最佳运输（OT）理论描述了定义和选择在许多可能的选择中，将概率度量映射到另一个概率的最有效方法。该理论主要用于估计，给定一对源和目标概率测量$（\ MU，\ nu）$，这是一个可以有效地将$ \ mu $映射到$ \ nu $的参数化映射$ t_ \ theta $。在许多应用程序中，例如预测细胞对治疗的响应，数据测量$ \ mu，\ nu $（未处理/处理过的单元的功能）定义了最佳运输问题并非孤立地出现，但与上下文$ c $相关联（治疗）。为了说明并将该上下文纳入OT估计，我们介绍了Condot，一种使用上下文标签$ C_I $标记的几对测量$（\ mu_i，\ nu_i）$使用几对测量$（\ mu_i，\ nu_i）$。我们的目标是从标记对的数据集$ \ {（c_i，（（\ mu_i，\ nu_i））中提取％\}）\} $学习全局映射$ \ mathcal {t} _ {\ theta} $，不仅是预期的适合数据集中的所有对$ \ {（（c_i，（\ mu_i，\ nu_i）））\} $，即$，但应概括以产生有意义的地图$ \ Mathcal {t} _ {\ theta}（c _ {\ text {new}}）$在未看到的上下文上调节的$ c _ {\ text {new}} $。我们的方法利用并为部分输入凸神经网络提供了新颖的用法，为此我们引入了受高斯近似启发的强大而有效的初始化策略。我们仅使用对所述扰动的作用观察到遗传或治疗性扰动对单个细胞的任意组合对单个细胞的任意组合的影响的能力。

计算分布之间的最佳传输（OT）耦合在机器学习中起着越来越重要的作用。虽然可以将OT问题求解为线性程序，但添加熵平滑项会导致求解器对离群值更快，更强大，可区分且易于并行化。 Sinkhorn固定点算法是这些方法的基石，结果，已经进行了多次尝试以缩短其运行时，例如退火，动量或加速度。本文的前提是，\ textit {initialization}的sindhorn算法受到了相对较少的关注，可能是由于两个先入为主的：由于正规化的ot问题是凸的，因此可能不值得制定量身定制的初始化，因为\ textit {\ textit { }保证工作；其次，由于sindhorn算法在端到端管道中通常是区分的，因此数据依赖性初始化可能会通过展开迭代而获得的偏差梯度估计。我们挑战了这种传统的观点，并表明精心选择的初始化可能会导致巨大的加速，并且不会偏向梯度，这些梯度是通过隐式分化计算的。我们详细介绍如何使用1D或高斯设置中的已知结果从封闭形式或近似OT解决方案中恢复初始化。我们从经验上表明，这些初始化可以在现成的情况下使用，几乎没有调整，并且导致各种OT问题的速度持续加速。

最佳运输（OT）背后的匹配原理在机器学习中起着越来越重要的作用，这一趋势可以观察到ot被用来消除应用程序中的数据集（例如，单细胞基因组学）或用于改善更复杂的方法（例如，平衡平衡）注意变形金刚或自我监督的学习）。为了扩展到更具挑战性的问题，越来越多的共识要求求解器可以在数百万而不是数千点上运作。在\ cite {scetbon2021lowrank}中提倡的低级最佳运输方法（LOT）方法在这方面有几个诺言，并被证明可以补充更确定的熵正则化方法，能够将自己插入更复杂的管道中，例如Quadratic OT。批次将低成本耦合的搜索限制在具有低位级等级的耦合方面，在感兴趣的情况下产生线性时间算法。但是，只有在比较感兴趣的属性时，只有将批次方法视为熵正则化的合法竞争者，这些诺言才能实现，记分卡通常包含理论属性（统计复杂性和与其他方法）或实际方面（偏见，偏见，偏见，依据，，依据，统计复杂性和关系）高参数调整，初始化）。我们针对本文中的每个领域，以巩固计算OT中低级别方法的影响。

越来越多的机器学习问题，例如现有算法的鲁棒或对抗性变体，需要最小化自己定义为最大值的损耗函数。在（内部）最大化问题上携带随机梯度上升（SGA）步骤的环路，然后在（外部）最小化上进行SGD步骤，称为时期随机梯度\脑短幕（ESGDA）。虽然成功在实践中，ESGDA的理论分析仍然具有挑战性，但没有明确指导内部环路尺寸的选择，也没有内部/外部步长尺寸之间的相互作用。我们提出RSGDA（随机SGDA），是ESGDA的变种，具有随机环形尺寸，具有更简单的理论分析。 RSGDA在非透露X分钟/强凹幅最大设置上使用时，rsgda附带第一个（在SGDA算法中）几乎肯定的融合速率。 RSGDA可以使用最佳环路大小进行参数化，以保证已知为SGDA的最佳收敛速率。我们在玩具和更大的尺度问题上测试RSGDA，使用作为测试用最佳运输的分布鲁棒优化和单细胞数据匹配。

考虑随时间演变的粒子群，通过快照监测，使用在连续时间戳的群体内采样的粒子。仅提供对这些快照的访问，我们可以重建这些粒子的单个轨迹吗？这个问题在我们时代的许多重要科学挑战中，特别是单细胞基因组学。在本文中，我们建议将人口动态模拟为欧洲因果乔丹 - 古德莱尔 - 奥托（JKO）的措施的实现：JKO计划陷入困境，即在时间T + 1的人口采取的新配置是交易的新配置在它减少能量的情况下，群体的更好配置，同时保持关闭（在Wasserstein距离）到在T.中观察到的先前配置。我们在这项工作中的目标是学习这样的能源给定数据。为此，我们提出了JKONET，一种计算的神经结构（以端到端可分子的方式），JKO流量给出了参数化能量和初始配置点。与更直接的前进方法相比，我们展示了JKONET配件程序的良好性能和稳健性。

