数据分析、统计与概率
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显示 2025年09月09日， 星期二 新的列表
- [1] arXiv:2509.05792 [中文pdf, pdf, html, 其他]
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标题： TPCpp-10M：用于人工智能基础模型的时隙投影室中的模拟质子-质子碰撞标题： TPCpp-10M: Simulated proton-proton collisions in a Time Projection Chamber for AI Foundation ModelsShuhang Li, Yi Huang, David Park, Xihaier Luo, Haiwang Yu, Yeonju Go, Christopher Pinkenburg, Yuewei Lin, Shinjae Yoo, Joseph Osborn, Christof Roland, Jin Huang, Yihui Ren主题： 数据分析、统计与概率 (physics.data-an)
科学基础模型在推动核物理和粒子物理发展方面具有巨大潜力，通过提高分析精度和加速发现。然而，该领域的发展往往受到缺乏公开可用的大规模数据集以及标准化评估任务和指标的限制。此外，处理粒子物理数据通常需要专门的知识和软件，这给与更广泛的机器学习社区进行跨学科合作带来了重大障碍。本工作介绍了一个包含1000万次模拟质子-质子碰撞的大规模、公开可访问的数据集，旨在支持基础模型的自监督训练。为了便于使用，该数据集以常见的NumPy格式提供。此外，它还包括70,000个标记示例，涵盖三个定义明确的下游任务：轨迹查找、粒子识别和噪声标记，以实现对基础模型适应性的系统评估。模拟数据是使用Pythia蒙特卡洛事件生成器在质心系能量为sqrt(s) = 200 GeV的情况下生成的，并通过Geant4进行处理，以在相对论重离子对撞机（位于布鲁克海文国家实验室）的sPHENIX时间投影室中包含现实的探测器条件和信号模拟。这个数据集资源为跨学科研究建立了共同基础，使机器学习科学家和物理学家都能探索扩展行为、评估可转移性，并加速向核物理和高能物理中的基础模型进展。完整的模拟和重建链可以通过sPHENIX软件堆栈进行再现。所有数据和代码位置均在数据可访问性下提供。
Scientific foundation models hold great promise for advancing nuclear and particle physics by improving analysis precision and accelerating discovery. Yet, progress in this field is often limited by the lack of openly available large scale datasets, as well as standardized evaluation tasks and metrics. Furthermore, the specialized knowledge and software typically required to process particle physics data pose significant barriers to interdisciplinary collaboration with the broader machine learning community. This work introduces a large, openly accessible dataset of 10 million simulated proton-proton collisions, designed to support self-supervised training of foundation models. To facilitate ease of use, the dataset is provided in a common NumPy format. In addition, it includes 70,000 labeled examples spanning three well defined downstream tasks: track finding, particle identification, and noise tagging, to enable systematic evaluation of the foundation model's adaptability. The simulated data are generated using the Pythia Monte Carlo event generator at a center of mass energy of sqrt(s) = 200 GeV and processed with Geant4 to include realistic detector conditions and signal emulation in the sPHENIX Time Projection Chamber at the Relativistic Heavy Ion Collider, located at Brookhaven National Laboratory. This dataset resource establishes a common ground for interdisciplinary research, enabling machine learning scientists and physicists alike to explore scaling behaviors, assess transferability, and accelerate progress toward foundation models in nuclear and high energy physics. The complete simulation and reconstruction chain is reproducible with the sPHENIX software stack. All data and code locations are provided under Data Accessibility.
