# The origins of Zipf's meaning-frequency law

arXiv: https://arxiv.org/abs/1801.00168 · HTML: https://mlsanity.com/paper/1801.00168/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Dec 2017.

## Built on by (most cited first, 7 of 7)

- [How (Non-)Optimal is the Lexicon?](https://mlsanity.com/paper/2104.14279/) (2021)
- [Feature-rich multiplex lexical networks reveal mental strategies of early language learning](https://mlsanity.com/paper/2201.05061/) (2022)
- [Linguistic laws in biology](https://mlsanity.com/paper/2310.07387/) (2023)
- [The advent and fall of a vocabulary learning bias from communicative efficiency](https://mlsanity.com/paper/2105.11519/) (2021)
- [Pragmatic Constraint on Distributional Semantics](https://mlsanity.com/paper/2211.11041/) (2022)
- [Zipf's laws of meaning in Catalan](https://mlsanity.com/paper/2107.00042/) (2021)
- [Early Language Learning via Spreading Activation and Category Exploration in Complex Networks](https://mlsanity.com/paper/2607.06258/) (2026)

## Abstract (arXiv)

In his pioneering research, G. K. Zipf observed that more frequent words tend to have more meanings, and showed that the number of meanings of a word grows as the square root of its frequency. He derived this relationship from two assumptions: that words follow Zipf's law for word frequencies (a power law dependency between frequency and rank) and Zipf's law of meaning distribution (a power law dependency between number of meanings and rank). Here we show that a single assumption on the joint probability of a word and a meaning suffices to infer Zipf's meaning-frequency law or relaxed versions. Interestingly, this assumption can be justified as the outcome of a biased random walk in the process of mental exploration.