Adaptive mesh refinement (AMR) is necessary for efficient finite element simulations of complex physical phenomenon, as it allocates limited computational budget based on the need for higher or lower resolution, which varies over space and time. We present a novel formulation of AMR as a fully-cooperative Markov game, in which each element is an independent agent who makes refinement and de-refinement choices based on local information. We design a novel deep multi-agent reinforcement learning (MARL) algorithm called Value Decomposition Graph Network (VDGN), which solves the two core challenges that AMR poses for MARL: posthumous credit assignment due to agent creation and deletion, and unstructured observations due to the diversity of mesh geometries. For the first time, we show that MARL enables anticipatory refinement of regions that will encounter complex features at future times, thereby unlocking entirely new regions of the error-cost objective landscape that are inaccessible by traditional methods based on local error estimators. Comprehensive experiments show that VDGN policies significantly outperform error threshold-based policies in global error and cost metrics. We show that learned policies generalize to test problems with physical features, mesh geometries, and longer simulation times that were not seen in training. We also extend VDGN with multi-objective optimization capabilities to find the Pareto front of the tradeoff between cost and error.

符号回归是识别拟合从黑盒过程中观察到的输出的数学表达式的过程。它通常认为是一个离散的优化问题是NP - 硬。解决问题的前提方法包括神经引导的搜索（例如，使用强化学习）和遗传编程。在这项工作中，我们介绍了一种混合神经引导/基因编程方法来象征性回归和其他组合优化问题。我们提出了一种神经引导组件，用于种子随机重启遗传编程组件的起始群体，逐渐学习更好的起始群体。在许多常见的基准任务中从数据集中恢复底层表达式，我们的方法使用相同的实验设置恢复比最近发布的顶部执行模型更多的表达式65％。我们证明在没有对神经引导的组件上的不相互依存的情况下运行许多遗传编程一代，而不是比两个更强烈地耦合的替代配方更好地对象征性回归更好地执行符号回归。最后，我们介绍了一组新的22个符号回归基准问题，而现有的基准难度增加。源代码在www.github.com/brendenpetersen/deep-symbolic -optimization提供。

We study the generalization capacity of group convolutional neural networks. We identify precise estimates for the VC dimensions of simple sets of group convolutional neural networks. In particular, we find that for infinite groups and appropriately chosen convolutional kernels, already two-parameter families of convolutional neural networks have an infinite VC dimension, despite being invariant to the action of an infinite group.

Strategic test allocation plays a major role in the control of both emerging and existing pandemics (e.g., COVID-19, HIV). Widespread testing supports effective epidemic control by (1) reducing transmission via identifying cases, and (2) tracking outbreak dynamics to inform targeted interventions. However, infectious disease surveillance presents unique statistical challenges. For instance, the true outcome of interest - one's positive infectious status, is often a latent variable. In addition, presence of both network and temporal dependence reduces the data to a single observation. As testing entire populations regularly is neither efficient nor feasible, standard approaches to testing recommend simple rule-based testing strategies (e.g., symptom based, contact tracing), without taking into account individual risk. In this work, we study an adaptive sequential design involving n individuals over a period of {\tau} time-steps, which allows for unspecified dependence among individuals and across time. Our causal target parameter is the mean latent outcome we would have obtained after one time-step, if, starting at time t given the observed past, we had carried out a stochastic intervention that maximizes the outcome under a resource constraint. We propose an Online Super Learner for adaptive sequential surveillance that learns the optimal choice of tests strategies over time while adapting to the current state of the outbreak. Relying on a series of working models, the proposed method learns across samples, through time, or both: based on the underlying (unknown) structure in the data. We present an identification result for the latent outcome in terms of the observed data, and demonstrate the superior performance of the proposed strategy in a simulation modeling a residential university environment during the COVID-19 pandemic.

This white paper lays out a vision of research and development in the field of artificial intelligence for the next decade (and beyond). Its denouement is a cyber-physical ecosystem of natural and synthetic sense-making, in which humans are integral participants$\unicode{x2014}$what we call ''shared intelligence''. This vision is premised on active inference, a formulation of adaptive behavior that can be read as a physics of intelligence, and which inherits from the physics of self-organization. In this context, we understand intelligence as the capacity to accumulate evidence for a generative model of one's sensed world$\unicode{x2014}$also known as self-evidencing. Formally, this corresponds to maximizing (Bayesian) model evidence, via belief updating over several scales: i.e., inference, learning, and model selection. Operationally, this self-evidencing can be realized via (variational) message passing or belief propagation on a factor graph. Crucially, active inference foregrounds an existential imperative of intelligent systems; namely, curiosity or the resolution of uncertainty. This same imperative underwrites belief sharing in ensembles of agents, in which certain aspects (i.e., factors) of each agent's generative world model provide a common ground or frame of reference. Active inference plays a foundational role in this ecology of belief sharing$\unicode{x2014}$leading to a formal account of collective intelligence that rests on shared narratives and goals. We also consider the kinds of communication protocols that must be developed to enable such an ecosystem of intelligences and motivate the development of a shared hyper-spatial modeling language and transaction protocol, as a first$\unicode{x2014}$and key$\unicode{x2014}$step towards such an ecology.

