# The Vector Grounding Problem

Dimitri Coelho Mollo
Department of Historical  Philosophical and Religious Studies
Umeå University
<EMAIL_ADDRESS>
&Raphaël Millière
Philosophy Department
Center for Science and Society
Columbia University
<EMAIL_ADDRESS>

###### Abstract

The remarkable performance of large language models (LLMs) on complex
linguistic tasks has sparked a lively debate on the nature of their
capabilities. Unlike humans, these models learn language exclusively from
textual data, without direct interaction with the real world. Nevertheless,
they can generate seemingly meaningful text about a wide range of topics. This
impressive accomplishment has rekindled interest in the classical ‘Symbol
Grounding Problem,’ which questioned whether the internal representations and
outputs of classical symbolic AI systems could possess intrinsic meaning.
Unlike these systems, modern LLMs are artificial neural networks that compute
over vectors rather than symbols. However, an analogous problem arises for
such systems, which we dub the Vector Grounding Problem. This paper has two
primary objectives. First, we differentiate various ways in which internal
representations can be grounded in biological or artificial systems,
identifying five distinct notions discussed in the literature: referential,
sensorimotor, relational, communicative, and epistemic grounding.
Unfortunately, these notions of grounding are often conflated. We clarify the
differences between them, and argue that referential grounding is the one that
lies at the heart of the Vector Grounding Problem. Second, drawing on theories
of representational content in philosophy and cognitive science, we propose
that certain LLMs, particularly those fine-tuned with Reinforcement Learning
from Human Feedback (RLHF), possess the necessary features to overcome the
Vector Grounding Problem, as they stand in the requisite causal-historical
relations to the world that underpin intrinsic meaning. We also argue that,
perhaps unexpectedly, multimodality and embodiment are neither necessary nor
sufficient conditions for referential grounding in artificial systems.

##  1 Introduction

Over the past decade, the field of artificial intelligence has witnessed
remarkable advancements, largely attributable to the emergence and maturation
of deep learning techniques (LeCun et al. 2015, Buckner 2019). Several factors
contributed to this progress. The exponential increase in computational power
has facilitated the development and training of larger artificial neural
networks on specialised hardware. Additionally, the availability of extensive
textual and audiovisual datasets, primarily sourced from the internet, has
enabled the application of deep learning methods to a wide array of tasks. One
notable development within the domain of natural language processing has been
the creation of massive neural networks trained on an abundance of linguistic
data, known as Large Language Models (LLMs).111The term ‘model’ can be
somewhat misleading, as these systems are often not scientific models created
for representing or explaining phenomena; rather, they are engineered systems
with practical applications, frequently becoming the subject of scientific
investigation themselves.

LLMs such as BERT (Devlin et al. 2018), GPT-3 (Brown et al. 2020), and PaLM
(Chowdhery et al. 2022) are built upon the Transformer architecture (Vaswani
et al. 2017), which features a mechanism—self-attention—specifically designed
to model long-range dependencies between linguistic elements across extensive
text sequences. Transformer-based LLMs have showcased remarkable capabilities,
such as generating coherent and contextually relevant texts spanning a diverse
range of subjects, from current events to philosophical essays; answering
commonsense questions; explaining novel jokes; and consistently demonstrating
near-human, human, or even super-human performance across numerous linguistic
tasks (Kiela et al. 2021, Bubeck et al. 2023). This progress has also laid the
foundation for vision-language models (VLMs), such as DALL-E 2 (Ramesh et al.
2022), Flamingo (Alayrac et al. 2022), and GPT-4 (OpenAI 2023), which are
trained on images in addition to text.

The exceptional performance of LLMs on sophisticated linguistic tasks, which
were once considered strong indicators of human-like intelligence, raises
intriguing questions regarding the nature of language processing, language
understanding, and linguistic acts such as writing or speaking. These
questions encompass broad and complex issues, and efforts to address them are
still in their infancy. In this paper, we aim to make modest progress toward
understanding the capabilities of LLMs and interpreting their outputs.
Specifically, we will revisit the so-called ‘Symbol Grounding Problem’, which
engaged philosophers and natural language processing researchers during an
earlier wave of AI research, and explore its implications for contemporary
approaches to artificial language modelling. The core issue can be summarised
as follows: if AI systems are merely designed to process linguistic inputs,
how can their outputs be grounded in a world with which they have no direct
interaction? How can those outputs possess any meaning beyond the
interpretations that we, as intelligent beings embedded in the world, may
project onto them?

