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Intelligent agents stand out as a potential path toward artificial general intelligence (AGI). Thus, researchers have dedicated significant effort to diverse implementations for them. Benefiting from recent progress in large language models (LLMs), LLM-based agents that use universal natural language as an interface exhibit robust generalization capabilities across various applications -- from serving as autonomous general-purpose task assistants to applications in coding, social, and economic domains, LLM-based agents offer extensive exploration opportunities. This paper surveys current research to provide an in-depth overview of LLM-based intelligent agents within single-agent and multi-agent systems. It covers their definitions, research frameworks, and foundational components such as their composition, cognitive and planning methods, tool utilization, and responses to environmental feedback. We also delve into the mechanisms of deploying LLM-based agents in multi-agent systems, including multi-role collaboration, message passing, and strategies to alleviate communication issues between agents. The discussions also shed light on popular datasets and application scenarios. We conclude by envisioning prospects for LLM-based agents, considering the evolving landscape of AI and natural language processing.

Modern society's reliance on power systems is at risk from the escalating effects of wind-related climate change. Yet, failure to identify the intricate relationship between wind-related climate risks and power systems could lead to serious short- and long-term issues, including partial or complete blackouts. Here, we develop a comprehensive framework to assess China's power system resilience across various climate change scenarios, enabling a holistic evaluation of the repercussions induced by wind-related climate change. Our findings indicate that China's current wind projects and planning strategies could be jeopardized by wind-related climate change, with up to a 12\% decline in regional wind power availability. Moreover, our results underscore a pronounced vulnerability of power system resilience amidst the rigors of hastened climate change, unveiling a potential amplification of resilience deterioration, even approaching fourfold by 2060 under the most severe scenario, relative to the 2020 benchmark. This work advocates for strategic financial deployment within the power sector aimed at climate adaptation, enhancing power system resilience to avert profound losses from long-term, wind-influenced climatic fluctuations., Comment: Not suitable for publication

Based on good algebraic structures and practicabilities, generalized quasi-cyclic (GQC) codes play important role in coding theory. In this paper, we study some results on GQC codes over $\mathbb{Z}_4$ including the normalized generating set, the minimum generating set and the normalized generating set of their dual codes. As an application, new $\mathbb{Z}_4$-linear codes and good nonlinear binary codes are constructed from GQC codes over $\mathbb{Z}_4$.

Statistical moments are widely used in descriptive statistics. Therefore efficient and numerically stable implementations are important in practice. Pebay [1] derives online update formulas for arbitrary-order central moments. We present a simpler version that is also easier to implement.

We describe matrix computations available in the cluster programming framework, Apache Spark. Out of the box, Spark provides abstractions and implementations for distributed matrices and optimization routines using these matrices. When translating single-node algorithms to run on a distributed cluster, we observe that often a simple idea is enough: separating matrix operations from vector operations and shipping the matrix operations to be ran on the cluster, while keeping vector operations local to the driver. In the case of the Singular Value Decomposition, by taking this idea to an extreme, we are able to exploit the computational power of a cluster, while running code written decades ago for a single core. Another example is our Spark port of the popular TFOCS optimization package, originally built for MATLAB, which allows for solving Linear programs as well as a variety of other convex programs. We conclude with a comprehensive set of benchmarks for hardware accelerated matrix computations from the JVM, which is interesting in its own right, as many cluster programming frameworks use the JVM. The contributions described in this paper are already merged into Apache Spark and available on Spark installations by default, and commercially supported by a slew of companies which provide further services.

Apache Spark is a popular open-source platform for large-scale data processing that is well-suited for iterative machine learning tasks. In this paper we present MLlib, Spark's open-source distributed machine learning library. MLlib provides efficient functionality for a wide range of learning settings and includes several underlying statistical, optimization, and linear algebra primitives. Shipped with Spark, MLlib supports several languages and provides a high-level API that leverages Spark's rich ecosystem to simplify the development of end-to-end machine learning pipelines. MLlib has experienced a rapid growth due to its vibrant open-source community of over 140 contributors, and includes extensive documentation to support further growth and to let users quickly get up to speed.

