucker-type tensor factor model and general tensor CP decomposition procedures. Theoretical investigation provides statistical error bounds for the proposed methods, which shows the significant advantage of utilizing the special model structure. Simulation study is conducted to further demonstrate the finite sample properties of the estimators. Real data application is used to illustrate the model and its interpretations.

stat.ME↗
arXiv2024

Time-Varying Matrix Factor Models

Matrix-variate data of high dimensions are frequently observed in finance and economics, spanning extended time periods, such as the long-term data on international trade flows among numerous countries. To address potential structural shifts and explore the matrix structure's informational context, we propose a time-varying matrix factor model. This model accommodates changing factor loadings over time, revealing the underlying dynamic structure through nonparametric principal component analysis and facilitating dimension reduction. We establish the consistency and asymptotic normality of our estimators under general conditions that allow for weak correlations across time, rows, or columns of the noise. A novel approach is introduced to overcome rotational ambiguity in the estimators, enhancing the clarity and interpretability of the estimated loading matrices. Our simulation study highlights the merits of the proposed estimators and the effective of the smoothing operation. In an application to international trade flow, we investigate the trading hubs, centrality, patterns, and trends in the trading network.

stat.ME↗
arXiv2024

Characterizing Network Requirements for GPU API Remoting in AI Applications

GPU remoting is a promising technique for supporting AI applications. Networking plays a key role in enabling remoting. However, for efficient remoting, the network requirements in terms of latency and bandwidth are unknown. In this paper, we take a GPU-centric approach to derive the minimum latency and bandwidth requirements for GPU remoting, while ensuring no (or little) performance degradation for AI applications. Our study including theoretical model demonstrates that, with careful remoting design, unmodified AI applications can run on the remoting setup using commodity networking hardware without any overhead or even with better performance, with low network demands.

cs.OS↗
arXiv2024

Cross-target Stance Detection by Exploiting Target Analytical Perspectives

Cross-target stance detection (CTSD) is an important task, which infers the attitude of the destination target by utilizing annotated data derived from the source target. One important approach in CTSD is to extract domain-invariant features to bridge the knowledge gap between multiple targets. However, the analysis of informal and short text structure, and implicit expressions, complicate the extraction of domain-invariant knowledge. In this paper, we propose a Multi-Perspective Prompt-Tuning (MPPT) model for CTSD that uses the analysis perspective as a bridge to transfer knowledge. First, we develop a two-stage instruct-based chain-of-thought method (TsCoT) to elicit target analysis perspectives and provide natural language explanations (NLEs) from multiple viewpoints by formulating instructions based on large language model (LLM). Second, we propose a multi-perspective prompt-tuning framework (MultiPLN) to fuse the NLEs into the stance predictor. Extensive experiments results demonstrate the superiority of MPPT against the state-of-the-art baseline methods.

cs.CL↗
arXiv2023

Graphs with girth $2\ell+1$ and without longer odd holes that contain an odd $K_4$-subdivision

We say that a graph $G$ has an {\em odd $K_4$-subdivision} if some subgraph of $G$ is isomorphic to a $K_4$-subdivision and whose faces are all odd holes of $G$. For a number $\ell\geq 2$, let $\mathcal{G}_{\ell}$ denote the family of graphs which have girth $2\ell+1$ and have no odd hole with length greater than $2\ell+1$. Wu, Xu and Xu conjectured that every graph in $\bigcup_{\ell\geq2}\mathcal{G}_{\ell}$ is 3-colorable. Recently, Chudnovsky et al. and Wu et al., respectively, proved that every graph in $\mathcal{G}_2$ and $\mathcal{G}_3$ is 3-colorable. In this paper, we prove that no $4$-vertex-critical graph in $\bigcup_{\ell\geq5}\mathcal{G}_{\ell}$ has an odd $K_4$-subdivision. Using this result, Chen proved that all graphs in $\bigcup_{\ell\geq5}\mathcal{G}_{\ell}$ are 3-colorable.