We will show that a similar conundrum arises for LLMs. Since these systems do
not compute over symbols, but over vectors and matrices instead, the problem
assumes a slightly different form. We call this the Vector Grounding Problem.
After outlining this new version of the classical problem and acknowledging
its difficulty, we will suggest that there are grounds for optimism,
especially in light of recent advancements in the field, such as the use of
Reinforcement Learning through Human Feedback (RLHF), and the emergence of in-
context learning. We will argue that the Vector Grounding Problem for LLMs is
far from insurmountable today, as those novel features of current models allow
them to stand in relations to the world that are sufficient to ground their
representations and outputs. One surprising implication of our argument is
that multimodality and embodiment are neither necessary nor sufficient to
escape the Vector Grounding Problem. Indeed, LLMs trained on text only may
achieve the relevant form of grounding, while VLMs trained on images in
addition to text might not (at least not without meeting additional
requirements).

Importantly, this paper does not address whether LLMs or VLMs understand
language (or anything at all), engage in linguistic acts, or possess cognitive
or mental properties. We do not claim that these models ‘know’ what they mean,
or even what meaning is, nor that they have any conception of truth or
falsity. Our sole contention is that the problem of grounding internal states
in the world is solvable for LLMs and related models. While having grounded
internal states may be a crucial step toward understanding, agency, knowledge,
and various other cognitive and mental capacities, it is improbable that they
are, by themselves, sufficient for those capacities. This clarification is
especially important as the current debate occasionally blurs these
distinctions—–a conflation we strive to avoid in this paper.

With these caveats in mind, we will proceed as follows. In section 2, we
briefly introduce two main approaches to artificial intelligence—classical (or
symbolic) and connectionist AI—and introduce the Symbol Grounding Problem in
the context of the former. In section 3, we present in more detail the family
of connectionist systems to which LLMs and VLMs belong—Large Pre-Trained
Models—and reveal that a similar grounding issue arises for them: the Vector
Grounding Problem. We differentiate between various senses of grounding and
show that referential grounding is the one essential to the Vector Grounding
Problem in section 4. Finally, in section 5, we argue that at least some LLMs
and related multimodal models possess the necessary elements for being
grounded in the world.

##  2 Classical and Connectionist Approaches to AI

Since its inception, research on artificial intelligence has been divided
between two main paradigms. The classical or symbolic paradigm focuses on
designing systems that represent and manipulate information using discrete
symbols (such as words, numbers, and logical expressions). Classical AI
systems manipulate symbols based on explicit rules or procedures that are also
represented symbolically. Symbolic manipulation is purely syntactic; it is
based on the shapes of symbols and the way in which they can be combined into
complex symbolic structures (Simon & Newell 1971).

SHRDLU, developed by Terry Winograd at MIT in 1968, is a canonical example of
a symbolic system designed for natural language understanding (Winograd 1971).
The system could parse simple English instructions and questions about a basic
virtual environment called the ‘blocks world’. The blocks world contained
virtual objects, such as blocks, cones, and balls. SHRDLU could respond to
user commands in natural language to move these virtual objects and describe
the state of the blocks world. In this system, the meaning of linguistic
symbols such as ‘move’, ‘red’ and ‘block’ is programmatically determined to
correspond to features of virtual objects and actions in the blocks world.
Various hand-coded rules are provided for the system to respond appropriately
to user input. These include parsing rules to interpret the syntactic
structure of the input (e.g., “Pick up a big red block”), inference rules to
infer new or implicit facts (e.g., inferring the location of a block after it
has been moved), and action rules specifying changes to the world state in
response to commands (e.g., rules for changing block positions after
determining that a move was possible based on the parsing and inference
rules). SHRDLU’s code also includes explicit axioms used to constrain possible
interpretations of sentences by ruling out certain meanings that would violate
these axioms. For example, an axiom specifies that no two blocks can be in the
same place at the same time, to rule out interpretations of sentences that
would require two blocks to be in the same location. Axioms like these encode
background knowledge and constraints on what is possible in the blocks world.