Projection robust Wasserstein (PRW) distance, or Wasserstein projection pursuit (WPP), is a robust variant of the Wasserstein distance. Recent work suggests that this quantity is more robust than the standard Wasserstein distance, in particular when comparing probability measures in high-dimensions. However, it is ruled out for practical application because the optimization model is essentially non-convex and non-smooth which makes the computation intractable. Our contribution in this paper is to revisit the original motivation behind WPP/PRW, but take the hard route of showing that, despite its non-convexity and lack of nonsmoothness, and even despite some hardness results proved by~\citet{Niles-2019-Estimation} in a minimax sense, the original formulation for PRW/WPP \textit{can} be efficiently computed in practice using Riemannian optimization, yielding in relevant cases better behavior than its convex relaxation. More specifically, we provide three simple algorithms with solid theoretical guarantee on their complexity bound (one in the appendix), and demonstrate their effectiveness and efficiency by conducing extensive experiments on synthetic and real data. This paper provides a first step into a computational theory of the PRW distance and provides the links between optimal transport and Riemannian optimization.

Computational units in artificial neural networks follow a simplified model of biological neurons. In the biological model, the output signal of a neuron runs down the axon, splits following the many branches at its end, and passes identically to all the downward neurons of the network. Each of the downward neurons will use their copy of this signal as one of many inputs dendrites, integrate them all and fire an output, if above some threshold. In the artificial neural network, this translates to the fact that the nonlinear filtering of the signal is performed in the upward neuron, meaning that in practice the same activation is shared between all the downward neurons that use that signal as their input. Dendrites thus play a passive role. We propose a slightly more complex model for the biological neuron, where dendrites play an active role: the activation in the output of the upward neuron becomes optional, and instead the signals going through each dendrite undergo independent nonlinear filterings, before the linear combination. We implement this new model into a ReLU computational unit and discuss its biological plausibility. We compare this new computational unit with the standard one and describe it from a geometrical point of view. We provide a Keras implementation of this unit into fully connected and convolutional layers and estimate their FLOPs and weights change. We then use these layers in ResNet architectures on CIFAR-10, CIFAR-100, Imagenette, and Imagewoof, obtaining performance improvements over standard ResNets up to 1.73%. Finally, we prove a universal representation theorem for continuous functions on compact sets and show that this new unit has more representational power than its standard counterpart.

The open-radio access network (O-RAN) embraces cloudification and network function virtualization for base-band function processing by dis-aggregated radio units (RUs), distributed units (DUs), and centralized units (CUs). These enable the cloud-RAN vision in full, where multiple mobile network operators (MNOs) can install their proprietary or open RUs, but lease on-demand computational resources for DU-CU functions from commonly available open-clouds via open x-haul interfaces. In this paper, we propose and compare the performances of min-max fairness and Vickrey-Clarke-Groves (VCG) auction-based x-haul and DU-CU resource allocation mechanisms to create a multi-tenant O-RAN ecosystem that is sustainable for small, medium, and large MNOs. The min-max fair approach minimizes the maximum OPEX of RUs through cost-sharing proportional to their demands, whereas the VCG auction-based approach minimizes the total OPEX for all resources utilized while extracting truthful demands from RUs. We consider time-wavelength division multiplexed (TWDM) passive optical network (PON)-based x-haul interfaces where PON virtualization technique is used to flexibly provide optical connections among RUs and edge-clouds at macro-cell RU locations as well as open-clouds at the central office locations. Moreover, we design efficient heuristics that yield significantly better economic efficiency and network resource utilization than conventional greedy resource allocation algorithms and reinforcement learning-based algorithms.

When testing conditions differ from those represented in training data, so-called out-of-distribution (OOD) inputs can mar the reliability of black-box learned components in the modern robot autonomy stack. Therefore, coping with OOD data is an important challenge on the path towards trustworthy learning-enabled open-world autonomy. In this paper, we aim to demystify the topic of OOD data and its associated challenges in the context of data-driven robotic systems, drawing connections to emerging paradigms in the ML community that study the effect of OOD data on learned models in isolation. We argue that as roboticists, we should reason about the overall system-level competence of a robot as it performs tasks in OOD conditions. We highlight key research questions around this system-level view of OOD problems to guide future research toward safe and reliable learning-enabled autonomy.

Autoencoders are a popular model in many branches of machine learning and lossy data compression. However, their fundamental limits, the performance of gradient methods and the features learnt during optimization remain poorly understood, even in the two-layer setting. In fact, earlier work has considered either linear autoencoders or specific training regimes (leading to vanishing or diverging compression rates). Our paper addresses this gap by focusing on non-linear two-layer autoencoders trained in the challenging proportional regime in which the input dimension scales linearly with the size of the representation. Our results characterize the minimizers of the population risk, and show that such minimizers are achieved by gradient methods; their structure is also unveiled, thus leading to a concise description of the features obtained via training. For the special case of a sign activation function, our analysis establishes the fundamental limits for the lossy compression of Gaussian sources via (shallow) autoencoders. Finally, while the results are proved for Gaussian data, numerical simulations on standard datasets display the universality of the theoretical predictions.