ICECUBE是一种用于检测1 GEV和1 PEV之间大气和天体中微子的光学传感器的立方公斤阵列，该阵列已部署1.45 km至2.45 km的南极的冰盖表面以下1.45 km至2.45 km。来自ICE探测器的事件的分类和重建在ICeCube数据分析中起着核心作用。重建和分类事件是一个挑战，这是由于探测器的几何形状，不均匀的散射和冰中光的吸收，并且低于100 GEV的光，每个事件产生的信号光子数量相对较少。为了应对这一挑战，可以将ICECUBE事件表示为点云图形，并将图形神经网络（GNN）作为分类和重建方法。 GNN能够将中微子事件与宇宙射线背景区分开，对不同的中微子事件类型进行分类，并重建沉积的能量，方向和相互作用顶点。基于仿真，我们提供了1-100 GEV能量范围的比较与当前ICECUBE分析中使用的当前最新最大似然技术，包括已知系统不确定性的影响。对于中微子事件分类，与当前的IceCube方法相比，GNN以固定的假阳性速率（FPR）提高了信号效率的18％。另外，GNN在固定信号效率下将FPR的降低超过8（低于半百分比）。对于能源，方向和相互作用顶点的重建，与当前最大似然技术相比，分辨率平均提高了13％-20％。当在GPU上运行时，GNN能够以几乎是2.7 kHz的中位数ICECUBE触发速率的速率处理ICECUBE事件，这打开了在在线搜索瞬态事件中使用低能量中微子的可能性。

使用深度学习技术，可以在MRI图像中自动检测到旁那鼻鼻窦系统中的异常，并可以根据其体积，形状和其他参数（例如局部对比度）进行进一步分析和分类。但是，由于培训数据有限，传统的监督学习方法通​​常无法概括。现有的旁那间异常分类中的深度学习方法最多可诊断出一种异常。在我们的工作中，我们考虑三个异常。具体而言，我们采用3D CNN来分离上颌鼻窦体积，而没有异常的鼻窦体积，并具有异常。为了从一个小标记的数据集中学习强大的表示形式，我们提出了一种新颖的学习范式，结合了对比损失和跨内向损失。特别是，我们使用有监督的对比损失，鼓励有或没有异常的上颌窦量的嵌入来形成两个不同的簇，而跨层损失则鼓励3D CNN保持其歧视能力。我们报告说，两种损失的优化是有利的，而不是仅通过一次损失而优化。我们还发现我们的培训策略会提高标签效率。使用我们的方法，3D CNN分类器的AUROC为0.85，而用横向渗透损失优化的3D CNN分类器可实现0.66的AUROC。

经典算法和机器学习系统（如神经网络）在日常生活中都很丰富。虽然经典的计算机科学算法适合精确执行精确定义的任务，例如在大图中找到最短路径，但神经网络允许从数据中学习来预测更为复杂的任务中最可能的答案，例如图像分类，无法减少。到确切的算法。为了获得两全其美，本文探讨了将这两个概念结合起来，从而导致更健壮，表现更好，更容易解释，计算效率更高，并且具有更高的数据有效体系结构。该论文正式化了算法监督的想法，该算法可以使神经网络与算法一起学习或结合学习。当将算法集成到神经体系结构中时，重要的是，算法是可区分的，因此可以端对端训练架构，并且可以以有意义的方式通过算法传播梯度。为了使算法可区分，本文提出了一种通过扰动变量并以封闭形式的期望值（即无需采样）近似期望值来连续放松算法的通用方法。此外，本文提出了可区分的算法，例如可区分的排序网络，可区分的渲染器和可区分的逻辑门网络。最后，本文提出了使用算法学习的替代培训策略。

自适应实验可以增加当前学生从教学干预的现场实验中获得更好结果的机会。在此类实验中，在收集更多数据时将学生分配到条件变化的可能性，因此可以将学生分配给可能表现更好的干预措施。数字教育环境降低了进行此类适应性实验的障碍，但很少在教育中应用。原因之一可能是研究人员可以访问很少的现实案例研究，这些案例研究说明了在特定情况下这些实验的优势和缺点。我们通过使用Thompson采样算法进行自适应实验来评估学生在学生中提醒的效果，并将其与传统的统一随机实验进行比较。我们将其作为有关如何进行此类实验的案例研究，并提出了有关自适应随机实验可能或多或少有用的条件的一系列开放问题。

在罕见的时间条件下（例如，公共假期，学校假期等）预测旅行时间是由于历史数据的限制而构成的挑战。如果所有可用的话，历史数据通常会形成异质时间序列，这是由于长时间其他变化的可能性很高（例如，道路工程，引入的交通镇定计划等）。这在城市和郊区特别突出。我们提出了一个用于编码罕见时间条件的矢量空间模型，该模型允许在不同时间条件上进行连贯的表示。当利用矢量空间编码来表示时间设置时，我们显示出对不同基线的旅行时间预测的性能提高。