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The expressivity of Graph Neural Networks (GNNs) can be entirely characterized by appropriate fragments of the first-order logic. Namely, any query of the two variable fragment of graded modal logic (GC2) interpreted over labeled graphs can be expressed using a GNN whose size depends only on the depth of the query. As pointed out by [Barcelo & Al., 2020, Grohe, 2021], this description holds for a family of activation functions, leaving the possibility for a hierarchy of logics expressible by GNNs depending on the chosen activation function. In this article, we show that such hierarchy indeed exists by proving that GC2 queries cannot be expressed by GNNs with polynomial activation functions. This implies a separation between polynomial and popular non-polynomial activations (such as ReLUs, sigmoid and hyperbolic tan and others) and answers an open question formulated by [Grohe, 2021].

The computing in the network (COIN) paradigm has emerged as a potential solution for computation-intensive applications like the metaverse by utilizing unused network resources. The blockchain (BC) guarantees task-offloading privacy, but cost reduction, queueing delays, and redundancy elimination remain open problems. This paper presents a redundancy-aware BC-based approach for the metaverse's partial computation offloading (PCO). Specifically, we formulate a joint BC redundancy factor (BRF) and PCO problem to minimize computation costs, maximize incentives, and meet delay and BC offloading constraints. We proved this problem is NP-hard and transformed it into two subproblems based on their temporal correlation: real-time PCO and Markov decision process-based BRF. We formulated the PCO problem as a multiuser game, proposed a decentralized algorithm for Nash equilibrium under any BC redundancy state, and designed a double deep Q-network-based algorithm for the optimal BRF policy. The BRF strategy is updated periodically based on user computation demand and network status to assist the PCO algorithm. The experimental results suggest that the proposed approach outperforms existing schemes, resulting in a remarkable 47% reduction in cost overhead, delivering approximately 64% higher rewards, and achieving convergence in just a few training episodes.

Purpose: To provide a simulation framework for routine neuroimaging test data, which allows for "stress testing" of deep segmentation networks against acquisition shifts that commonly occur in clinical practice for T2 weighted (T2w) fluid attenuated inversion recovery (FLAIR) Magnetic Resonance Imaging (MRI) protocols. Approach: The approach simulates "acquisition shift derivatives" of MR images based on MR signal equations. Experiments comprise the validation of the simulated images by real MR scans and example stress tests on state-of-the-art MS lesion segmentation networks to explore a generic model function to describe the F1 score in dependence of the contrast-affecting sequence parameters echo time (TE) and inversion time (TI). Results: The differences between real and simulated images range up to 19 % in gray and white matter for extreme parameter settings. For the segmentation networks under test the F1 score dependency on TE and TI can be well described by quadratic model functions (R^2 > 0.9). The coefficients of the model functions indicate that changes of TE have more influence on the model performance than TI. Conclusions: We show that these deviations are in the range of values as may be caused by erroneous or individual differences of relaxation times as described by literature. The coefficients of the F1 model function allow for quantitative comparison of the influences of TE and TI. Limitations arise mainly from tissues with the low baseline signal (like CSF) and when the protocol contains contrast-affecting measures that cannot be modelled due to missing information in the DICOM header.

The synthesis of information deriving from complex networks is a topic receiving increasing relevance in ecology and environmental sciences. In particular, the aggregation of multilayer networks, i.e. network structures formed by multiple interacting networks (the layers), constitutes a fast-growing field. In several environmental applications, the layers of a multilayer network are modelled as a collection of similarity matrices describing how similar pairs of biological entities are, based on different types of features (e.g. biological traits). The present paper first discusses two main techniques for combining the multi-layered information into a single network (the so-called monoplex), i.e. Similarity Network Fusion (SNF) and Similarity Matrix Average (SMA). Then, the effectiveness of the two methods is tested on a real-world dataset of the relative abundance of microbial species in the ecosystems of nine glaciers (four glaciers in the Alps and five in the Andes). A preliminary clustering analysis on the monoplexes obtained with different methods shows the emergence of a tightly connected community formed by species that are typical of cryoconite holes worldwide. Moreover, the weights assigned to different layers by the SMA algorithm suggest that two large South American glaciers (Exploradores and Perito Moreno) are structurally different from the smaller glaciers in both Europe and South America. Overall, these results highlight the importance of integration methods in the discovery of the underlying organizational structure of biological entities in multilayer ecological networks.