新提交 (展示 1 之 1 条目 )
- [2] arXiv:2509.03652 (交叉列表自 cs.LG) [中文pdf, pdf, html, 其他]
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标题： 非负矩阵分解和共同原因原理标题： Nonnegative matrix factorization and the principle of the common cause主题： 机器学习 (cs.LG)
非负矩阵分解（NMF）是一种已知的无监督数据降维方法。共同原因原理（PCC）是概率因果关系中的基本方法论方法，它寻求两个相关随机变量联合概率的独立混合模型。结果表明，这两个概念密切相关。这种关系在几个灰度图像数据集上被相互探讨，这些数据集可以方便地映射到概率模型。一方面，PCC提供了一个可预测工具，导致对NMF有效秩的稳健估计。与其他估计（例如基于贝叶斯信息准则的估计）不同，我们的秩估计对弱噪声是稳定的。我们证明，围绕这个秩实现的NMF会产生特征（基图像），这些特征对噪声和局部优化的种子也是稳定的，从而有效地解决了NMF不可识别问题。另一方面，NMF提供了一种以近似方式实现PCC的可能性，其中较大且正相关的联合概率可以通过独立混合模型更好地解释。我们提出了一种聚类方法，将具有相同共同原因的数据点分组到同一簇中。我们还展示了如何使用NMF进行数据去噪。
Nonnegative matrix factorization (NMF) is a known unsupervised data-reduction method. The principle of the common cause (PCC) is a basic methodological approach in probabilistic causality, which seeks an independent mixture model for the joint probability of two dependent random variables. It turns out that these two concepts are closely related. This relationship is explored reciprocally for several datasets of gray-scale images, which are conveniently mapped into probability models. On one hand, PCC provides a predictability tool that leads to a robust estimation of the effective rank of NMF. Unlike other estimates (e.g., those based on the Bayesian Information Criteria), our estimate of the rank is stable against weak noise. We show that NMF implemented around this rank produces features (basis images) that are also stable against noise and against seeds of local optimization, thereby effectively resolving the NMF nonidentifiability problem. On the other hand, NMF provides an interesting possibility of implementing PCC in an approximate way, where larger and positively correlated joint probabilities tend to be explained better via the independent mixture model. We work out a clustering method, where data points with the same common cause are grouped into the same cluster. We also show how NMF can be employed for data denoising.
- [3] arXiv:2509.05541 (交叉列表自 stat.ML) [中文pdf, pdf, html, 其他]
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标题： 冷冻电镜作为随机逆问题标题： Cryo-EM as a Stochastic Inverse Problem评论： 25页，8图主题： 机器学习 (stat.ML) ; 机器学习 (cs.LG) ; 数值分析 (math.NA) ; 优化与控制 (math.OC) ; 数据分析、统计与概率 (physics.data-an)
冷冻电子显微镜（冷冻-EM）能够对生物分子进行高分辨率成像，但结构异质性仍然是三维重建中的主要挑战。 传统方法假设一组离散的构象，这限制了它们恢复连续结构变异的能力。 在本工作中，我们将冷冻-EM重建表述为概率测度上的随机逆问题（SIP），其中观测到的图像被建模为通过随机正向算子对分子结构未知分布的推前映射。 我们将重建问题表述为观测和模拟图像分布之间的变分差异的最小化，使用统计距离如KL散度和最大均值差异。 通过Wasserstein梯度流在概率测度空间中进行优化，我们使用粒子来表示和演化构象集合来数值求解。 我们使用合成示例验证我们的方法，包括一个现实的蛋白质模型，这表明其能够恢复结构状态的连续分布。 我们分析了我们公式与最大后验（MAP）方法之间的联系，这些方法可以被解释为离散化-然后-优化（DTO）框架的实例。 我们进一步提供了相容性分析，建立了DTO方法（如MAP估计）收敛于底层无限维连续问题的解的条件。 除了冷冻-EM之外，该框架提供了一种解决涉及随机正向算子的SIP的一般方法。
Cryo-electron microscopy (Cryo-EM) enables high-resolution imaging of biomolecules, but structural heterogeneity remains a major challenge in 3D reconstruction. Traditional methods assume a discrete set of conformations, limiting their ability to recover continuous structural variability. In this work, we formulate cryo-EM reconstruction as a stochastic inverse problem (SIP) over probability measures, where the observed images are modeled as the push-forward of an unknown distribution over molecular structures via a random forward operator. We pose the reconstruction problem as the minimization of a variational discrepancy between observed and simulated image distributions, using statistical distances such as the KL divergence and the Maximum Mean Discrepancy. The resulting optimization is performed over the space of probability measures via a Wasserstein gradient flow, which we numerically solve using particles to represent and evolve conformational ensembles. We validate our approach using synthetic examples, including a realistic protein model, which demonstrates its ability to recover continuous distributions over structural states. We analyze the connection between our formulation and Maximum A Posteriori (MAP) approaches, which can be interpreted as instances of the discretize-then-optimize (DTO) framework. We further provide a consistency analysis, establishing conditions under which DTO methods, such as MAP estimation, converge to the solution of the underlying infinite-dimensional continuous problem. Beyond cryo-EM, the framework provides a general methodology for solving SIPs involving random forward operators.
