39 research outputs found
Compression as a universal principle of animal behavior
A key aim in biology and psychology is to identify fundamental principles
underpinning the behavior of animals, including humans. Analyses of human
language and the behavior of a range of non-human animal species have provided
evidence for a common pattern underlying diverse behavioral phenomena: words
follow Zipf's law of brevity (the tendency of more frequently used words to be
shorter), and conformity to this general pattern has been seen in the behavior
of a number of other animals. It has been argued that the presence of this law
is a sign of efficient coding in the information theoretic sense. However, no
strong direct connection has been demonstrated between the law and compression,
the information theoretic principle of minimizing the expected length of a
code. Here we show that minimizing the expected code length implies that the
length of a word cannot increase as its frequency increases. Furthermore, we
show that the mean code length or duration is significantly small in human
language, and also in the behavior of other species in all cases where
agreement with the law of brevity has been found. We argue that compression is
a general principle of animal behavior, that reflects selection for efficiency
of coding.Comment: This is the pre-proofed version. The published version will be
available at
http://onlinelibrary.wiley.com/journal/10.1111/%28ISSN%291551-670
Compression and the origins of Zipf's law for word frequencies
Here we sketch a new derivation of Zipf's law for word frequencies based on
optimal coding. The structure of the derivation is reminiscent of Mandelbrot's
random typing model but it has multiple advantages over random typing: (1) it
starts from realistic cognitive pressures (2) it does not require fine tuning
of parameters and (3) it sheds light on the origins of other statistical laws
of language and thus can lead to a compact theory of linguistic laws. Our
findings suggest that the recurrence of Zipf's law in human languages could
originate from pressure for easy and fast communication.Comment: arguments have been improved; in press in Complexity (Wiley
Thoughts about disordered thinking: measuring and quantifying the laws of order and disorder
Peer ReviewedPostprint (author's final draft
The meaning-frequency law in Zipfian optimization models of communication
According to Zipf's meaning-frequency law, words that are more frequent tend
to have more meanings. Here it is shown that a linear dependency between the
frequency of a form and its number of meanings is found in a family of models
of Zipf's law for word frequencies. This is evidence for a weak version of the
meaning-frequency law. Interestingly, that weak law (a) is not an inevitable of
property of the assumptions of the family and (b) is found at least in the
narrow regime where those models exhibit Zipf's law for word frequencies
Towards a theory of word order: comment on "Dependency distance: a new perspective on syntactic patterns in natural language" by Haitao Liu et al.
Peer ReviewedPostprint (author's final draft
The infochemical core
Vocalizations, and less often gestures, have been the object of linguistic research for decades. However, the development of a general theory of communication with human language as a particular case requires a clear understanding of the organization of communication through other means. Infochemicals are chemical compounds that carry information and are employed by small organisms that cannot emit acoustic signals of an optimal frequency to achieve successful communication. Here, we investigate the distribution of infochemicals across species when they are ranked by their degree or the number of species with which they are associated (because they produce them or are sensitive to them). We evaluate the quality of the fit of different functions to the dependency between degree and rank by means of a penalty for the number of parameters of the function. Surprisingly, a double Zipf (a Zipf distribution with two regimes, each with a different exponent) is the model yielding the best fit although it is the function with the largest number of parameters. This suggests that the worldwide repertoire of infochemicals contains a core which is shared by many species and is reminiscent of the core vocabularies found for human language in dictionaries or large corpora.Peer ReviewedPostprint (author's final draft
The optimality of attaching unlinked labels to unlinked meanings
Vocabulary learning by children can be characterized by many biases. When encountering a
new word, children as well as adults, are biased towards assuming that it means something totally
different from the words that they already know. To the best of our knowledge, the 1st mathematical
proof of the optimality of this bias is presented here. First, it is shown that this bias is a particular case of the maximization of mutual information between words and meanings. Second, the optimality is proven within a more general information theoretic framework where mutual information maximization competes with other information theoretic principles. The bias is a prediction from modern information theory. The relationship between information theoretic principles and the principles of contrast and mutual exclusivity is also shown.Peer ReviewedPostprint (published version
Optimal coding and the origins of Zipfian laws
The problem of compression in standard information theory consists of
assigning codes as short as possible to numbers. Here we consider the problem
of optimal coding -- under an arbitrary coding scheme -- and show that it
predicts Zipf's law of abbreviation, namely a tendency in natural languages for
more frequent words to be shorter. We apply this result to investigate optimal
coding also under so-called non-singular coding, a scheme where unique
segmentation is not warranted but codes stand for a distinct number. Optimal
non-singular coding predicts that the length of a word should grow
approximately as the logarithm of its frequency rank, which is again consistent
with Zipf's law of abbreviation. Optimal non-singular coding in combination
with the maximum entropy principle also predicts Zipf's rank-frequency
distribution. Furthermore, our findings on optimal non-singular coding
challenge common beliefs about random typing. It turns out that random typing
is in fact an optimal coding process, in stark contrast with the common
assumption that it is detached from cost cutting considerations. Finally, we
discuss the implications of optimal coding for the construction of a compact
theory of Zipfian laws and other linguistic laws.Comment: in press in the Journal of Quantitative Linguistics; definition of
concordant pair corrected, proofs polished, references update