By contrast, the connectionist paradigm centres around Artificial Neural
Networks (ANNs) (Mcclelland et al. 1986). ANNs do not represent information
through symbols and explicit rules. Instead, they are composed of
interconnected nodes (or ‘neurons’) that collectively encode and process
information in a distributed way. In addition, they are ‘trained’ using data
relevant to the task they are designed to perform, which often involves
classification or prediction. During the training process, the network’s
parameters (i.e., the numerical values, or weights, of each node-to-node
connection) are gradually and automatically adjusted until the ANN succeeds in
the task, typically by means of capturing statistical patterns in the training
data. Connectionist systems are thus data-driven and bottom-up: their
behaviour emerges from processing signals across weighted connections, rather
than by being explicitly programmed with symbolic rules.

From the 1980s on, increased computing power enabled the development of ANNs
with increasingly larger number of nodes, organised in several layers, and
endowed with non-linear activation functions (LeCun et al. 2015). Larger
numbers of nodes and layers allow ANNs to transform the inputs they receive in
increasingly abstract ways, and the backpropagation learning algorithm makes
it possible for such larger ANNs to be efficiently trained on data with known
classifications (Rumelhart et al. 1986). These innovations allowed ANNs to
achieve significantly better performance than earlier ones, especially in
complex, non-linear real-world problems like computer vision and speech
recognition.

In a classical system like SHRDLU, representations and computations are easily
interpretable, because rules and symbols have an explicitly programmed
interpretation. In contrast, the internal workings of a sufficiently large
trained ANN are like a ‘black box’ that maps inputs to outputs. The mechanisms
by which this mapping occurs are extremely difficult for humans to understand.
There are no simple symbolic interpretations of the patterns of activation
over nodes, and no explicit rules or procedures that can be inspected to shed
light on how the network functions. While ANNs are able to discover complex
patterns and generalise beyond specific examples, their black box nature makes
the nature of their internal representations opaque (Castelvecchi 2016).

###  2.1 The Symbol Grounding Problem

The Symbol Grounding Problem, as identified by Harnad (1990), is the problem
of how artificial intelligence systems can come to have internal
representations and outputs that possess intrinsic meaning—that is to say,
that are meaningful in themselves, independently of the interpretation of
those representations and outputs by external agents, such as humans. It is
common to take Harnad’s Symbol Grounding Problem as an elaboration of an
earlier, highly influential criticism of AI: Searle’s 1980 (in)famous Chinese
Room thought experiment.222Harnad (1990) himself followed this line.

There are important differences, however, between the Symbol Grounding Problem
and Searle’s points. First, Searle is concerned with the elusive notion of
understanding, which he leaves unexplained. Harnad, on the other hand, is
interested in how symbols internal to AI systems can be meaningful, regardless
of whether the system itself is capable of understanding (whatever that ends
up consisting in). Searle’s criticism, moreover, is targeted at both symbolic
and connectionist approaches to AI, while Harnad’s Symbol Grounding Problem is
more constrained, aiming only at symbolic AI. Finally, Searle uses the Chinese
Room thought experiment to cast doubt on the possibility of strong, or real
artificial intelligence in general. Harnad is hopeful that the Symbol
Grounding Problem is solvable, and indeed suggests a solution, which involves
hybridising symbolic and connectionist AI (see subsection 4.6). For these
reasons, we will leave aside Searle’s Chinese Room thought experiment, on
which, incidentally, probably too much ink has already been spilled.

Harnad (1990) provides a simple and powerful intuition pump to motivate the
existence of a Symbol Grounding Problem in classical, symbolic AI: the Chinese
Dictionary. Take a system, be it biological or artificial, which knows no
natural language. Suppose that we want it to learn Chinese (or any other
language), but the only resource we have available to provide the system is a
single language dictionary, say a comprehensive Chinese-Chinese dictionary.
Will the system be able to learn Chinese just by using the dictionary? The
thought experiment invites the intuition that the system would not be able to
do so. After all, the most it can do is to look up strings of symbols and see
what other strings of symbols follow them. The former would be the words to be
defined, the latter their definitions. However, for the system they are just
meaningless shapes followed by other shapes, and it seems intuitively hopeless
that the meaning of words (parts of those strings of symbols) could be learned
in this way. What seems to be missing is a way out from the symbolic ‘merry-
go-round’: to connect those symbols in the dictionary to what they pick out in
the world. But how can that be possible if the system has no access to the
world, but only to further symbols?

