有证据表明，诸如大脑之类的生物系统在噪声方面的临界状态稳健，因此能够在扰动下保持其中。在这项工作中，我们解决了关键系统对噪声的鲁棒性问题。特别是，我们研究了临界时随机细胞自动机（CA）的鲁棒性。随机CA是显示关键性的最简单随机模型之一。随机CA的过渡状态是通过一组概率来定义的。我们系统地扰动已知会产生关键行为的最佳随机CA的概率，我们报告说，这样的CA能够保持在一定程度的噪声中的关键状态。我们使用所得幂律拟合的误差指标（例如Kolmogorov-Smirnov统计量和Kullback-Leibler Divergence）介绍了结果。我们讨论了我们的结果在未来实现脑启发的人工智能系统的意义。

在扰动环境下，成群质和自我组织关键性（SoC）可能有助于鲁棒计算。在临界状态下在计算系统中实现逻辑门是研究弥撒和SOC的作用的有趣方式之一。在这里，我们研究了蜂窝自动机，生命游戏（GL），异步更新和实现概率逻辑门的行为，通过使用异步GL来实现概率逻辑门。我们发现异步G1显示相变，即1衰减的状态的密度在关键点处衰减，并且临界点处的系统具有异步GL中最多的可计算性。我们在异步GL中实现和或键入临界，显示出良好的性能。由于调整扰动在操作逻辑门中发挥着重要作用，我们的研究揭示了概率逻辑门中操纵与扰动之间的干扰。

我们训练神经形态硬件芯片以通过变分能最小化近似Quantum旋转模型的地面状态。与使用马尔可夫链蒙特卡罗进行样品生成的变分人工神经网络相比，这种方法具有优点：神经形态器件以快速和固有的并行方式产生样品。我们开发培训算法，并将其应用于横向场介绍模型，在中等系统尺寸下显示出良好的性能（$ n \ LEQ 10 $）。系统的普遍开心研究表明，较大系统尺寸的可扩展性主要取决于样品质量，该样品质量受到模拟神经芯片上的参数漂移的限制。学习性能显示阈值行为作为ansatz的变分参数的数量的函数，大约为50美元的隐藏神经元，足以表示关键地位，最高$ n = 10 $。网络参数的6 + 1位分辨率不会限制当前设置中的可达近似质量。我们的工作为利用神经形态硬件的能力提供了一种重要的一步，以解决量子数量问题中的维数诅咒。

This chapter sheds light on the synaptic organization of the brain from the perspective of computational neuroscience. It provides an introductory overview on how to account for empirical data in mathematical models, implement them in software, and perform simulations reflecting experiments. This path is demonstrated with respect to four key aspects of synaptic signaling: the connectivity of brain networks, synaptic transmission, synaptic plasticity, and the heterogeneity across synapses. Each step and aspect of the modeling and simulation workflow comes with its own challenges and pitfalls, which are highlighted and addressed in detail.

我们开发了一种多尺度方法，以从实验或模拟中观察到的物理字段或配置的数据集估算高维概率分布。通过这种方式，我们可以估计能量功能（或哈密顿量），并有效地在从统计物理学到宇宙学的各个领域中生成多体系统的新样本。我们的方法 - 小波条件重新归一化组（WC-RG） - 按比例进行估算，以估算由粗粒磁场来调节的“快速自由度”的条件概率的模型。这些概率分布是由与比例相互作用相关的能量函数建模的，并以正交小波为基础表示。 WC-RG将微观能量函数分解为各个尺度上的相互作用能量之和，并可以通过从粗尺度到细度来有效地生成新样品。近相变，它避免了直接估计和采样算法的“临界减速”。理论上通过结合RG和小波理论的结果来解释这一点，并为高斯和$ \ varphi^4 $字段理论进行数值验证。我们表明，多尺度WC-RG基于能量的模型比局部电位模型更通用，并且可以在所有长度尺度上捕获复杂的多体相互作用系统的物理。这是针对反映宇宙学中暗物质分布的弱透镜镜头的，其中包括与长尾概率分布的长距离相互作用。 WC-RG在非平衡系统中具有大量的潜在应用，其中未知基础分布{\ it先验}。最后，我们讨论了WC-RG和深层网络体系结构之间的联系。