math.CO↗
arXiv2023

LSCD: A Large-Scale Screen Content Dataset for Video Compression

Multimedia compression allows us to watch videos, see pictures and hear sounds within a limited bandwidth, which helps the flourish of the internet. During the past decades, multimedia compression has achieved great success using hand-craft features and systems. With the development of artificial intelligence and video compression, there emerges a lot of research work related to using the neural network on the video compression task to get rid of the complicated system. Not only producing the advanced algorithms, but researchers also spread the compression to different content, such as User Generated Content(UGC). With the rapid development of mobile devices, screen content videos become an important part of multimedia data. In contrast, we find community lacks a large-scale dataset for screen content video compression, which impedes the fast development of the corresponding learning-based algorithms. In order to fulfill this blank and accelerate the research of this special type of videos, we propose the Large-scale Screen Content Dataset(LSCD), which contains 714 source sequences. Meanwhile, we provide the analysis of the proposed dataset to show some features of screen content videos, which will help researchers have a better understanding of how to explore new algorithms. Besides collecting and post-processing the data to organize the dataset, we also provide a benchmark containing the performance of both traditional codec and learning-based methods.

cs.MM↗
arXiv2023

Transactional Indexes on (RDMA or CXL-based) Disaggregated Memory with Repairable Transaction

The failure atomic and isolated execution of clients operations is a default requirement for a system that serve multiple loosely coupled clients at a server. However, disaggregated memory breaks this requirement in remote indexes because a client operation is disaggregated to multiple remote reads/writes. Current indexes focus on performance improvements and largely ignore tolerating client failures. We argue that a practical DM index should be transactional: each index operation should be failure atomic and isolated in addition to being concurrency isolated. We present repairable transaction (rTX), a lightweight primitive to execute DM index operations. Each rTX can detect other failed rTXes on-the-fly with the help of concurrency control. Upon detection, it will repair their non-atomic updates online with the help of logging, thus hiding their failures from healthy clients. By further removing unnecessary logging and delegating concurrency control to existing carefully-tuned index algorithms, we show that transactional indexes can be built at a low performance overhead on disaggregated memory. We have refactored two state-of-the-art DM indexes, RaceHashing and Sherman (B+Tree), with rTX. Evaluations show that rTX is 1.2 to 2X faster than other alternatives, e.g., distributed transaction. Meanwhile, its overhead is up to 42% compared to non-fault-tolerant indexes.

cs.DB↗
arXiv2023

Characterizing Off-path SmartNIC for Accelerating Distributed Systems

SmartNICs have recently emerged as an appealing device for accelerating distributed systems. However, there has not been a comprehensive characterization of SmartNICs, and existing designs typically only leverage a single communication path for workload offloading. This paper presents the first holistic study of a representative off-path SmartNIC, specifically the Bluefield-2, from a communication-path perspective. Our experimental study systematically explores the key performance characteristics of communication among the client, on-board SoC, and host, and offers insightful findings and advice for designers. Moreover, we propose the concurrent use of multiple communication paths of a SmartNIC and present a pioneering guideline to expose new optimization opportunities for various distributed systems. To demonstrate the effectiveness of our approach, we conducted case studies on a SmartNIC-based distributed file system (LineFS) and an RDMA-based disaggregated key-value store (DrTM-KV). Our experimental results show improvements of up to 30% and 25% for LineFS and DrTM-KV, respectively.

cs.DC↗
arXiv2023

NPSA: Nonparametric Simulated Annealing for Global Optimization

In this paper we describe NPSA, the first parallel nonparametric global maximum likelihood optimization algorithm using simulated annealing (SA). Unlike the nonparametric adaptive grid search method NPAG, which is not guaranteed to find a global optimum solution, and may suffer from the curse of dimensionality, NPSA is a global optimizer and it is free from these grid related issues. We illustrate NPSA by a number of examples including a pharmacokinetics (PK) model for Voriconazole and show that NPSA may be taken as an upgrade to the current grid search based nonparametric methods.

stat.ME↗
arXiv2022

Graphs with girth $2\ell+1$ and without longer odd holes are $3$-colorable

For a number $\ell\geq 2$, let $\mathcal{G}_{\ell}$ denote the family of graphs which have girth $2\ell+1$ and have no odd hole with length greater than $2\ell+1$. Plummer and Zha conjectured that every 3-connected and internally 4-connected graph in $\mathcal{G}_2$ is 3-colorable. Wu, Xu, and Xu conjectured that every graph in $\bigcup_{\ell\geq2}\mathcal{G}_{\ell}$ is 3-colorable. Chudnovsky et al. and Wu et al., respectively, proved that every graph in $\mathcal{G}_2$ and $\mathcal{G}_3$ is 3-colorable. In this paper, we prove that every graph in $\bigcup_{\ell\geq5}\mathcal{G}_{\ell}$ is 3-colorable.