Symbolic AI systems, according to Harnad, find themselves in this predicament.
All they have access to are strings of symbols and how they follow each other.
There seems to be no way for connections between such symbols and the world to
be established, and thus no way for the symbols to have intrinsic meaning.
They are just strings of computationally-relevant shapes, deprived from any
meaning in themselves, insofar as the system itself has no way to learn what
it is that they pick out in the world. Humans, who do have representations
arguably acquired by means of engagement with the world, are, on the other
hand, able to interpret those symbolic representations and outputs as
meaningful. The meaning of the representations is hence extrinsic, depending
on human interpreters. Take out the interpreter, and no meaning is to be
found.

In brief, symbolic AI systems, the argument goes, manipulate symbols that are
not connected to the world, that are not grounded in the world; and thereby
have no intrinsic meaning. Classical AI systems, in other words, suffer from
the Symbol Grounding Problem.

##  3 Large Pre-Trained Models

Connectionist models have come a long way since the 1980s. The increasing
availability of large datasets and more powerful computers enabled the
development of deep neural networks (DNNs), characterised by having a very
large number of layers between input and output. Early DNNs were typically
task-specific architectures, designed and trained separately for individual
problems like image classification or speech recognition. In the 2010s,
researchers began investigating more general-purpose deep network
architectures that could be pre-trained on large datasets, then fine-tuned for
new tasks (LeCun et al. 2015, Radford et al. 2018).

Research on DNNs recently converged on a unified approach to many problems
that previously required dedicated solutions: training large models on a vast
amount of data to perform a broad range of tasks they have not been explicitly
designed for. The suggestive phrase ‘Foundation Models’ was coined to capture
the significance of this trend (Bommasani et al. 2022), although we will
prefer the more neutral label ‘Large Pre-Trained Models’. These models share a
few key characteristics. They are trained through self-supervision, that is,
without relying on manually labelled data; they are relatively adaptable to
novel tasks without requiring task-specific fine-tuning; and, finally, scaling
up their size (parameter count) and training data has generally proven to be a
very effective way to improve their capabilities.

Almost all Large Pre-Trained Models are powered by the Transformer
architecture, first introduced by Vaswani et al. (2017). Transformers use an
attention mechanism to model global dependencies between sequential elements
in the input, such as sentences in natural language. The general inductive
biases supplied by this mechanism make Transformers suitable for many domains,
including natural language processing and computer vision.

Some Large Pre-Trained Models, called _Large Language Models_ (LLMs), are
trained exclusively on text. LLMs like GPT-3 and PaLM have over $10^{11}$
parameters and are trained on massive corpora spanning hundred of billions of
words, containing a significant subset of all written text on the internet
(e.g., millions of web pages, hundreds of thousands of books, and all of
English Wikipedia). After training, LLMs can generate well-written and
coherent paragraphs about virtually any topic. Furthermore, given explicit
instructions in natural language in the input sequence, or ‘prompts’, they can
perform a broad range of tasks, including: summarising long-form content,
translating between multiple languages, answering complex questions, engaging
in commonsense reasoning, solving simple logic and maths problems, generating
code for simple programs, or explaining jokes.

LLMs learn distributed representations of words conditioned on the contexts in
which they appear in the training data. More specifically, these models
process input text into a sequence of tokens (i.e., full words, word-parts
such as ‘-ing’, punctuation marks, and other linguistic symbols). LLMs encode
each token as a vector of real-valued numbers in a high-dimensional vector
space, and estimate the probabilities of all possible next tokens in the
sequence based on the previous context vectors. The resulting prediction of
the next token in the sequence is then compared to the actual next token, and
the model’s parameters are subsequently updated to make the correct token more
probable in that context, and other tokens less probable. This encourages the
model to learn representations of tokens conditioned on the contexts in which
they tend to occur, with semantically similar tokens having vectors that are
close together in the high-dimensional space.

