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1. Embedding properties of network realizations of dissipative reduced order models

   Druskin, Guddati ( July 2022 , HOUSEHOLDER SYMPOSIUM XXI)

   Embedding properties of network realizations of dissipative reduced order models Jörn Zimmerling, Mikhail Zaslavsky,Rob Remis, Shasri Moskow, Alexander Mamonov, Murthy Guddati, Vladimir Druskin, and Liliana Borcea Mathematical Sciences Department, Worcester Polytechnic Institute https://www.wpi.edu/people/vdruskin Abstract Realizations of reduced order models of passive SISO or MIMO LTI problems can be transformed to tridiagonal and block-tridiagonal forms, respectively, via dierent modications of the Lanczos algorithm. Generally, such realizations can be interpreted as ladder resistor-capacitor-inductor (RCL) networks. They gave rise to network syntheses in the rst half of the 20th century that was at the base of modern electronics design and consecutively to MOR that tremendously impacted many areas of engineering (electrical, mechanical, aerospace, etc.) by enabling ecient compression of the underlining dynamical systems. In his seminal 1950s works Krein realized that in addition to their compressing properties, network realizations can be used to embed the data back into the state space of the underlying continuum problems. In more recent works of the authors Krein's ideas gave rise to so-called nite-dierence Gaussian quadrature rules (FDGQR), allowing to approximately map the ROM state-space representation to its full order continuum counterpart on a judicially chosen grid. Thus, the state variables can be accessed directly from the transfer function without solving the full problem and even explicit knowledge of the PDE coecients in the interior, i.e., the FDGQR directly learns" the problem from its transfer function. This embedding property found applications in PDE solvers, inverse problems and unsupervised machine learning. Here we show a generalization of this approach to dissipative PDE problems, e.g., electromagnetic and acoustic wave propagation in lossy dispersive media. Potential applications include solution of inverse scattering problems in dispersive media, such as seismic exploration, radars and sonars. To x the idea, we consider a passive irreducible SISO ROM fn(s) = Xn j=1 yi s + σj , (62) assuming that all complex terms in (62) come in conjugate pairs. We will seek ladder realization of (62) as rjuj + vj − vj−1 = −shˆjuj , uj+1 − uj + ˆrj vj = −shj vj , (63) for j = 0, . . . , n with boundary conditions un+1 = 0, v1 = −1, and 4n real parameters hi, hˆi, ri and rˆi, i = 1, . . . , n, that can be considered, respectively, as the equivalent discrete inductances, capacitors and also primary and dual conductors. Alternatively, they can be viewed as respectively masses, spring stiness, primary and dual dampers of a mechanical string. Reordering variables would bring (63) into tridiagonal form, so from the spectral measure given by (62 ) the coecients of (63) can be obtained via a non-symmetric Lanczos algorithm written in J-symmetric form and fn(s) can be equivalently computed as fn(s) = u1. The cases considered in the original FDGQR correspond to either (i) real y, θ or (ii) real y and imaginary θ. Both cases are covered by the Stieltjes theorem, that yields in case (i) real positive h, hˆ and trivial r, rˆ, and in case (ii) real positive h,r and trivial hˆ,rˆ. This result allowed us a simple interpretation of (62) as the staggered nite-dierence approximation of the underlying PDE problem [2]. For PDEs in more than one variables (including topologically rich data-manifolds), a nite-dierence interpretation is obtained via a MIMO extensions in block form, e.g., [4, 3]. The main diculty of extending this approach to general passive problems is that the Stieltjes theory is no longer applicable. Moreover, the tridiagonal realization of a passive ROM transfer function (62) via the ladder network (63) cannot always be obtained in port-Hamiltonian form, i.e., the equivalent primary and dual conductors may change sign [1]. 100 Embedding of the Stieltjes problems, e.g., the case (i) was done by mapping h and hˆ into values of acoustic (or electromagnetic) impedance at grid cells, that required a special coordinate stretching (known as travel time coordinate transform) for continuous problems. Likewise, to circumvent possible non-positivity of conductors for the non-Stieltjes case, we introduce an additional complex s-dependent coordinate stretching, vanishing as s → ∞ [1]. This stretching applied in the discrete setting induces a diagonal factorization, removes oscillating coecients, and leads to an accurate embedding for moderate variations of the coecients of the continuum problems, i.e., it maps discrete coecients onto the values of their continuum counterparts. Not only does this embedding yields an approximate linear algebraic algorithm for the solution of the inverse problems for dissipative PDEs, it also leads to new insight into the properties of their ROM realizations. We will also discuss another approach to embedding, based on Krein-Nudelman theory [5], that results in special data-driven adaptive grids. References [1] Borcea, Liliana and Druskin, Vladimir and Zimmerling, Jörn, A reduced order model approach to inverse scattering in lossy layered media, Journal of Scientic Computing, V. 89, N1, pp. 136,2021 [2] Druskin, Vladimir and Knizhnerman, Leonid, Gaussian spectral rules for the three-point second dierences: I. A two-point positive denite problem in a semi-innite domain, SIAM Journal on Numerical Analysis, V. 37, N 2, pp.403422, 1999 [3] Druskin, Vladimir and Mamonov, Alexander V and Zaslavsky, Mikhail, Distance preserving model order reduction of graph-Laplacians and cluster analysis, Druskin, Vladimir and Mamonov, Alexander V and Zaslavsky, Mikhail, Journal of Scientic Computing, V. 90, N 1, pp 130, 2022 [4] Druskin, Vladimir and Moskow, Shari and Zaslavsky, Mikhail LippmannSchwingerLanczos algorithm for inverse scattering problems, Inverse Problems, V. 37, N. 7, 2021, [5] Mark Adolfovich Nudelman The Krein String and Characteristic Functions of Maximal Dissipative Operators, Journal of Mathematical Sciences, 2004, V 124, pp 49184934 Go back to Plenary Speakers Go back to Speakers Go back 

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2. On the Power of Pre-Trained Text Representations: Models and Applications in Text Mining

   https://doi.org/10.1145/3447548.3470810  

   Meng, Yu ; Huang, Jiaxin ; Zhang, Yu ; Han, Jiawei ( August 2021 , KDD'21:The 27th {ACM} {SIGKDD} Conference on Knowledge Discovery and Data Mining, August 14-18, 2021)

   null (Ed.)

