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Named Tensor Notation

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 Added by Alexander M. Rush
 Publication date 2021
and research's language is English




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We propose a notation for tensors with named axes, which relieves the author, reader, and future implementers from the burden of keeping track of the order of axes and the purpose of each. It also makes it easy to extend operations on low-order tensors to higher order ones (e.g., to extend an operation on images to minibatches of images, or extend the attention mechanism to multiple attention heads). After a brief overview of our notation, we illustrate it through several examples from modern machine learning, from building blocks like attention and convolution to full models like Transformers and LeNet. Finally, we give formal definitions and describe some extensions. Our proposals build on ideas from many previous papers and software libraries. We hope that this document will encourage more authors to use named tensors, resulting in clearer papers and less bug-prone implementations. The source code for this document can be found at https://github.com/namedtensor/notation/. We invite anyone to make comments on this proposal by submitting issues or pull requests on this repository.

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We present a weakly-supervised data augmentation approach to improve Named Entity Recognition (NER) in a challenging domain: extracting biomedical entities (e.g., proteins) from the scientific literature. First, we train a neural NER (NNER) model over a small seed of fully-labeled examples. Second, we use a reference set of entity names (e.g., proteins in UniProt) to identify entity mentions with high precision, but low recall, on an unlabeled corpus. Third, we use the NNER model to assign weak labels to the corpus. Finally, we retrain our NNER model iteratively over the augmented training set, including the seed, the reference-set examples, and the weakly-labeled examples, which improves model performance. We show empirically that this augmented bootstrapping process significantly improves NER performance, and discuss the factors impacting the efficacy of the approach.
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As the field of recommender systems has developed, authors have used a myriad of notations for describing the mathematical workings of recommendation algorithms. These notations ap-pear in research papers, books, lecture notes, blog posts, and software documentation. The dis-ciplinary diversity of the field has not contributed to consistency in notation; scholars whose home base is in information retrieval have different habits and expectations than those in ma-chine learning or human-computer interaction. In the course of years of teaching and research on recommender systems, we have seen the val-ue in adopting a consistent notation across our work. This has been particularly highlighted in our development of the Recommender Systems MOOC on Coursera (Konstan et al. 2015), as we need to explain a wide variety of algorithms and our learners are not well-served by changing notation between algorithms. In this paper, we describe the notation we have adopted in our work, along with its justification and some discussion of considered alternatives. We present this in hope that it will be useful to others writing and teaching about recommender systems. This notation has served us well for some time now, in research, online education, and traditional classroom instruction. We feel it is ready for broad use.
In this paper, we present a series of complementary approaches to improve the recognition of underrepresented named entities (NE) in hybrid ASR systems without compromising overall word error rate performance. The underrepresented words correspond to rare or out-of-vocabulary (OOV) words in the training data, and thereby cant be modeled reliably. We begin with graphemic lexicon which allows to drop the necessity of phonetic models in hybrid ASR. We study it under different settings and demonstrate its effectiveness in dealing with underrepresented NEs. Next, we study the impact of neural language model (LM) with letter-based features derived to handle infrequent words. After that, we attempt to enrich representations of underrepresented NEs in pretrained neural LM by borrowing the embedding representations of rich-represented words. This let us gain significant performance improvement on underrepresented NE recognition. Finally, we boost the likelihood scores of utterances containing NEs in the word lattices rescored by neural LMs and gain further performance improvement. The combination of the aforementioned approaches improves NE recognition by up to 42% relatively.
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