基因调节网络是负责确定蛋白质和肽生产水平的生物生物体相互作用的网络。蛋白质是细胞工厂的工人，其生产定义了细胞及其开发的目标。已经进行了各种尝试来建模此类网络，以更好地了解这些生物系统，并利用了解它们的灵感来解决计算问题。在这项工作中，提出了一个针对基因调节网络的生物学上更现实的模型，该模型结合了细胞自动机和人工化学，以模拟称为转录因子和基因调节位点的调节蛋白之间的相互作用。这项工作的结果表明，复杂的动力学接近自然界中可以观察到的东西。在这里，对系统的初始状态对产生的动力学的影响进行了分析，这表明可以将这种可转化的模型针对产生所需的蛋白质动力学。

受限的玻尔兹曼机器（RBMS）提供了一种用于无监督的机器学习的多功能体系结构，原则上可以以任意准确性近似任何目标概率分布。但是，RBM模型通常由于其计算复杂性而无法直接访问，并调用了Markov-Chain采样以分析学习概率分布。因此，对于培训和最终应用，希望拥有既准确又有效的采样器。我们强调，这两个目标通常相互竞争，无法同时实现。更具体地说，我们确定并定量地表征了RBM学习的三个制度：独立学习，精度提高而不会失去效率；相关学习，较高的精度需要较低的效率；和退化，精度和效率都不再改善甚至恶化。这些发现基于数值实验和启发式论点。

Agent-based modeling (ABM) is a well-established paradigm for simulating complex systems via interactions between constituent entities. Machine learning (ML) refers to approaches whereby statistical algorithms 'learn' from data on their own, without imposing a priori theories of system behavior. Biological systems -- from molecules, to cells, to entire organisms -- consist of vast numbers of entities, governed by complex webs of interactions that span many spatiotemporal scales and exhibit nonlinearity, stochasticity and intricate coupling between entities. The macroscopic properties and collective dynamics of such systems are difficult to capture via continuum modelling and mean-field formalisms. ABM takes a 'bottom-up' approach that obviates these difficulties by enabling one to easily propose and test a set of well-defined 'rules' to be applied to the individual entities (agents) in a system. Evaluating a system and propagating its state over discrete time-steps effectively simulates the system, allowing observables to be computed and system properties to be analyzed. Because the rules that govern an ABM can be difficult to abstract and formulate from experimental data, there is an opportunity to use ML to help infer optimal, system-specific ABM rules. Once such rule-sets are devised, ABM calculations can generate a wealth of data, and ML can be applied there too -- e.g., to probe statistical measures that meaningfully describe a system's stochastic properties. As an example of synergy in the other direction (from ABM to ML), ABM simulations can generate realistic datasets for training ML algorithms (e.g., for regularization, to mitigate overfitting). In these ways, one can envision various synergistic ABM$\rightleftharpoons$ML loops. This review summarizes how ABM and ML have been integrated in contexts that span spatiotemporal scales, from cellular to population-level epidemiology.

Machine learning frameworks such as Genetic Programming (GP) and Reinforcement Learning (RL) are gaining popularity in flow control. This work presents a comparative analysis of the two, bench-marking some of their most representative algorithms against global optimization techniques such as Bayesian Optimization (BO) and Lipschitz global optimization (LIPO). First, we review the general framework of the model-free control problem, bringing together all methods as black-box optimization problems. Then, we test the control algorithms on three test cases. These are (1) the stabilization of a nonlinear dynamical system featuring frequency cross-talk, (2) the wave cancellation from a Burgers' flow and (3) the drag reduction in a cylinder wake flow. We present a comprehensive comparison to illustrate their differences in exploration versus exploitation and their balance between `model capacity' in the control law definition versus `required complexity'. We believe that such a comparison paves the way toward the hybridization of the various methods, and we offer some perspective on their future development in the literature on flow control problems.

贝叶斯脑假设假设大脑根据贝叶斯定理进行准确地运行统计分布。突触前囊泡释放神经递质的随机性失效可以让大脑从网络参数的后部分布中样本，被解释为认知不确定性。尚未显示出先前随机故障可能允许网络从观察到的分布中采样，也称为炼肠或残留不确定性。两个分布的采样使概率推断，高效搜索和创造性或生成问题解决。我们证明，在基于人口码的神经活动的解释下，可以用单独的突触衰竭来表示和对两种类型的分布进行分布。我们首先通过突触故障和横向抑制来定义生物学限制的神经网络和采样方案。在该框架内，我们派生基于辍学的认知不确定性，然后从突触功效证明了允许网络从任意，由接收层表示的分布来释放概率的分析映射。其次，我们的结果导致了本地学习规则，突触将适应其发布概率。我们的结果表明，在生物学限制的网络中，仅使用本地学习的突触失败率，与变分的贝叶斯推断相关的完整贝叶斯推断。