- [4] arXiv:2509.05567 (交叉列表自 physics.soc-ph) [中文pdf, pdf, 其他]
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标题： 递归分层网络与功能进化定律：复杂系统的通用框架标题： Recursive Hierarchical Networks and the Law of Functional Evolution: A Universal Framework for Complex Systems主题： 物理与社会 (physics.soc-ph) ; 社会与信息网络 (cs.SI) ; 适应性与自组织系统 (nlin.AO) ; 数据分析、统计与概率 (physics.data-an)
理解并预测复杂系统的发展仍然是一个基本挑战，这是由于缺乏统一且可计算测试的框架。 在这里，我们提出了递归分层网络（RHN），将进化概念化为沿着节点轨迹的递归封装，$\to$模块$\to$系统$\to$新节点，由渐进积累和突然转变所控制。 理论上，我们形式化并证明了功能进化的定律，揭示了一个从结构主导到调控主导再到智能主导阶段的不可逆进程。 经验上，我们将功能层次进行操作化，并将生命、宇宙、信息和社会系统对齐到这个尺度上。 所产生的轨迹是严格单调的，并表现出强烈的跨系统相似性，具有高成对余弦相似性和稳健的阶段共振。 我们定位当前系统状态并预测未来的转变。 RHN提供了一个数学严谨的多尺度框架，用于重建和预测系统演化，为设计下一代智能系统提供了理论指导。
Understanding and predicting the evolution of across complex systems remains a fundamental challenge due to the absence of unified and computationally testable frameworks. Here we propose the Recursive Hierarchical Network(RHN), conceptualizing evolution as recursive encapsulation along a trajectory of node $\to$ module $\to$ system $\to$ new node, governed by gradual accumulation and abrupt transition. Theoretically, we formalize and prove the law of functional evolution, revealing an irreversible progression from structure-dominated to regulation-dominated to intelligence-dominated stages. Empirically, we operationalize functional levels and align life, cosmic, informational, and social systems onto this scale. The resulting trajectories are strictly monotonic and exhibit strong cross-system similarity, with high pairwise cosine similarities and robust stage resonance. We locate current system states and project future transitions. RHN provides a mathematically rigorous, multi-scale framework for reconstructing and predicting system evolution, offering theoretical guidance for designing next-generation intelligent systems.
