Related papers: Named Tensor Notation

These lecture notes are intended as an introduction to several notions of tensor rank and their connections to the asymptotic complexity of matrix multiplication. The latter is studied with the exponent of matrix multiplication, which will…

We propose a novel framework in high-dimensional factor models to simultaneously analyse multiple tensor time series, each with potentially different tensor orders and dimensionality. The connection between different tensor time series is…

As the demand for processing extended textual data grows, the ability to handle long-range dependencies and maintain computational efficiency is more critical than ever. One of the key issues for long-sequence modeling using attention-based…

In this paper, we propose a novel tensor learning and coding model for third-order data completion. Our model is to learn a data-adaptive dictionary from the given observations, and determine the coding coefficients of third-order tensor…

Named entity recognition (NER) is the task to detect and classify the entity spans in the text. When entity spans overlap between each other, this problem is named as nested NER. Span-based methods have been widely used to tackle the nested…

A tensor network is a type of decomposition used to express and approximate large arrays of data. A given data-set, quantum state or higher dimensional multi-linear map is factored and approximated by a composition of smaller multi-linear…

Tensor completion is a problem of filling the missing or unobserved entries of partially observed tensors. Due to the multidimensional character of tensors in describing complex datasets, tensor completion algorithms and their applications…

The (efficient and parsimonious) decomposition of higher-order tensors is a fundamental problem with numerous applications in a variety of fields. Several methods have been proposed in the literature to that end, with the Tucker and PARAFAC…

The quadratic complexity of dot-product attention introduced in Transformer remains a fundamental bottleneck impeding the progress of foundation models toward unbounded context lengths. Addressing this challenge, we introduce the Deep…

Named entity recognition (NER) identifies typed entity mentions in raw text. While the task is well-established, there is no universally used tagset: often, datasets are annotated for use in downstream applications and accordingly only…

Encoder-decoder models have become an effective approach for sequence learning tasks like machine translation, image captioning and speech recognition, but have yet to show competitive results for handwritten text recognition. To this end,…

Named entity recognition (NER) is an important research problem in natural language processing. There are three types of NER tasks, including flat, nested and discontinuous entity recognition. Most previous sequential labeling models are…

In this paper we propose an algorithm to classify tensor data. Our methodology is built on recent studies about matrix classification with the trace norm constrained weight matrix and the tensor trace norm. Similar to matrix classification,…

Text alignment finds application in tasks such as citation recommendation and plagiarism detection. Existing alignment methods operate at a single, predefined level and cannot learn to align texts at, for example, sentence and document…

Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and…

Transformer-based models have brought a radical change to neural machine translation. A key feature of the Transformer architecture is the so-called multi-head attention mechanism, which allows the model to focus simultaneously on different…

Named Entity Recognition (NER) is a machine learning task that traditionally relies on supervised learning and annotated data. Acquiring such data is often a challenge, particularly in specialized fields like medical, legal, and financial…

Named Entity Recognition (NER) is a key step in the creation of structured data from digitised historical documents. Traditional NER approaches deal with flat named entities, whereas entities often are nested. For example, a postal address…

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…

In this paper, we extend some classes of structured matrices to higher order tensors. We discuss their relationships with positive semi-definite tensors and some other structured tensors. We show that every principal sub-tensor of such a…