In this work, we study the problem of stability of Graph Convolutional Neural Networks (GCNs) under random small perturbations in the underlying graph topology, i.e. under a limited number of insertions or deletions of edges. We derive a novel bound on the expected difference between the outputs of unperturbed and perturbed GCNs. The proposed bound explicitly depends on the magnitude of the perturbation of the eigenpairs of the Laplacian matrix, and the perturbation explicitly depends on which edges are inserted or deleted. Then, we provide a quantitative characterization of the effect of perturbing specific edges on the stability of the network. We leverage tools from small perturbation analysis to express the bounds in closed, albeit approximate, form, in order to enhance interpretability of the results, without the need to compute any perturbed shift operator. Finally, we numerically evaluate the effectiveness of the proposed bound.
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Networking：IFIP International Conferences on Networking。
Explanation：國際網絡會議。
Publisher：IFIP。
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In this paper, we provide an analysis of a recently proposed multicontinuum homogenization technique. The analysis differs from those used in classical homogenization methods for several reasons. First, the cell problems in multicontinuum homogenization use constraint problems and can not be directly substituted into the differential operator. Secondly, the problem contains high contrast that remains in the homogenized problem. The homogenized problem averages the microstructure while containing the small parameter. In this analysis, we first based on our previous techniques, CEM-GMsFEM, to define a CEM-downscaling operator that maps the multicontinuum quantities to an approximated microscopic solution. Following the regularity assumption of the multicontinuum quantities, we construct a downscaling operator and the homogenized multicontinuum equations using the information of linear approximation of the multicontinuum quantities. The error analysis is given by the residual estimate of the homogenized equations and the well-posedness assumption of the homogenized equations.
We propose a generalization of nonlinear stability of numerical one-step integrators to Riemannian manifolds in the spirit of Butcher's notion of B-stability. Taking inspiration from Simpson-Porco and Bullo, we introduce non-expansive systems on such manifolds and define B-stability of integrators. In this first exposition, we provide concrete results for a geodesic version of the Implicit Euler (GIE) scheme. We prove that the GIE method is B-stable on Riemannian manifolds with non-positive sectional curvature. We show through numerical examples that the GIE method is expansive when applied to a certain non-expansive vector field on the 2-sphere, and that the GIE method does not necessarily possess a unique solution for large enough step sizes. Finally, we derive a new improved global error estimate for general Lie group integrators.
Current state-of-the-art 6d pose estimation is too compute intensive to be deployed on edge devices, such as Microsoft HoloLens (2) or Apple iPad, both used for an increasing number of augmented reality applications. The quality of AR is greatly dependent on its capabilities to detect and overlay geometry within the scene. We propose a synthetically trained client-server-based augmented reality application, demonstrating state-of-the-art object pose estimation of metallic and texture-less industry objects on edge devices. Synthetic data enables training without real photographs, i.e. for yet-to-be-manufactured objects. Our qualitative evaluation on an AR-assisted sorting task, and quantitative evaluation on both renderings, as well as real-world data recorded on HoloLens 2, sheds light on its real-world applicability.
In this note, we apply some techniques developed in [1]-[3] to give a particular construction of bivariate Abelian Codes from cyclic codes, multiplying their dimension and preserving their apparent distance. We show that, in the case of cyclic codes whose maximum BCH bound equals its minimum distance the obtained abelian code verifies the same property; that is, the strong apparent distance and the minimum distance coincide. We finally use this construction to multiply Reed-Solomon codes to abelian codes
Software Engineering (SE) Pre-trained Language Models (PLMs), such as CodeBERT, are pre-trained on large code corpora, and their learned knowledge has shown success in transferring into downstream tasks (e.g., code clone detection) through the fine-tuning of PLMs. In Natural Language Processing (NLP), an alternative in transferring the knowledge of PLMs is explored through the use of adapter, a compact and parameter efficient module that is inserted into a PLM. Although the use of adapters has shown promising results in many NLP-based downstream tasks, their application and exploration in SE-based downstream tasks are limited. Here, we study the knowledge transfer using adapters on multiple down-stream tasks including cloze test, code clone detection, and code summarization. These adapters are trained on code corpora and are inserted into a PLM that is pre-trained on English corpora or code corpora. We called these PLMs as NL-PLM and C-PLM, respectively. We observed an improvement in results using NL-PLM over a PLM that does not have adapters, and this suggested that adapters can transfer and utilize useful knowledge from NL-PLM to SE tasks. The results are sometimes on par with or exceed the results of C-PLM; while being more efficient in terms of the number of parameters and training time. Interestingly, adapters inserted into a C-PLM generally yield better results than a traditional fine-tuned C-PLM. Our results open new directions to build more compact models for SE tasks.