- [5] arXiv:2509.06383 (交叉列表自 cs.LG) [中文pdf, pdf, html, 其他]
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标题： 基于统计物理的稀疏和稳健变量选择的变分剪枝方法标题： Variational Garrote for Statistical Physics-based Sparse and Robust Variable Selection评论： 11页，4图主题： 机器学习 (cs.LG) ; 数据分析、统计与概率 (physics.data-an)
从高维数据中选择关键变量在大数据时代变得越来越重要。稀疏回归通过促进模型的简洁性和可解释性，成为一种强大的工具。在本工作中，我们重新审视一种有价值但未被充分利用的方法——基于统计物理的变分软阈值（VG），该方法引入了显式的特征选择自旋变量，并利用变分推断来推导出一个易于处理的损失函数。我们通过结合现代自动微分技术来增强VG，从而实现可扩展且高效的优化。我们在完全可控的合成数据集和复杂的现实数据集上评估了VG。我们的结果表明，VG在高度稀疏的情况下表现尤为出色，在不同稀疏水平下，其变量选择的一致性和鲁棒性优于岭回归和LASSO回归。我们还发现了一个尖锐的转变：当冗余变量被引入时，泛化能力会突然下降，选择变量的不确定性会增加。这个转变点提供了一个实用的信号，用于估计相关变量的正确数量，我们成功地将这一见解应用于识别现实数据中的关键预测因子。我们预计，VG在广泛的稀疏建模应用中具有强大的潜力，包括机器学习中的压缩感知和模型剪枝。
Selecting key variables from high-dimensional data is increasingly important in the era of big data. Sparse regression serves as a powerful tool for this purpose by promoting model simplicity and explainability. In this work, we revisit a valuable yet underutilized method, the statistical physics-based Variational Garrote (VG), which introduces explicit feature selection spin variables and leverages variational inference to derive a tractable loss function. We enhance VG by incorporating modern automatic differentiation techniques, enabling scalable and efficient optimization. We evaluate VG on both fully controllable synthetic datasets and complex real-world datasets. Our results demonstrate that VG performs especially well in highly sparse regimes, offering more consistent and robust variable selection than Ridge and LASSO regression across varying levels of sparsity. We also uncover a sharp transition: as superfluous variables are admitted, generalization degrades abruptly and the uncertainty of the selection variables increases. This transition point provides a practical signal for estimating the correct number of relevant variables, an insight we successfully apply to identify key predictors in real-world data. We expect that VG offers strong potential for sparse modeling across a wide range of applications, including compressed sensing and model pruning in machine learning.
- [6] arXiv:2509.06445 (交叉列表自 gr-qc) [中文pdf, pdf, html, 其他]
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标题： 学习检测连续引力波：一个开放的数据分析竞赛标题： Learning to detect continuous gravitational waves: an open data-analysis competitionRodrigo Tenorio, Michael J. Williams, Joseph Bayley, Christopher Messenger, Maggie Demkin, Walter Reade, Kaggle Competitors评论： 31页，5 + 2张图表，欢迎提出意见主题： 广义相对论与量子宇宙学 (gr-qc) ; 高能天体物理现象 (astro-ph.HE) ; 天体物理学的仪器与方法 (astro-ph.IM) ; 数据分析、统计与概率 (physics.data-an) ; 物理与社会 (physics.soc-ph)
我们报告了在开放数据科学平台Kaggle上举办的公开数据分析挑战的结果，以检测模拟的连续引力波信号。 这些是来自快速旋转中子星的微弱信号，在广泛的搜索中仍未被检测到。 竞赛数据集包含了一组CW信号，使用了模拟和真实的LIGO探测器数据，符合实际CW搜索的条件。 该竞赛吸引了超过1000名参与者来开发现实的CW搜索算法。 我们描述了前10种方法，并讨论了它们作为预处理步骤与标准CW搜索方法相比的适用性。 对于竞赛的数据集，我们发现顶级方法可以在2%的排除概率下将计算成本降低1到3个数量级。 此外，竞赛推动了新的GPU加速检测流程的开发，并将CW启发的统计方法扩展到了其他领域。 我们发布了相关数据集，这是第一个开放的标准基准用于CW检测，以实现可重复的方法比较，并鼓励进一步发展以实现这些难以捉摸的信号的首次检测。
We report results of a public data-analysis challenge, hosted on the open data-science platform Kaggle, to detect simulated continuous gravitational-wave signals. These are weak signals from rapidly spinning neutron stars that remain undetected despite extensive searches. The competition dataset consisted of a population of CW signals using both simulated and real LIGO detector data matching the conditions of actual CW searches. The competition attracted more than 1,000 participants to develop realistic CW search algorithms. We describe the top 10 approaches and discuss their applicability as a pre-processing step compared to standard CW-search approaches. For the competition's dataset, we find that top approaches can reduce the computing cost by 1 to 3 orders of magnitude at a 2% dismissal probability. Additionally, the competition drove the development of new GPU-accelerated detection pipelines and extended CW-inspired statistics to other domains. We release the associated dataset, which constitutes the first open standardized benchmark for CW detection, to enable reproducible method comparisons and to encourage further developments toward the first detection of these elusive signals.