In this era of large-scale data, distributed systems built on top of clusters of commodity hardware provide cheap and reliable storage and scalable processing of massive data. Here, we review recent work on developing and implementing randomized matrix algorithms in large-scale parallel and distributed environments. Randomized algorithms for matrix problems have received a great deal of attention in recent years, thus far typically either in theory or in machine learning applications or with implementations on a single machine. Our main focus is on the underlying theory and practical implementation of random projection and random sampling algorithms for very large very overdetermined (i.e., overconstrained) $\ell_1$ and $\ell_2$ regression problems. Randomization can be used in one of two related ways: either to construct sub-sampled problems that can be solved, exactly or approximately, with traditional numerical methods; or to construct preconditioned versions of the original full problem that are easier to solve with traditional iterative algorithms. Theoretical results demonstrate that in near input-sparsity time and with only a few passes through the data one can obtain very strong relative-error approximate solutions, with high probability. Empirical results highlight the importance of various trade-offs (e.g., between the time to construct an embedding and the conditioning quality of the embedding, between the relative importance of computation versus communication, etc.) and demonstrate that $\ell_1$ and $\ell_2$ regression problems can be solved to low, medium, or high precision in existing distributed systems on up to terabyte-sized data.

Quantile regression is a method to estimate the quantiles of the conditional distribution of a response variable, and as such it permits a much more accurate portrayal of the relationship between the response variable and observed covariates than methods such as Least-squares or Least Absolute Deviations regression. It can be expressed as a linear program, and, with appropriate preprocessing, interior-point methods can be used to find a solution for moderately large problems. Dealing with very large problems, \emph(e.g.), involving data up to and beyond the terabyte regime, remains a challenge. Here, we present a randomized algorithm that runs in nearly linear time in the size of the input and that, with constant probability, computes a $(1+\epsilon)$ approximate solution to an arbitrary quantile regression problem. As a key step, our algorithm computes a low-distortion subspace-preserving embedding with respect to the loss function of quantile regression. Our empirical evaluation illustrates that our algorithm is competitive with the best previous work on small to medium-sized problems, and that in addition it can be implemented in MapReduce-like environments and applied to terabyte-sized problems., Comment: 35 pages; long version of a paper appearing in the 2013 ICML. Version to appear in the SIAM Journal on Scientific Computing

Low-distortion embeddings are critical building blocks for developing random sampling and random projection algorithms for linear algebra problems. We show that, given a matrix $A \in \R^{n \times d}$ with $n \gg d$ and a $p \in [1, 2)$, with a constant probability, we can construct a low-distortion embedding matrix $\Pi \in \R^{O(\poly(d)) \times n}$ that embeds $\A_p$, the $\ell_p$ subspace spanned by $A$'s columns, into $(\R^{O(\poly(d))}, \| \cdot \|_p)$; the distortion of our embeddings is only $O(\poly(d))$, and we can compute $\Pi A$ in $O(\nnz(A))$ time, i.e., input-sparsity time. Our result generalizes the input-sparsity time $\ell_2$ subspace embedding by Clarkson and Woodruff [STOC'13]; and for completeness, we present a simpler and improved analysis of their construction for $\ell_2$. These input-sparsity time $\ell_p$ embeddings are optimal, up to constants, in terms of their running time; and the improved running time propagates to applications such as $(1\pm \epsilon)$-distortion $\ell_p$ subspace embedding and relative-error $\ell_p$ regression. For $\ell_2$, we show that a $(1+\epsilon)$-approximate solution to the $\ell_2$ regression problem specified by the matrix $A$ and a vector $b \in \R^n$ can be computed in $O(\nnz(A) + d^3 \log(d/\epsilon) /\epsilon^2)$ time; and for $\ell_p$, via a subspace-preserving sampling procedure, we show that a $(1\pm \epsilon)$-distortion embedding of $\A_p$ into $\R^{O(\poly(d))}$ can be computed in $O(\nnz(A) \cdot \log n)$ time, and we also show that a $(1+\epsilon)$-approximate solution to the $\ell_p$ regression problem $\min_{x \in \R^d} \|A x - b\|_p$ can be computed in $O(\nnz(A) \cdot \log n + \poly(d) \log(1/\epsilon)/\epsilon^2)$ time. Moreover, we can improve the embedding dimension or equivalently the sample size to $O(d^{3+p/2} \log(1/\epsilon) / \epsilon^2)$ without increasing the complexity., Comment: 22 pages

