Related papers: LLM-Guided Evolutionary Program Synthesis for Quas…
SMC (Sequential Monte Carlo) is a class of Monte Carlo algorithms for filtering and related sequential problems. Gerber and Chopin (2015) introduced SQMC (Sequential quasi-Monte Carlo), a QMC version of SMC. This paper has two objectives:…
Quasi-Monte Carlo rules are equal weight quadrature rules defined over the domain $[0,1]^s$. Here we introduce quasi-Monte Carlo type rules for numerical integration of functions defined on $\mathbb{R}^s$. These rules are obtained by way of…
Quasi-Monte Carlo (QMC) integration over unbounded domains $\mathbb{R}^s$ remains challenging due to the high dimensionality of sampling space and the boundary growth of the integrand. In applications such as uncertainty quantification…
In recent years, large language models (LLMs) have demonstrated significant potential in complex reasoning tasks like mathematical problem-solving. However, existing research predominantly relies on reinforcement learning (RL) frameworks…
We derive and study SQMC (Sequential Quasi-Monte Carlo), a class of algorithms obtained by introducing QMC point sets in particle filtering. SQMC is related to, and may be seen as an extension of, the array-RQMC algorithm of L'Ecuyer et al.…
We consider the higher-order resummation of Sudakov double logarithms in the presence of multiple coupled gauge interactions. The associated evolution equations depend on the coupled $\beta$ functions of two (or more) coupling constants…
Families of "asymptotically regular" LDPC block code ensembles can be formed by terminating (J,K)-regular protograph-based LDPC convolutional codes. By varying the termination length, we obtain a large selection of LDPC block code ensembles…
As AI-based code generation becomes widespread, researchers are investigating the calibration of code LLMs - ensuring their confidence scores faithfully represent the true likelihood of code correctness. To do so, we investigate…
Non-convex optimization problems are pervasive across mathematical programming, engineering design, and scientific computing, often posing intractable challenges for traditional solvers due to their complex objective functions and…
Tackling complex optimization problems often relies on expert-designed heuristics, typically crafted through extensive trial and error. Recent advances demonstrate that large language models (LLMs), when integrated into well-designed…
LLM-based RTL code generation methods increasingly target both functional correctness and PPA quality, yet existing approaches universally decouple the two objectives, optimizing PPA only after correctness is fully achieved. Whether through…
Loop transformations are semantics-preserving optimization techniques, widely used to maximize objectives such as parallelism. Despite decades of research, applying the optimal composition of loop transformations remains challenging due to…
Supervised Fine-Tuning (SFT) Large Language Models (LLM) fundamentally rely on high-quality training data. While data selection and data synthesis are two common strategies to improve data quality, existing approaches often face limitations…
Optimizing a target function over the space of organic molecules is an important problem appearing in many fields of applied science, but also a very difficult one due to the vast number of possible molecular systems. We propose an…
Many machine learning problems optimize an objective that must be measured with noise. The primary method is a first order stochastic gradient descent using one or more Monte Carlo (MC) samples at each step. There are settings where…
An adaptive Monte Carlo localization algorithm based on coevolution mechanism of ecological species is proposed. Samples are clustered into species, each of which represents a hypothesis of the robots pose. Since the coevolution between the…
Quadrature Hybrid Couplers (QHDC) are critical components in RF, mm-wave, and sub-mm wave astronomical instrumentation, where wideband performance with minimal passband ripple is essential. Traditional designs have been limited to…
Large Language Models (LLMs) have demonstrated great promise in generating code, especially when used inside an evolutionary computation framework to iteratively optimize the generated algorithms. However, in some cases they fail to…
In this paper, we study an efficient algorithm for constructing node sets of high-quality quasi-Monte Carlo integration rules for weighted Korobov, Walsh, and Sobolev spaces. The algorithm presented is a reduced fast successive coordinate…
Quasi-Monte Carlo (QMC) is a powerful method for evaluating high-dimensional integrals. However, its use is typically limited to distributions where direct sampling is straightforward, such as the uniform distribution on the unit hypercube…