交叉提交 (展示 5 之 5 条目 )
- [7] arXiv:2508.07423 (替换) [中文pdf, pdf, html, 其他]
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标题： 实时分析异构架构上的非结构化数据的机器学习标题： Real-Time Analysis of Unstructured Data with Machine Learning on Heterogeneous Architectures评论： 博士论文，第8章和第9章包含与安东尼·科雷亚合作完成的工作结果主题： 数据分析、统计与概率 (physics.data-an) ; 人工智能 (cs.AI) ; 分布式、并行与集群计算 (cs.DC) ; 机器学习 (cs.LG) ; 高能物理 - 实验 (hep-ex)
随着粒子物理界需要更高的精度来检验我们对亚原子世界的当前模型，需要更大规模的数据集。 随着全球对撞机实验探测器的升级计划，特别是在欧洲核子研究中心（CERN）的大型强子对撞机上，预计将产生更多的碰撞和更复杂的相互作用。 这直接意味着数据量的增加，从而导致处理这些数据所需的计算资源增加。 在CERN，产生的数据量非常庞大。 这就是为什么数据必须在永久存储之前实时进行大量过滤和选择。 然后可以使用这些数据进行物理分析，以扩展我们对宇宙的当前理解并改进物理学的标准模型。 这种实时过滤，称为触发，涉及复杂处理，通常频率高达40 MHz。 本论文致力于理解如何在这样的环境中高效部署机器学习模型，以最大化吞吐量并最小化能耗。 显然，为了应对严格、高频的数据率所带来的挑战，需要为这类任务设计的现代硬件和当代算法。 在这项工作中，我介绍了我们基于图神经网络的管道，该管道是为CERN的LHCb实验中的带电粒子轨迹重建而开发的。 该管道在LHCb的一级触发系统中端到端实现，完全在GPU上。 其性能与目前在LHCb生产中使用的经典跟踪算法进行了比较。 该管道还被加速在FPGA架构上，并将其在功耗和处理速度方面的性能与GPU实现进行了比较。
As the particle physics community needs higher and higher precisions in order to test our current model of the subatomic world, larger and larger datasets are necessary. With upgrades scheduled for the detectors of colliding-beam experiments around the world, and specifically at the Large Hadron Collider at CERN, more collisions and more complex interactions are expected. This directly implies an increase in data produced and consequently in the computational resources needed to process them. At CERN, the amount of data produced is gargantuan. This is why the data have to be heavily filtered and selected in real time before being permanently stored. This data can then be used to perform physics analyses, in order to expand our current understanding of the universe and improve the Standard Model of physics. This real-time filtering, known as triggering, involves complex processing happening often at frequencies as high as 40 MHz. This thesis contributes to understanding how machine learning models can be efficiently deployed in such environments, in order to maximize throughput and minimize energy consumption. Inevitably, modern hardware designed for such tasks and contemporary algorithms are needed in order to meet the challenges posed by the stringent, high-frequency data rates. In this work, I present our graph neural network-based pipeline, developed for charged particle track reconstruction at the LHCb experiment at CERN. The pipeline was implemented end-to-end inside LHCb's first-level trigger, entirely on GPUs. Its performance was compared against the classical tracking algorithms currently in production at LHCb. The pipeline was also accelerated on the FPGA architecture, and its performance in terms of power consumption and processing speed was compared against the GPU implementation.
