具有测试（KAT）的Kleene代数是一个用于推理计划的基本公正框架，这些框架在许多其他领域中发现了在程序转换，网络和编译优化中的应用程序。在他的开创性工作中，Kozen证明了Kat归结了命题Hoare逻辑，表明通过KAT的等级理论，可以推理（部分）的计划。在这项工作中，我们调查了KAT提供了对不正确的推理的支持，而是由Ohearn最近提出的错误逻辑所体现的。我们表明KAT不能直接表达错误的逻辑。这种限制的主要原因可以追溯到KAT无法明确表达Codomain的概念，这对于表达不正确的三元组是必不可少的。为了解决这个问题，我们使用顶部和测试（Topkat）研究Kleene代数，kat的延伸，顶部元素。我们表明Topkat足够强大，以表达Codomain操作，以表达错误的三元组，并证明所有错误逻辑声音的规则。这表明可以通过Topkat的等级理论来推理米内的米兰的不正确性。

在本文中，我们研究了非交互性局部差异隐私（NLDP）模型中估计平滑普遍线性模型（GLM）的问题。与其经典设置不同，我们的模型允许服务器访问一些其他公共但未标记的数据。在本文的第一部分中，我们专注于GLM。具体而言，我们首先考虑每个数据记录均为I.I.D.的情况。从零均值的多元高斯分布中取样。由Stein的引理动机，我们提出了GLMS的$（Epsilon，\ delta）$ -NLDP算法。此外，算法的公共数据和私人数据的示例复杂性以实现$ \ alpha $的$ \ ell_2 $ -norm估计错误（具有高概率）为$ {o}（p \ alpha^{ - 2}）$和$ \ tilde {o}（p^3 \ alpha^{ - 2} \ epsilon^{ - 2}）$，其中$ p $是特征向量的维度。这是对$ \ alpha^{ - 1} $中先前已知的指数或准过程的重大改进，或者在$ p $中的指数smack sample sample smack glms的复杂性，没有公共数据。然后，我们考虑一个更通用的设置，每个数据记录为I.I.D.从某些次高斯分布中取样，有限制的$ \ ell_1 $ -norm。基于Stein的引理的变体，我们提出了一个$（\ epsilon，\ delta）$ - NLDP算法，用于GLMS的公共和私人数据的样本复杂性，以实现$ \ ell_ \ elfty $ - infty $ -NOMM估计的$ \ alpha误差$是$ is $ {o}（p^2 \ alpha^{ - 2}）$和$ \ tilde {o}（p^2 \ alpha^{ - 2} \ epsilon^{ - 2}）$，温和的假设，如果$ \ alpha $不太小（{\ em i.e.，} $ \ alpha \ geq \ omega（\ frac {1} {\ sqrt {p}}}）$）。在本文的第二部分中，我们将我们的想法扩展到估计非线性回归的问题，并显示出与多元高斯和次高斯案例的GLMS相似的结果。最后，我们通过对合成和现实世界数据集的实验来证明算法的有效性。

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.

Profile extrusion is a continuous production process for manufacturing plastic profiles from molten polymer. Especially interesting is the design of the die, through which the melt is pressed to attain the desired shape. However, due to an inhomogeneous velocity distribution at the die exit or residual stresses inside the extrudate, the final shape of the manufactured part often deviates from the desired one. To avoid these deviations, the shape of the die can be computationally optimized, which has already been investigated in the literature using classical optimization approaches. A new approach in the field of shape optimization is the utilization of Reinforcement Learning (RL) as a learning-based optimization algorithm. RL is based on trial-and-error interactions of an agent with an environment. For each action, the agent is rewarded and informed about the subsequent state of the environment. While not necessarily superior to classical, e.g., gradient-based or evolutionary, optimization algorithms for one single problem, RL techniques are expected to perform especially well when similar optimization tasks are repeated since the agent learns a more general strategy for generating optimal shapes instead of concentrating on just one single problem. In this work, we investigate this approach by applying it to two 2D test cases. The flow-channel geometry can be modified by the RL agent using so-called Free-Form Deformation, a method where the computational mesh is embedded into a transformation spline, which is then manipulated based on the control-point positions. In particular, we investigate the impact of utilizing different agents on the training progress and the potential of wall time saving by utilizing multiple environments during training.

The recent emergence of new algorithms for permuting models into functionally equivalent regions of the solution space has shed some light on the complexity of error surfaces, and some promising properties like mode connectivity. However, finding the right permutation is challenging, and current optimization techniques are not differentiable, which makes it difficult to integrate into a gradient-based optimization, and often leads to sub-optimal solutions. In this paper, we propose a Sinkhorn re-basin network with the ability to obtain the transportation plan that better suits a given objective. Unlike the current state-of-art, our method is differentiable and, therefore, easy to adapt to any task within the deep learning domain. Furthermore, we show the advantage of our re-basin method by proposing a new cost function that allows performing incremental learning by exploiting the linear mode connectivity property. The benefit of our method is compared against similar approaches from the literature, under several conditions for both optimal transport finding and linear mode connectivity. The effectiveness of our continual learning method based on re-basin is also shown for several common benchmark datasets, providing experimental results that are competitive with state-of-art results from the literature.

Digital media have enabled the access to unprecedented literary knowledge. Authors, readers, and scholars are now able to discover and share an increasing amount of information about books and their authors. Notwithstanding, digital archives are still unbalanced: writers from non-Western countries are less represented, and such a condition leads to the perpetration of old forms of discrimination. In this paper, we present the Under-Represented Writers Knowledge Graph (URW-KG), a resource designed to explore and possibly amend this lack of representation by gathering and mapping information about works and authors from Wikidata and three other sources: Open Library, Goodreads, and Google Books. The experiments based on KG embeddings showed that the integrated information encoded in the graph allows scholars and users to be more easily exposed to non-Western literary works and authors with respect to Wikidata alone. This opens to the development of fairer and effective tools for author discovery and exploration.

Text detoxification has the potential to mitigate the harms of toxicity by rephrasing text to remove offensive meaning, but subtle toxicity remains challenging to tackle. We introduce MaRCo, a detoxification algorithm that combines controllable generation and text rewriting methods using a Product of Experts with autoencoder language models (LMs). MaRCo uses likelihoods under a non-toxic LM (expert) and a toxic LM (anti-expert) to find candidate words to mask and potentially replace. We evaluate our method on several subtle toxicity and microaggressions datasets, and show that it not only outperforms baselines on automatic metrics, but MaRCo's rewrites are preferred 2.1 $\times$ more in human evaluation. Its applicability to instances of subtle toxicity is especially promising, demonstrating a path forward for addressing increasingly elusive online hate.