The escalating risk of collisions and the accumulation of space debris in Low Earth Orbit (LEO) has reached critical concern due to the ever increasing number of spacecraft. Addressing this crisis, especially in dealing with non-cooperative and unidentified space debris, is of paramount importance. This paper contributes to efforts in enabling autonomous swarms of small chaser satellites for target geometry determination and safe flight trajectory planning for proximity operations in LEO. Our research explores on-orbit use of the You Only Look Once v5 (YOLOv5) object detection model trained to detect satellite components. While this model has shown promise, its inherent lack of interpretability hinders human understanding, a critical aspect of validating algorithms for use in safety-critical missions. To analyze the decision processes, we introduce Probabilistic Explanations for Entropic Knowledge extraction (PEEK), a method that utilizes information theoretic analysis of the latent representations within the hidden layers of the model. Through both synthetic in hardware-in-the-loop experiments, PEEK illuminates the decision-making processes of the model, helping identify its strengths, limitations and biases.

Large-sample Bayesian analogs exist for many frequentist methods, but are less well-known for the widely-used 'sandwich' or 'robust' variance estimates. We review existing approaches to Bayesian analogs of sandwich variance estimates and propose a new analog, as the Bayes rule under a form of balanced loss function, that combines elements of standard parametric inference with fidelity of the data to the model. Our development is general, for essentially any regression setting with independent outcomes. Being the large-sample equivalent of its frequentist counterpart, we show by simulation that Bayesian robust standard error estimates can faithfully quantify the variability of parameter estimates even under model misspecification -- thus retaining the major attraction of the original frequentist version. We demonstrate our Bayesian analog of standard error estimates when studying the association between age and systolic blood pressure in NHANES.

Empirical studies have widely demonstrated that neural networks are highly sensitive to small, adversarial perturbations of the input. The worst-case robustness against these so-called adversarial examples can be quantified by the Lipschitz constant of the neural network. However, only few theoretical results regarding this quantity exist in the literature. In this paper, we initiate the study of the Lipschitz constant of random ReLU neural networks, i.e., neural networks whose weights are chosen at random and which employ the ReLU activation function. For shallow neural networks, we characterize the Lipschitz constant up to an absolute numerical constant. Moreover, we extend our analysis to deep neural networks of sufficiently large width where we prove upper and lower bounds for the Lipschitz constant. These bounds match up to a logarithmic factor that depends on the depth.

We show a deterministic constant-time local algorithm for constructing an approximately maximum flow and minimum fractional cut in multisource-multitarget networks with bounded degrees and bounded edge capacities. Locality means that the decision we make about each edge only depends on its constant radius neighborhood. We show two applications of the algorithms: one is related to the Aldous-Lyons Conjecture, and the other is about approximating the neighborhood distribution of graphs by bounded-size graphs. The scope of our results can be extended to unimodular random graphs and networks. As a corollary, we generalize the Maximum Flow Minimum Cut Theorem to unimodular random flow networks.

The widespread popularity of equivariant networks underscores the significance of parameter efficient models and effective use of training data. At a time when robustness to unseen deformations is becoming increasingly important, we present H-NeXt, which bridges the gap between equivariance and invariance. H-NeXt is a parameter-efficient roto-translation invariant network that is trained without a single augmented image in the training set. Our network comprises three components: an equivariant backbone for learning roto-translation independent features, an invariant pooling layer for discarding roto-translation information, and a classification layer. H-NeXt outperforms the state of the art in classification on unaugmented training sets and augmented test sets of MNIST and CIFAR-10.

Although measuring held-out accuracy has been the primary approach to evaluate generalization, it often overestimates the performance of NLP models, while alternative approaches for evaluating models either focus on individual tasks or on specific behaviors. Inspired by principles of behavioral testing in software engineering, we introduce CheckList, a task-agnostic methodology for testing NLP models. CheckList includes a matrix of general linguistic capabilities and test types that facilitate comprehensive test ideation, as well as a software tool to generate a large and diverse number of test cases quickly. We illustrate the utility of CheckList with tests for three tasks, identifying critical failures in both commercial and state-of-art models. In a user study, a team responsible for a commercial sentiment analysis model found new and actionable bugs in an extensively tested model. In another user study, NLP practitioners with CheckList created twice as many tests, and found almost three times as many bugs as users without it.