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Boolean tensor decomposition approximates data of multi-way binary relationships as product of interpretable low-rank binary factors, following the rules of Boolean algebra. Here, we present its first probabilistic treatment. We facilitate…
Linear sequences of words are implicitly represented in our brains by hierarchical structures that organize the composition of words in sentences. Linguists formalize different frameworks to model this hierarchy; two of the most common…
Transformer-based pre-trained language models (PLMs) have dramatically improved the state of the art in NLP across many tasks. This has led to substantial interest in analyzing the syntactic knowledge PLMs learn. Previous approaches to this…
In the literature, tensors have been effectively used for capturing the context information in language models. However, the existing methods usually adopt relatively-low order tensors, which have limited expressive power in modeling…
Modelling compositionality has been a longstanding area of research in the field of vector space semantics. The categorical approach to compositionality maps grammar onto vector spaces in a principled way, but comes under fire for requiring…
Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…
In this work, we present tensor-based linear and nonlinear models for hyperspectral data classification and analysis. By exploiting principles of tensor algebra, we introduce new classification architectures, the weight parameters of which…
Tree-structured neural networks have proven to be effective in learning semantic representations by exploiting syntactic information. In spite of their success, most existing models suffer from the underfitting problem: they recursively use…
In this paper, we propose a compositional nonparametric method in which a model is expressed as a labeled binary tree of $2k+1$ nodes, where each node is either a summation, a multiplication, or the application of one of the $q$ basis…
Latent tree learning models represent sentences by composing their words according to an induced parse tree, all based on a downstream task. These models often outperform baselines which use (externally provided) syntax trees to drive the…
We propose a new approach to image segmentation, which exploits the advantages of both conditional random fields (CRFs) and decision trees. In the literature, the potential functions of CRFs are mostly defined as a linear combination of…
We consider the problem of discriminatively learning restricted Boltzmann machines in the presence of relational data. Unlike previous approaches that employ a rule learner (for structure learning) and a weight learner (for parameter…
Decoupling multivariate polynomials is useful for obtaining an insight into the workings of a nonlinear mapping, performing parameter reduction, or approximating nonlinear functions. Several different tensor-based approaches have been…
This chapter studies the problem of decomposing a tensor into a sum of constituent rank one tensors. While tensor decompositions are very useful in designing learning algorithms and data analysis, they are NP-hard in the worst-case. We will…
Modern NLP models rely heavily on engineered features, which often combine word and contextual information into complex lexical features. Such combination results in large numbers of features, which can lead to over-fitting. We present a…
This paper is concerned with the approximation of high-dimensional functions in a statistical learning setting, by empirical risk minimization over model classes of functions in tree-based tensor format. These are particular classes of…
Several classification methods assume that the underlying distributions follow tree-structured graphical models. Indeed, trees capture statistical dependencies between pairs of variables, which may be crucial to attain low classification…
Tensors are a natural way to express correlations among many physical variables, but storing tensors in a computer naively requires memory which scales exponentially in the rank of the tensor. This is not optimal, as the required memory is…
Deep neural networks (DNNs) and decision trees (DTs) are both state-of-the-art classifiers. DNNs perform well due to their representational learning capabilities, while DTs are computationally efficient as they perform inference along one…
Extractive compression is a challenging natural language processing problem. This work contributes by formulating neural extractive compression as a parse tree transduction problem, rather than a sequence transduction task. Motivated by…