By abstracting over well-known properties of De Bruijn's representation with nameless dummies, we design a new theory of syntax with variable binding and capture-avoiding substitution. We propose it as a simpler alternative to Fiore, Plotkin, and Turi's approach, with which we establish a strong formal link. We also show that our theory easily incorporates simple types and equations between terms.
This paper investigates the language of propaganda and its stylistic features. It presents the PPN dataset, standing for Propagandist Pseudo-News, a multisource, multilingual, multimodal dataset composed of news articles extracted from websites identified as propaganda sources by expert agencies. A limited sample from this set was randomly mixed with papers from the regular French press, and their URL masked, to conduct an annotation-experiment by humans, using 11 distinct labels. The results show that human annotators were able to reliably discriminate between the two types of press across each of the labels. We propose different NLP techniques to identify the cues used by the annotators, and to compare them with machine classification. They include the analyzer VAGO to measure discourse vagueness and subjectivity, a TF-IDF to serve as a baseline, and four different classifiers: two RoBERTa-based models, CATS using syntax, and one XGBoost combining syntactic and semantic features. Keywords: Propaganda, Fake News, Explainability, AI alignment, Vagueness, Subjectivity, Exaggeration, Stylistic analysis
Traditional stabilizer codes operate over prime power local-dimensions. In this work we extend the stabilizer formalism using the local-dimension-invariant setting to import stabilizer codes from these standard local-dimensions to other cases. In particular, we show that any traditional stabilizer code can be used for analog continuous-variable codes, and consider restrictions in phase space and discretized phase space. This puts this framework on an equivalent footing as traditional stabilizer codes. Following this, using extensions of prior ideas, we show that a stabilizer code originally designed with a finite field local-dimension can be transformed into a code with the same $n$, $k$, and $d$ parameters for any integral domain. This is of theoretical interest and can be of use for systems whose local-dimension is better described by mathematical rings, which permits the use of traditional stabilizer codes for protecting their information as well.
An emerging trend in approximate counting is to show that certain `low-temperature' problems are easy on typical instances, despite worst-case hardness results. For the class of regular graphs one usually shows that expansion can be exploited algorithmically, and since random regular graphs are good expanders with high probability the problem is typically tractable. Inspired by approaches used in subexponential-time algorithms for Unique Games, we develop an approximation algorithm for the partition function of the ferromagnetic Potts model on graphs with a small-set expansion condition. In such graphs it may not suffice to explore the state space of the model close to ground states, and a novel feature of our method is to efficiently find a larger set of `pseudo-ground states' such that it is enough to explore the model around each pseudo-ground state.
Within the rapidly developing Internet of Things (IoT), numerous and diverse physical devices, Edge devices, Cloud infrastructure, and their quality of service requirements (QoS), need to be represented within a unified specification in order to enable rapid IoT application development, monitoring, and dynamic reconfiguration. But heterogeneities among different configuration knowledge representation models pose limitations for acquisition, discovery and curation of configuration knowledge for coordinated IoT applications. This paper proposes a unified data model to represent IoT resource configuration knowledge artifacts. It also proposes IoT-CANE (Context-Aware recommendatioN systEm) to facilitate incremental knowledge acquisition and declarative context driven knowledge recommendation.
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