- [8] arXiv:2407.15946 (替换) [中文pdf, pdf, html, 其他]
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标题： 局部齐普夫定律的普遍出现标题： Universal emergence of local Zipf's law评论： 6+5页，3+1图主题： 物理与社会 (physics.soc-ph) ; 数据分析、统计与概率 (physics.data-an)
大量自然和社会经济现象共享一种显著的统计规律性，即元素的大小随着其在大小排名中的位置按幂律减小。 这种规律性被称为齐普夫-曼德布罗特定律（ZM），在不同领域已经提出了许多针对特定问题的解释。 然而，目前尚缺乏对ZM普遍性的解释。 在本文中，我们首先提供了一个独立同分布随机变量排序后的任何排名样本的累积量的解析表达式。 然后，我们利用这一结果严格证明，当考虑此类排名数据集的一小部分时，它在统计上与ZM定律无法区分。 最后，我们将我们的结果与几个相关示例进行了验证。
A plethora of natural and socio-economic phenomena share a striking statistical regularity, that is the magnitude of elements decreases with a power law as a function of their position in a ranking of magnitude. Such regularity is known as Zipf-Mandelbrot law (ZM), and plenty of problem-specific explanations for its emergence have been provided in different fields. Yet, an explanation for ZM ubiquity is currently lacking. In this paper we first provide an analytical expression for the cumulants of any ranked sample of i.i.d. random variables once sorted in decreasing order. Then we make use of this result to rigorously demonstrate that, whenever a small fraction of such ranked dataset is considered, it becomes statistically indistinguishable from a ZM law. We finally validate our results against several relevant examples.
- [9] arXiv:2410.02867 (替换) [中文pdf, pdf, html, 其他]
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标题： FAIR 天空 HiggsML 不确定性挑战竞赛标题： FAIR Universe HiggsML Uncertainty Challenge CompetitionWahid Bhimji, Paolo Calafiura, Ragansu Chakkappai, Po-Wen Chang, Yuan-Tang Chou, Sascha Diefenbacher, Jordan Dudley, Steven Farrell, Aishik Ghosh, Isabelle Guyon, Chris Harris, Shih-Chieh Hsu, Elham E Khoda, Rémy Lyscar, Alexandre Michon, Benjamin Nachman, Peter Nugent, Mathis Reymond, David Rousseau, Benjamin Sluijter, Benjamin Thorne, Ihsan Ullah, Yulei Zhang评论： FAIR宇宙HiggsML不确定性挑战赛白皮书 比赛，可访问：https://fair-universe.lbl.gov主题： 高能物理 - 现象学 (hep-ph) ; 机器学习 (cs.LG) ; 高能物理 - 实验 (hep-ex) ; 数据分析、统计与概率 (physics.data-an)
FAIR宇宙——HiggsML不确定性挑战专注于在模拟器不完美情况下测量基本粒子的物理特性，这是由于建模系统误差的差异所致。 此外，该挑战利用大规模计算AI平台来共享数据集、训练模型和举办机器学习竞赛。 我们的挑战将物理学和机器学习社区聚集在一起，以推进我们对在AI技术中处理系统（认识论）不确定性的理解和方法。
The FAIR Universe -- HiggsML Uncertainty Challenge focuses on measuring the physics properties of elementary particles with imperfect simulators due to differences in modelling systematic errors. Additionally, the challenge is leveraging a large-compute-scale AI platform for sharing datasets, training models, and hosting machine learning competitions. Our challenge brings together the physics and machine learning communities to advance our understanding and methodologies in handling systematic (epistemic) uncertainties within AI techniques.
