Natural language syntax complies with the free-e nergy principle Elliot Murphy12 Emma Holmes34 Karl Fri ston4 1. Vivian L. Smith Department of Neurosurgery McGovern Medical School

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Natural language syntax complies with the free-energy principle

Elliot Murphy1,2, Emma Holmes3,4, Karl Friston4

1. Vivian L. Smith Department of Neurosurgery, McGovern Medical School,

University of Texas Health Science Center, Houston, Texas, 77030, USA

2. Texas Institute for Restorative Neurotechnologies, University of Texas Health

Science Center, Houston, Texas, 77030, USA

3. Department of Speech Hearing and Phonetic Sciences, University College

London, London, WC1N 1PF, UK

4. The Wellcome Centre for Human Neuroimaging, UCL Queen Square Institute

of Neurology, London, WC1N 3AR, UK

Correspondence concerning this article should be addressed to Elliot Murphy

(elliot.murphy@uth.tmc.edu).

Word count: 13,443

Figure count: 1

NATURAL LANGUAGE SYNTAX COMPLIES WITH THE FREE-ENERGY PRINCIPLE

Abstract:

Natural language syntax yields an unbounded array of hierarchically structured

expressions. We claim that these are used in the service of active inference in accord

with the free-energy principle (FEP). While conceptual advances alongside modelling

and simulation work have attempted to connect speech segmentation and linguistic

communication with the FEP, we extend this program to the underlying computations

responsible for generating syntactic objects. We argue that recently proposed

principles of economy in language design—such as “minimal search” criteria from

theoretical syntax—adhere to the FEP. This affords a greater degree of explanatory

power to the FEP—with respect to higher language functions—and offers linguistics a

grounding in first principles with respect to computability. We show how both tree-

geometric depth and a Kolmogorov complexity estimate (recruiting a Lempel–Ziv

compression algorithm) can be used to accurately predict legal operations on syntactic

workspaces, directly in line with formulations of variational free energy minimization.

This is used to motivate a general principle of language design that we term Turing–

Chomsky Compression (TCC). We use TCC to align concerns of linguists with the

normative account of self-organization furnished by the FEP, by marshalling evidence

from theoretical linguistics and psycholinguistics to ground core principles of efficient

syntactic computation within active inference.

Keywords: Free-energy principle; active inference; language; Kolmogorov

complexity; Lempel–Ziv; compression

NATURAL LANGUAGE SYNTAX COMPLIES WITH THE FREE-ENERGY PRINCIPLE

Implementational models of language must be plausible from the perspective of

neuroanatomy (Embick & Poeppel 2015), but they must also be plausible from the

perspective of how biophysical systems behave. We will argue that the structuring

influence of the free-energy principle (FEP) can be detected in language, not only via

narrative (Bouizegarene et al. 2020), interpersonal dialogue (Friston et al. 2020),

cooperative/intentional communication (Vasil et al. 2020) and speech segmentation

(Friston et al. 2021), but also at the more fundamental level of what linguists consider

to be basic phrase-level computations (Berwick & Stabler 2019, Chomsky 1949, 1951,

1956, 1959, 2021a, 2021b, 2021c).

Natural language syntax yields an unbounded array of hierarchically structured

expressions. We argue that many historical insights into syntax are consistent with the

FEP—providing a novel perspective under which the principles governing syntax are

not limited to language, but rather reflect domain-general processes. This is consistent

with a strain within theoretical linguistics that explores how syntactic computation may

adhere to “general principles that may well fall within extra-biological natural law,

particularly considerations of minimal computation” (Chomsky 2011: 263), such that

certain linguistic theories might be engaging with general properties of organic

systems (Chomsky 2004, 2014). Here, we consider the idea that many aspects of

natural language syntax may be special cases of a variational principle of least free-

energy. To this end, we examine whether a complexity measure relevant to

formulations of free-energy—namely, Kolmogorov complexity (Hutter 2006, MacKay

1995, Wallace & Dowe 1999)—relates to legal syntactic processes.