We provide fast algorithms for overconstrained $\ell_p$ regression and related problems: for an $n\times d$ input matrix $A$ and vector $b\in\mathbb{R}^n$, in $O(nd\log n)$ time we reduce the problem $\min_{x\in\mathbb{R}^d} \|Ax-b\|_p$ to the same problem with input matrix $\tilde A$ of dimension $s \times d$ and corresponding $\tilde b$ of dimension $s\times 1$. Here, $\tilde A$ and $\tilde b$ are a coreset for the problem, consisting of sampled and rescaled rows of $A$ and $b$; and $s$ is independent of $n$ and polynomial in $d$. Our results improve on the best previous algorithms when $n\gg d$, for all $p\in[1,\infty)$ except $p=2$. We also provide a suite of improved results for finding well-conditioned bases via ellipsoidal rounding, illustrating tradeoffs between running time and conditioning quality, including a one-pass conditioning algorithm for general $\ell_p$ problems. We also provide an empirical evaluation of implementations of our algorithms for $p=1$, comparing them with related algorithms. Our empirical results show that, in the asymptotic regime, the theory is a very good guide to the practical performance of these algorithms. Our algorithms use our faster constructions of well-conditioned bases for $\ell_p$ spaces and, for $p=1$, a fast subspace embedding of independent interest that we call the Fast Cauchy Transform: a distribution over matrices $\Pi:\mathbb{R}^n\mapsto \mathbb{R}^{O(d\log d)}$, found obliviously to $A$, that approximately preserves the $\ell_1$ norms: that is, with large probability, simultaneously for all $x$, $\|Ax\|_1 \approx \|\Pi Ax\|_1$, with distortion $O(d^{2+\eta})$, for an arbitrarily small constant $\eta>0$; and, moreover, $\Pi A$ can be computed in $O(nd\log d)$ time. The techniques underlying our Fast Cauchy Transform include fast Johnson-Lindenstrauss transforms, low-coherence matrices, and rescaling by Cauchy random variables., Comment: 48 pages; substantially extended and revised; short version in SODA 2013

We modify Nesterov's constant step gradient method for strongly convex functions with Lipschitz continuous gradient described in Nesterov's book. Nesterov shows that $f(x_k) - f^* \leq L \prod_{i=1}^k (1 - \alpha_k) \| x_0 - x^* \|_2^2$ with $\alpha_k = \sqrt{\rho}$ for all $k$, where $L$ is the Lipschitz gradient constant and $\rho$ is the reciprocal condition number of $f(x)$. Hence the convergence rate is $1-\sqrt{\rho}$. In this work, we try to accelerate Nesterov's method by adaptively searching for an $\alpha_k > \sqrt{\rho}$ at each iteration. The proposed method evaluates the gradient function at most twice per iteration and has some extra Level 1 BLAS operations. Theoretically, in the worst case, it takes the same number of iterations as Nesterov's method does but doubles the gradient calls. However, in practice, the proposed method effectively accelerates the speed of convergence for many problems including a smoothed basis pursuit denoising problem.

We describe a parallel iterative least squares solver named \texttt{LSRN} that is based on random normal projection. \texttt{LSRN} computes the min-length solution to $\min_{x \in \mathbb{R}^n} \|A x - b\|_2$, where $A \in \mathbb{R}^{m \times n}$ with $m \gg n$ or $m \ll n$, and where $A$ may be rank-deficient. Tikhonov regularization may also be included. Since $A$ is only involved in matrix-matrix and matrix-vector multiplications, it can be a dense or sparse matrix or a linear operator, and \texttt{LSRN} automatically speeds up when $A$ is sparse or a fast linear operator. The preconditioning phase consists of a random normal projection, which is embarrassingly parallel, and a singular value decomposition of size $\lceil \gamma \min(m,n) \rceil \times \min(m,n)$, where $\gamma$ is moderately larger than 1, e.g., $\gamma = 2$. We prove that the preconditioned system is well-conditioned, with a strong concentration result on the extreme singular values, and hence that the number of iterations is fully predictable when we apply LSQR or the Chebyshev semi-iterative method. As we demonstrate, the Chebyshev method is particularly efficient for solving large problems on clusters with high communication cost. Numerical results demonstrate that on a shared-memory machine, \texttt{LSRN} outperforms LAPACK's DGELSD on large dense problems, and MATLAB's backslash (SuiteSparseQR) on sparse problems. Further experiments demonstrate that \texttt{LSRN} scales well on an Amazon Elastic Compute Cloud cluster., Comment: 19 pages