Humans have been able to tackle biosphere complexities by acting as ecosystem engineers, profoundly changing the flows of matter, energy and information. This includes major innovations that allowed to reduce and control the impact of extreme events. Modelling the evolution of such adaptive dynamics can be challenging given the potentially large number of individual and environmental variables involved. This paper shows how to address this problem by using fire as the source of external, bursting and wide fluctuations. Fire propagates on a spatial landscape where a group of agents harvest and exploit trees while avoiding the damaging effects of fire spreading. The agents need to solve a conflict to reach a group-level optimal state: while tree harvesting reduces the propagation of fires, it also reduces the availability of resources provided by trees. It is shown that the system displays two major evolutionary innovations that end up in an ecological engineering strategy that favours high biomass along with the suppression of large fires. The implications for potential A.I. management of complex ecosystems are discussed.

为了测试一类深神经网络的泛化能力，我们基于John Conway的生活游戏，我们随机生成了2-D蜂窝自动机（CA）的大量不同规则集。使用这些规则，我们为每个CA实例计算多个轨迹。具有短路和长范围跳过连接的深度卷积编码器 - 解码器网络在各种生成的CA轨迹上培训，以预测给出其先前的州的下一个CA状态。结果表明，该网络能够学习各种，复杂的蜂窝自动机的规则，并概括到看不见的配置。在某种程度上，该网络显示统治集的概括和培训期间没有看到的邻域大小。重现实验的代码是公开可用的：https://github.com/slampai/一一化 - 细胞 - automata

历史流程表现出显着的多样性。尽管如此，学者们长期以来一直试图识别模式，并将历史行动者分类和对一些成功的影响。随机过程框架提供了一种结构化方法，用于分析大型历史数据集，允许检测有时令人惊讶的模式，鉴定内源性和外源对过程的相关因果作用者，以及不同历史案例的比较。随机过程的数据，分析工具和组织理论框架的组合使历史和考古中的传统叙事方法补充了传统的叙事方法。

在接触网络上重建缺失的流行扩展信息可能是预防和遏制策略必不可少的。例如，鉴定和警告感染性但无症状的个体（例如，手动接触跟踪）有助于在Covid-19流行中含有爆发。可能的流行病级联的数量通常随着所涉及的个体的数量呈指数级增长。流行病过程中推理问题所带来的挑战源于难以识别与证据兼容的几乎可忽略的子集（例如，医学测试）。在这里，我们提出了一种新的生成神经网络框架，可以对与观察相兼容的最可能的感染级联来进行样本。此外，该框架可以推断治疗感染扩散的参数。所提出的方法从患者零问题，风险评估和传染性参数的现有方法获得更好或比较的结果，综合性和实际情况中的传染性参数，如在工作场所和医院传播感染。

我们展示了一个端到端框架，以提高人造系统对不可预见的事件的弹性。该框架基于基于物理的数字双胞胎模型和三个负责实时故障诊断，预后和重新配置的模块。故障诊断模块使用基于模型的诊断算法来检测和分离断层，并在系统中产生干预措施，以消除不确定的诊断解决方案。我们通过使用基于物理学的数字双胞胎的平行化和替代模型来扩展故障诊断算法为所需的实时性能。预后模块跟踪故障进度，并训练在线退化模型，以计算系统组件的剩余使用寿命。此外，我们使用降解模型来评估断层进程对操作要求的影响。重新配置模块使用基于PDDL的计划，并带有语义附件来调整系统控件，从而最大程度地减少了对系统操作的故障影响。我们定义一个弹性度量，并以燃料系统模型的示例来说明该指标如何通过我们的框架改进。

We present a neural flow wavefunction, Gauge-Fermion FlowNet, and use it to simulate 2+1D lattice compact quantum electrodynamics with finite density dynamical fermions. The gauge field is represented by a neural network which parameterizes a discretized flow-based transformation of the amplitude while the fermionic sign structure is represented by a neural net backflow. This approach directly represents the $U(1)$ degree of freedom without any truncation, obeys Guass's law by construction, samples autoregressively avoiding any equilibration time, and variationally simulates Gauge-Fermion systems with sign problems accurately. In this model, we investigate confinement and string breaking phenomena in different fermion density and hopping regimes. We study the phase transition from the charge crystal phase to the vacuum phase at zero density, and observe the phase seperation and the net charge penetration blocking effect under magnetic interaction at finite density. In addition, we investigate a magnetic phase transition due to the competition effect between the kinetic energy of fermions and the magnetic energy of the gauge field. With our method, we further note potential differences on the order of the phase transitions between a continuous $U(1)$ system and one with finite truncation. Our state-of-the-art neural network approach opens up new possibilities to study different gauge theories coupled to dynamical matter in higher dimensions.