math.CO↗
arXiv2022

RPEM: Randomized Monte Carlo Parametric Expectation Maximization Algorithm

Inspired from quantum Monte Carlo, by using unbiased estimators all the time and sampling discrete and continuous variables at the same time using Metropolis algorithm, we present a novel, fast, and accurate high performance Monte Carlo Parametric Expectation Maximization (MCPEM) algorithm. We named it Randomized Parametric Expectation Maximization (RPEM). In particular, we compared RPEM with Monolix's SAEM and Certara's QRPEM for a realistic two-compartment Voriconazole model with ordinary differential equations (ODEs) and using simulated data. We show that RPEM is 3 to 4 times faster than SAEM and QRPEM, and more accurate than them in reconstructing the population parameters.

stat.ME↗
arXiv2022

Simultaneous Decorrelation of Matrix Time Series

We propose a contemporaneous bilinear transformation for a $p\times q$ matrix time series to alleviate the difficulties in modeling and forecasting matrix time series when $p$ and/or $q$ are large. The resulting transformed matrix assumes a block structure consisting of several small matrices, and those small matrix series are uncorrelated across all times. Hence an overall parsimonious model is achieved by modelling each of those small matrix series separately without the loss of information on the linear dynamics. Such a parsimonious model often has better forecasting performance, even when the underlying true dynamics deviates from the assumed uncorrelated block structure after transformation. The uniform convergence rates of the estimated transformation are derived, which vindicate an important virtue of the proposed bilinear transformation, i.e. it is technically equivalent to the decorrelation of a vector time series of dimension max$(p,q)$ instead of $p\times q$. The proposed method is illustrated numerically via both simulated and real data examples.

stat.ME↗
arXiv2022

Path Integral Quantum Monte Carlo Calculations of Light Nuclei

We describe a path-integral ground-state quantum Monte Carlo method for light nuclei in continuous space. We show how to efficiently update and sample the paths with spin-isospin dependent and spin-orbit interactions. We apply the method to the triton and alpha particle using both local chiral interactions with next-to-next-to-leading-order %(N$^2$LO) and the Argonne interactions. For operators, like the total energy, that commute with the Hamiltonian, our results agree with Green's function Monte Carlo and auxiliary field diffusion Monte Carlo calculations. For operators that do not commute with the Hamiltonian and for Euclidean response functions, the path-integral formulation allows straightforward calculation without forward walking or the increased variance typical of diffusion methods. We demonstrate this by calculating density distributions, root mean square radii, and Euclidean response functions for single-nucleon couplings.

nucl-th↗
arXiv2022

Constrained Factor Models for High-Dimensional Matrix-Variate Time Series

High-dimensional matrix-variate time series data are becoming widely available in many scientific fields, such as economics, biology, and meteorology. To achieve significant dimension reduction while preserving the intrinsic matrix structure and temporal dynamics in such data, Wang et al. (2017) proposed a matrix factor model that is shown to provide effective analysis. In this paper, we establish a general framework for incorporating domain or prior knowledge in the matrix factor model through linear constraints. The proposed framework is shown to be useful in achieving parsimonious parameterization, facilitating interpretation of the latent matrix factor, and identifying specific factors of interest. Fully utilizing the prior-knowledge-induced constraints results in more efficient and accurate modeling, inference, dimension reduction as well as a clear and better interpretation of the results. In this paper, constrained, multi-term, and partially constrained factor models for matrix-variate time series are developed, with efficient estimation procedures and their asymptotic properties. We show that the convergence rates of the constrained factor loading matrices are much faster than those of the conventional matrix factor analysis under many situations. Simulation studies are carried out to demonstrate the finite-sample performance of the proposed method and its associated asymptotic properties. We illustrate the proposed model with three applications, where the constrained matrix-factor models outperform their unconstrained counterparts in the power of variance explanation under the out-of-sample 10-fold cross-validation setting.

stat.ME↗