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Protocol sequences are used for channel access in the collision channel without feedback. Each user accesses the channel according to a deterministic zero-one pattern, called the protocol sequence. In order to minimize fluctuation of…
Quantum reservoir computers (QRCs) have emerged as a promising approach to quantum machine learning, since they utilize the natural dynamics of quantum systems for data processing and are simple to train. Here, we consider $n$-qubit quantum…
Bidirectional Encoder Representations from Transformers (BERT) has shown marvelous improvements across various NLP tasks, and consecutive variants have been proposed to further improve the performance of the pre-trained language models. In…
A wide variety of neural-network architectures have been proposed for the task of Chinese word segmentation. Surprisingly, we find that a bidirectional LSTM model, when combined with standard deep learning techniques and best practices, can…
Let $R$ be a finite ring and let $M, N$ be two finite left $R$-modules. We present two distinct deterministic algorithms that decide in polynomial time whether or not $M$ and $N$ are isomorphic, and if they are, exhibit an isomorphism. As…
Chinese word segmentation has entered the deep learning era which greatly reduces the hassle of feature engineering. Recently, some researchers attempted to treat it as character-level translation, which further simplified model designing,…
Model order reduction (MOR) methods that are designed to preserve structural features of a given full order model (FOM) often suffer from a lower accuracy when compared to their non-structure-preserving counterparts. In this paper, we…
Although end-to-end Neural Machine Translation (NMT) has achieved remarkable progress in the past two years, it suffers from a major drawback: translations generated by NMT systems often lack of adequacy. It has been widely observed that…
We introduce a new method for producing both maximal green and reddening sequences of quivers. The method, called component preserving mutations, generalizes the notion of direct sums of quivers and can be used as a tool to both recover…
In this paper, we establish a method for model order reduction of a certain class of physical network systems. The proposed method is based on clustering of the vertices of the underlying graph, and yields a reduced order model within the…
This paper addresses the problem of model reduction for dynamical system models that describe biochemical reaction networks. Inherent in such models are properties such as stability, positivity and network structure. Ideally these…
This paper introduces a unified regression framework based on the Lagrange formalism, demonstrating how polynomial and logistic regression can all be formulated within a common variational (Lagrangian formalism) structure. Within this…
We explain a method, inspired by control theory model reduction and interpolation theory, that rigorously establishes the types of coarse graining that are appropriate for systems with quadratic, generalized Hamiltonians. For such systems,…
Quotient regularization models (QRMs) are a class of powerful regularization techniques that have gained considerable attention in recent years, due to their ability to handle complex and highly nonlinear data sets. However, the nonconvex…
In Neural Machine Translation (NMT), the decoder can capture the features of the entire prediction history with neural connections and representations. This means that partial hypotheses with different prefixes will be regarded differently…
Chinese word segmentation (CWS) is the basic of Chinese natural language processing (NLP). The quality of word segmentation will directly affect the rest of NLP tasks. Recently, with the artificial intelligence tide rising again, Long…
Attention-based Encoder-Decoder has the effective architecture for neural machine translation (NMT), which typically relies on recurrent neural networks (RNN) to build the blocks that will be lately called by attentive reader during the…
Consistent Recalibration models (CRC) have been introduced to capture in necessary generality the dynamic features of term structures of derivatives' prices. Several approaches have been suggested to tackle this problem, but all of them,…
Entanglement is a defining property of quantum systems. For a subsystem of a larger quantum system, one can formally define an operator known as the modular Hamiltonian, which is closely linked to the entanglement properties of that…
Machine learning techniques for the solution of inverse problems have become an attractive approach in the last decade, while their theoretical foundations are still in their infancy. In this chapter we want to pursue the study of…