在机器学习中调用多种假设需要了解歧管的几何形状和维度，理论决定了需要多少样本。但是，在应用程序数据中，采样可能不均匀，歧管属性是未知的，并且（可能）非纯化；这意味着社区必须适应本地结构。我们介绍了一种用于推断相似性内核提供数据的自适应邻域的算法。从本地保守的邻域（Gabriel）图开始，我们根据加权对应物进行迭代率稀疏。在每个步骤中，线性程序在全球范围内产生最小的社区，并且体积统计数据揭示了邻居离群值可能违反了歧管几何形状。我们将自适应邻域应用于非线性维度降低，地球计算和维度估计。与标准算法的比较，例如使用K-Nearest邻居，证明了它们的实用性。

经常性神经网络（RNNS）是强大的动态模型，广泛用于机器学习（ML）和神经科学。之前的理论作品集中在具有添加剂相互作用的RNN上。然而，门控 - 即乘法 - 相互作用在真神经元中普遍存在，并且也是ML中最佳性能RNN的中心特征。在这里，我们表明Gating提供灵活地控制集体动态的两个突出特征：i）时间尺寸和ii）维度。栅极控制时间尺度导致新颖的稳定状态，网络用作灵活积分器。与以前的方法不同，Gating允许这种重要功能而没有参数微调或特殊对称。门还提供一种灵活的上下文相关机制来重置存储器跟踪，从而补充存储器功能。调制维度的栅极可以诱导新颖的不连续的混沌转变，其中输入将稳定的系统推向强的混沌活动，与通常稳定的输入效果相比。在这种转变之上，与添加剂RNN不同，关键点（拓扑复杂性）的增殖与混沌动力学的外观解耦（动态复杂性）。丰富的动态总结在相图中，从而为ML从业者提供了一个原理参数初始化选择的地图。

Recent work has shown that machine learning (ML) models can be trained to accurately forecast the dynamics of unknown chaotic dynamical systems. Such ML models can be used to produce both short-term predictions of the state evolution and long-term predictions of the statistical patterns of the dynamics (``climate''). Both of these tasks can be accomplished by employing a feedback loop, whereby the model is trained to predict forward one time step, then the trained model is iterated for multiple time steps with its output used as the input. In the absence of mitigating techniques, however, this technique can result in artificially rapid error growth, leading to inaccurate predictions and/or climate instability. In this article, we systematically examine the technique of adding noise to the ML model input during training as a means to promote stability and improve prediction accuracy. Furthermore, we introduce Linearized Multi-Noise Training (LMNT), a regularization technique that deterministically approximates the effect of many small, independent noise realizations added to the model input during training. Our case study uses reservoir computing, a machine-learning method using recurrent neural networks, to predict the spatiotemporal chaotic Kuramoto-Sivashinsky equation. We find that reservoir computers trained with noise or with LMNT produce climate predictions that appear to be indefinitely stable and have a climate very similar to the true system, while reservoir computers trained without regularization are unstable. Compared with other types of regularization that yield stability in some cases, we find that both short-term and climate predictions from reservoir computers trained with noise or with LMNT are substantially more accurate. Finally, we show that the deterministic aspect of our LMNT regularization facilitates fast hyperparameter tuning when compared to training with noise.

Artificial Intelligence (AI) and Machine Learning (ML) are weaving their way into the fabric of society, where they are playing a crucial role in numerous facets of our lives. As we witness the increased deployment of AI and ML in various types of devices, we benefit from their use into energy-efficient algorithms for low powered devices. In this paper, we investigate a scale and medium that is far smaller than conventional devices as we move towards molecular systems that can be utilized to perform machine learning functions, i.e., Molecular Machine Learning (MML). Fundamental to the operation of MML is the transport, processing, and interpretation of information propagated by molecules through chemical reactions. We begin by reviewing the current approaches that have been developed for MML, before we move towards potential new directions that rely on gene regulatory networks inside biological organisms as well as their population interactions to create neural networks. We then investigate mechanisms for training machine learning structures in biological cells based on calcium signaling and demonstrate their application to build an Analog to Digital Converter (ADC). Lastly, we look at potential future directions as well as challenges that this area could solve.