- [10] arXiv:2505.19903 (替换) [中文pdf, pdf, html, 其他]
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标题： 格点上的随机重置扩散标题： Diffusion with stochastic resetting on a lattice评论： 17页，7张图，绘图数据gnuplot文件可访问 https://doi.org/10.57782/VGCHTI期刊参考： 物理评论E 112, 034102 (2025)主题： 统计力学 (cond-mat.stat-mech) ; 数据分析、统计与概率 (physics.data-an)
我们提供了一个精确公式，用于计算单个粒子在$d$维超立方{\em 格子}上从固定初始位置$\vec R_0$出发，并以速率$r$重置到$\vec R_0$时，到达原点目标的平均首次通过时间（MFPT）。 在缩放极限$r\to 0$，$R_0=|\vec R_0|\to \infty$中恢复了连续空间中已知的结果，同时保持乘积$\sqrt{r}\, R_0$不变。 然而，我们的公式适用于任何$r$和任何$\vec R_0$，这使我们能够探索连续极限中无法到达的参数空间的更大区域。 例如，我们已经证明，对于固定的$\vec R_0$，MFPT作为$r$的函数在两个相反的极限$r\to 0$和$r\to \infty$处发散，并且在中间有一个唯一的最小值，前提是起点不是目标的最近邻。 在这种情况下，MFPT随着幂律$\sim r^{\phi}$发散，当$r\to \infty$时，但非常有趣的是，指数$\phi= (|m_1|+|m_2|+\ldots +|m_d|)-1$依赖于起始点$\vec R_0= a\, (m_1,m_2,\ldots, m_d)$，其中$a$是晶格间距，$m_i$的是整数。 如果起点恰好是目标的最近邻，那么MFPT随着$r$的增加而单调减少，当$r\to \infty$时趋近于一个普遍的极限值$1$，这表明在这种情况下最优重置率是无限的。我们提供了一个简单的物理原因和一个简单的马尔可夫链解释来说明这个有些出乎意料的普遍结果。我们的分析预测在高达$50$维的格点上的数值模拟中得到了验证。最后，在没有目标的情况下，我们也精确计算了非平衡稳态下行走者的位移分布，该分布也显示了一些连续理论未能捕捉到的有趣的格点效应。
We provide an exact formula for the mean first-passage time (MFPT) to a target at the origin for a single particle diffusing on a $d$-dimensional hypercubic {\em lattice} starting from a fixed initial position $\vec R_0$ and resetting to $\vec R_0$ with a rate $r$. Previously known results in the continuous space are recovered in the scaling limit $r\to 0$, $R_0=|\vec R_0|\to \infty$ with the product $\sqrt{r}\, R_0$ fixed. However, our formula is valid for any $r$ and any $\vec R_0$ that enables us to explore a much wider region of the parameter space that is inaccessible in the continuum limit. For example, we have shown that the MFPT, as a function of $r$ for fixed $\vec R_0$, diverges in the two opposite limits $r\to 0$ and $r\to \infty$ with a unique minimum in between, provided the starting point is not a nearest neighbour of the target. In this case, the MFPT diverges as a power law $\sim r^{\phi}$ as $r\to \infty$, but very interestingly with an exponent $\phi= (|m_1|+|m_2|+\ldots +|m_d|)-1$ that depends on the starting point $\vec R_0= a\, (m_1,m_2,\ldots, m_d)$ where $a$ is the lattice spacing and $m_i$'s are integers. If, on the other hand, the starting point happens to be a nearest neighbour of the target, then the MFPT decreases monotonically with increasing $r$, approaching a universal limiting value $1$ as $r\to \infty$, indicating that the optimal resetting rate in this case is infinity. We provide a simple physical reason and a simple Markov-chain explanation behind this somewhat unexpected universal result. Our analytical predictions are verified in numerical simulations on lattices up to $50$ dimensions. Finally, in the absence of a target, we also compute exactly the position distribution of the walker in the nonequlibrium stationary state that also displays interesting lattice effects not captured by the continuum theory.