While the FEP has a substantial explanatory scope, across a large range of

cognitive systems, it can also be seen as a method or principle of least action for multi-

NATURAL LANGUAGE SYNTAX COMPLIES WITH THE FREE-ENERGY PRINCIPLE

disciplinary research (Ramstead et al. 2021), in much the same way that the notion of

economy is typically entertained in linguistics as a programmatic notion (Chomsky

1995). The FEP itself has been argued to be more of a conceptual-mathematical

model for self-organizing systems (for some, it is a “generic” model; Barandiaran &

Chemero 2009), or a guiding framework (Colombo & Wright 2021). Thus, when we

argue that natural language syntax “complies” with the FEP, this is not to imply that

the FEP necessarily bears any specific, direct predictions for linguistic behaviour.

Rather, it motivates the construction of conceptual arguments for how some property

of organic systems might be seen as realizing the FEP.

We begin by summarising the FEP, and describe how syntactic principles are

consistent with it. We consider how the FEP is a variational principle of “least action”,

such as those that describe systems with conserved quantities (Coopersmith 2017).

We then review key observations from linguistics that speak to the structuring

influence of computational efficiency, involving “least effort” and “minimal search”

restrictions (Bošković & Lasnik 2007, Gallego & Martin 2018, Larson 2015), viewing

language as a product of an individual’s mind/brain, following the standard ‘I-language’

(Chomsky 1986, 2000) perspective in generative linguistics (i.e., ‘internal’, ‘individual’,

‘intensional’). After modeling the complexity of postulated minimal search

procedures—versus their ungrammatical alternatives across a small but

representative number of exemplar cases—we propose a unifying principle for how

the goals of the FEP might be realised during the derivation of syntactic structures,

which we term Turing–Chomsky Compression. We conclude by highlighting directions

for future work.

NATURAL LANGUAGE SYNTAX COMPLIES WITH THE FREE-ENERGY PRINCIPLE

1. Active Inference and the Free-Energy Principle

Before we evaluate any work pertaining to linguistic behaviour, this section introduces

key elements of the FEP that motivate its application to language.

1.1. The Free-Energy Principle

The FEP has a long history in theoretical neuroscience (see Friston 2010 for a review).

It states that any adaptive change in the brain will minimise free-energy, either over

evolutionary time or immediate, perceptual time (Ramstead et al. 2018). Free-energy

is an information-theoretic quantity and is a function of sensory data and brain states:

in brief, it is the upper bound on the ‘surprise’—or surprisal (Tribus 1961)—of sensory

data, given predictions that are based on an internal model of how those data were

generated. The difference between free-energy and surprise is the difference

(specified by the Kullback-Leibler divergence) between probabilistic representations

encoded by the brain and the true conditional distribution of the causes of sensory

input. This is evident in the following equation, which specifies variational free energy

(F) as the negative log probability of observations ( ) under a generative model (i.e.,

‘surprise’) plus the Kullback–Leibler divergence (DKL) between the approximate

posterior distribution and the true posterior distribution (where Q indicates posterior

beliefs, indicates the states in the generative model, and P indicates the probability

under the internal model):

(Eq. 1)



ln ( ) [ ( ) || ( | )]

F Po D Qs Ps o=−+

  

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摘要：

Naturallanguagesyntaxcomplieswiththefree-energyprincipleElliotMurphy1,2,EmmaHolmes3,4,KarlFriston41.VivianL.SmithDepartmentofNeurosurgery,McGovernMedicalSchool,UniversityofTexasHealthScienceCenter,Houston,Texas,77030,USA2.TexasInstituteforRestorativeNeurotechnologies,UniversityofTexasHealthScienceCe...

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Natural language syntax complies with the free-e nergy principle Elliot Murphy12 Emma Holmes34 Karl Fri ston4 1. Vivian L. Smith Department of Neurosurgery McGovern Medical School

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