This paper proposes formulating Zipf’s meaning-frequency law, the power law between word frequency and the number of meanings, as a relationship between word frequency and contextual diversity. The proposed formulation quantifies meaning counts as contextual diversity, which is based on the directions of contextualized word vectors obtained from a Language Model (LM). This formulation gives a new interpretation to the law and also enables us to examine it for a wider variety of words and corpora than previous studies have explored. In addition, this paper shows that the law becomes unobservable when the size of the LM used is small and that autoregressive LMs require much more parameters than masked LMs to be able to observe the law.

Previous works that integrated news articles to better process stock prices used a variety of neural networks to predict price movements. The textual and price information were both encoded in the neural network, and it is therefore difficult to apply this approach in situations other than the original framework of the notoriously hard problem of price prediction. In contrast, this paper presents a method to encode the influence of news articles through a vector representation of stocks called a stock embedding. The stock embedding is acquired with a deep learning framework using both news articles and price history. Because the embedding takes the operational form of a vector, it is applicable to other financial problems besides price prediction. As one example application, we show the results of portfolio optimization using Reuters & Bloomberg headlines, producing a capital gain 2.8 times larger than that obtained with a baseline method using only stock price data. This suggests that the proposed stock embedding can leverage textual financial semantics to solve financial prediction problems.

In this article, we evaluate computational models of natural language with respect to the universal statistical behaviors of natural language. Statistical mechanical analyses have revealed that natural language text is characterized by scaling properties, which quantify the global structure in the vocabulary population and the long memory of a text. We study whether five scaling properties (given by Zipf’s law, Heaps’ law, Ebeling’s method, Taylor’s law, and long-range correlation analysis) can serve for evaluation of computational models. Specifically, we test n-gram language models, a probabilistic context-free grammar, language models based on Simon/Pitman-Yor processes, neural language models, and generative adversarial networks for text generation. Our analysis reveals that language models based on recurrent neural networks with a gating mechanism (i.e., long short-term memory; a gated recurrent unit; and quasi-recurrent neural networks) are the only computational models that can reproduce the long memory behavior of natural language. Furthermore, through comparison with recently proposed model-based evaluation methods, we find that the exponent of Taylor’s law is a good indicator of model quality.

Taylor’s law describes the fluctuation characteristics underlying a system in which the variance of an event within a time span grows by a power law with respect to the mean. Although Taylor’s law has been applied in many natural and social systems, its application for language has been scarce. This article describes a new way to quantify Taylor’s law in natural language and conducts Taylor analysis of over 1100 texts across 14 languages. We found that the Taylor exponents of natural language written texts exhibit almost the same value. The exponent was also compared for other language-related data, such as the child-directed speech, music, and programming languages. The results show how the Taylor exponent serves to quantify the fundamental structural complexity underlying linguistic time series. The article also shows the applicability of these findings in evaluating language models.

The article presents results of entropy rate estimation for human languages across six languages by using large, state-of-the-art corpora of up to 7.8 gigabytes. To obtain the estimates for data length tending to infinity, we use an extrapolation function given by an ansatz. Whereas some ansatzes of this kind were proposed in previous research papers, here we introduce a stretched exponential extrapolation function that has a smaller error of fit. In this way, we uncover a possibility that the entropy rates of human languages are positive but 20% smaller than previously reported.