   Recent years have witnessed the enormous success of text representation learning in a wide range of text mining tasks. Earlier word embedding learning approaches represent words as fixed low-dimensional vectors to capture their semantics. The word embeddings so learned are used as the input features of task-specific models. Recently, pre-trained language models (PLMs), which learn universal language representations via pre-training Transformer-based neural models on large-scale text corpora, have revolutionized the natural language processing (NLP) field. Such pre-trained representations encode generic linguistic features that can be transferred to almost any text-related applications. PLMs outperform previous task-specific models in many applications as they only need to be fine-tuned on the target corpus instead of being trained from scratch. In this tutorial, we introduce recent advances in pre-trained text embeddings and language models, as well as their applications to a wide range of text mining tasks. Specifically, we first overview a set of recently developed self-supervised and weakly-supervised text embedding methods and pre-trained language models that serve as the fundamentals for downstream tasks. We then present several new methods based on pre-trained text embeddings and language models for various text mining applications such as topic discovery and text classification. We focus on methods that are weakly-supervised, domain-independent, language-agnostic, effective and scalable for mining and discovering structured knowledge from large-scale text corpora. Finally, we demonstrate with real world datasets how pre-trained text representations help mitigate the human annotation burden and facilitate automatic, accurate and efficient text analyses. 

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3. Temporal Attribute Prediction via Joint Modeling of Multi-Relational Structure Evolution

   https://doi.org/10.24963/ijcai.2020/386  

   Garg, Sankalp ; Sharma, Navodita ; Jin, Woojeong ; Ren, Xiang ( July 2020 , Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence)

   Time series prediction is an important problem in machine learning. Previous methods for time series prediction did not involve additional information. With a lot of dynamic knowledge graphs available, we can use this additional information to predict the time series better. Recently, there has been a focus on the application of deep representation learning on dynamic graphs. These methods predict the structure of the graph by reasoning over the interactions in the graph at previous time steps. In this paper, we propose a new framework to incorporate the information from dynamic knowledge graphs for time series prediction. We show that if the information contained in the graph and the time series data are closely related, then this inter-dependence can be used to predict the time series with improved accuracy. Our framework, DArtNet, learns a static embedding for every node in the graph as well as a dynamic embedding which is dependent on the dynamic attribute value (time-series). Then it captures the information from the neighborhood by taking a relation specific mean and encodes the history information using RNN. We jointly train the model link prediction and attribute prediction. We evaluate our method on five specially curated datasets for this problem and show a consistent improvement in time series prediction results. We release the data and code of model DArtNet for future research. 

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4. Adversarial Attacks on Deep Graph Matching

   Zhang, Zijie ; Zhang, Zeru ; Zhou, Yang ; Shen, Yelong ; Jin, Ruoming ; Dou, Dejing ( December 2020 , Advances in Neural Information Processing Systems 33: Annual Conference on Neural Information Processing Systems 2020, NeurIPS 2020)

   null (Ed.)

   Despite achieving remarkable performance, deep graph learning models, such as node classification and network embedding, suffer from harassment caused by small adversarial perturbations. However, the vulnerability analysis of graph matching under adversarial attacks has not been fully investigated yet. This paper proposes an adversarial attack model with two novel attack techniques to perturb the graph structure and degrade the quality of deep graph matching: (1) a kernel density estimation approach is utilized to estimate and maximize node densities to derive imperceptible perturbations, by pushing attacked nodes to dense regions in two graphs, such that they are indistinguishable from many neighbors; and (2) a meta learning-based projected gradient descent method is developed to well choose attack starting points and to improve the search performance for producing effective perturbations. We evaluate the effectiveness of the attack model on real datasets and validate that the attacks can be transferable to other graph learning models. 

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5. Fuzzy Logic Based Logical Query Answering on Knowledge Graphs

   https://doi.org/10.1609/aaai.v36i4.20310  

   Chen, Xuelu ; Hu, Ziniu ; Sun, Yizhou ( June 2022 , Proceedings of the AAAI Conference on Artificial Intelligence)

   Answering complex First-Order Logical (FOL) queries on large-scale incomplete knowledge graphs (KGs) is an important yet challenging task. Recent advances embed logical queries and KG entities in the same space and conduct query answering via dense similarity search. However, most logical operators designed in previous studies do not satisfy the axiomatic system of classical logic, limiting their performance. Moreover, these logical operators are parameterized and thus require many complex FOL queries as training data, which are often arduous to collect or even inaccessible in most real-world KGs. We thus present FuzzQE, a fuzzy logic based logical query embedding framework for answering FOL queries over KGs. FuzzQE follows fuzzy logic to define logical operators in a principled and learning-free manner, where only entity and relation embeddings require learning. FuzzQE can further benefit from labeled complex logical queries for training. Extensive experiments on two benchmark datasets demonstrate that FuzzQE provides significantly better performance in answering FOL queries compared to state-of-the-art methods. In addition, FuzzQE trained with only KG link prediction can achieve comparable performance to those trained with extra complex query data. 

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