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This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes…
We give an overview of our philosophy of pictures in mathematics. We emphasize a bi-directional process between picture language and mathematical concepts: abstraction and simulation. This motivates a program to understand different…
With the recent advancements in deep learning, neural solvers have gained promising results in solving math word problems. However, these SOTA solvers only generate binary expression trees that contain basic arithmetic operators and do not…
The purpose of this essay is to bring out the unique role of Mathematics in providing a base to the diverse sciences which conform to its rigid structure. Of these the physical and economic sciences are so intimately linked with…
This paper examines language modeling based on the theory of quantum mechanics. It focuses on the introduction of quantum mechanics into the symbol-meaning pairs of language in order to build a representation model of natural language. At…
We describe a generative probabilistic model of natural language, which we call HBG, that takes advantage of detailed linguistic information to resolve ambiguity. HBG incorporates lexical, syntactic, semantic, and structural information…
In natural language, words and phrases themselves imply the semantics. In contrast, the meaning of identifiers in mathematical formulae is undefined. Thus scientists must study the context to decode the meaning. The Mathematical Language…
Large language models (LLMs) offer a new empirical setting in which long-standing theories of linguistic meaning can be examined. This paper contrasts two broad approaches: social constructivist accounts associated with language games, and…
As Large Language Models (LLMs) are deployed more widely, customization with respect to vocabulary, style, and character becomes more important. In this work, we introduce model arithmetic, a novel inference framework for composing and…
Machine translation (MT) was developed as one of the hottest research topics in the natural language processing (NLP) literature. One important issue in MT is that how to evaluate the MT system reasonably and tell us whether the translation…
Recent advances in NLP have been attributed to the emergence of large-scale pre-trained language models. GPT-2, in particular, is suited for generation tasks given its left-to-right language modeling objective, yet the linguistic quality of…
Though the advancement of pre-trained large language models unfolds, the exploration of building a unified model for language and other multi-modal data, such as motion, remains challenging and untouched so far. Fortunately, human motion…
Generative spoken language models pretrained on large-scale raw audio can continue a speech prompt with appropriate content while preserving attributes like speaker and emotion, serving as foundation models for spoken dialogue. In prior…
Symbols (or more broadly, non-natural language textual representations) such as numerical sequences, molecular formulas, and table delimiters widely exist, playing important roles in various tasks such as abstract reasoning, chemical…
Vector representations have been pivotal in advancing natural language processing (NLP), with prior research focusing on embedding techniques for mathematical expressions using mathematically equivalent formulations. While effective, these…
The thesis presents an attempt at using the syntactic structure in natural language for improved language models for speech recognition. The structured language model merges techniques in automatic parsing and language modeling using an…
Mathematical expressions were generated, evaluated and used to train neural network models based on the transformer architecture. The expressions and their targets were analyzed as a character-level sequence transduction task in which the…
Texts present coherent stories that have a particular theme or overall setting, for example science fiction or western. In this paper, we present a text generation method called {\it rewriting} that edits existing human-authored narratives…
A practical automatic textual math word problems (MWPs) solver should be able to solve various textual MWPs while most existing works only focused on one-unknown linear MWPs. Herein, we propose a simple but efficient method called Universal…
The preservation of endangered languages is a widely discussed issue nowadays. Languages represent essential cultural heritage and can provide valuable botanical, biological, and geographical information. Therefore, it is necessary to…