There is a deep connection between the way in which LLMs learn contextual
representations from linguistic corpora, and the old idea from structural
linguistics according to which word meaning can be inferred from the contexts
in which they appear, known as the ‘distributional hypothesis’ (Harris 1954,
Firth 1957). In LLMs, semantic similarity is determined based on distribution
across contexts: tokens that appear in similar contexts are modelled by nearby
vectors. The dimensions of the vectors are tuned by the model to best predict
surrounding tokens, and capture distributional patterns. Though the individual
dimensions are not typically interpretable, the positions of vectors in the
space are a result of statistical patterns in the linguistic data, and reflect
semantic similarities in light of how the words are used in context. In this
way, vector representations of tokens in LLMs are not arbitrary or
conventional—as the symbols in classical AI systems typically are—since they
are shaped by statistical patterns in language.

It is worth noting that not all Large Pre-Trained Models are trained
exclusively on linguistic data. _Vision-language models_ (VLMs) are trained on
images (or videos) in addition to text, allowing them to perform a wide range
of tasks that involve exploiting relationships between visual and linguistic
information (Radford et al. 2021). For example, VLMs can caption images with
natural language descriptions, answer questions about their content, and
generate novel images based on text prompts (Ramesh et al. 2022, Alayrac et
al. 2022, OpenAI 2023). To do so, VLMs encode text and images as vector
representations in a single high-dimensional space. They can be trained on a
large corpus of image-caption pairs, where the goal is to predict if a given
image-text pair comes from the training data or not. This leads the VLM to
learn vector representations of images and text which reflect their semantic
relationships, such that images and captions with related content are encoded
as nearby vectors in high-dimensional space. Thus, like LLMs, VLMs learn
contextual representations that leverage distributional semantics, albeit
across modalities: semantically similar images and pieces of text have similar
representations because they tend to co-occur in the training data (Chen et
al. 2020).

###  3.1 The Vector Grounding Problem

As discussed in section 2, there are fundamental differences between the
symbolic approach to AI targeted by Harnad’s Symbol Grounding Problem and the
connectionist approach underlying Large Pre-Trained Models. Despite these
differences, a challenge analogous to the Symbol Grounding Problem can be
posed for connectionist systems. Instead of symbols, these systems employ
vectors as units of representation and computation. LLMs are trained
exclusively on vast amounts of text, which are translated into vectors
representing each text token. This ‘translation’ is achieved through self-
supervised learning with minimal hand-coding. Starting from these initial
vectors and adjusting connection weights (or parameters) during training,
LLMs’ internal processing generates new vectors that ultimately inform the
system’s output, i.e., the probability of each token being the next in the
given sequence.

LLMs appear to face a similar predicament to that of traditional symbolic AI
systems (_pace_ Harnad (1990), see 4.6). They rely on vectors as numerical
proxies for statistical relationships between tokens. This reliance on
continuous vectors, rather than discrete symbols, seems to make no difference
when it comes to escaping the merry-go-round of representations and being
connected to the external world—LLMs are trapped in a carousel of numbers,
rather than symbols. Much like their classical counterparts, LLMs manipulate
vectors that do not seem grounded in the world and thus lack intrinsic
meaning. Consequently, they grapple with an analogous difficulty, which we
term the _Vector Grounding Problem_.

Bender & Koller (2020) propose a thought-provoking thought experiment, the
“Octopus Test”, to pump intuitions about the inescapability of the Vector
Grounding Problem for LLMs.

> The Octopus Test. Two English-speaking castaways find themselves stranded on
> neighbouring islands, separated by treacherous waters. Fortuitously, they
> discover telegraphs left by previous inhabitants, connected via an
> underwater cable, which enables them to communicate by exchanging
> telegraphic messages. Unbeknownst to them, a superintelligent octopus
> inhabits these waters and taps into the underwater cable, intercepting their
> messages. Though the octopus lacks any knowledge of English, its
> superintelligence allows it to detect statistical patterns in the
> telegraphic messages and to form an accurate representation of the
> statistical relationships between various telegraphic signals. The octopus
> decides to sever the underwater cable and position itself at the ends of the
> two resulting cable segments, receiving and replying to telegraphic signals
> from both castaways based on the statistical patterns it has identified.
> Whether or not the castaways notice this change, the messages sent by the
> octopus intuitively seem to hold no intrinsic meaning. After all, the
> octopus simply adheres to the statistical patterns it has learned from
> listening in on the previous exchanges between the humans, without any
> understanding of the human interpretation of the signals, such as ‘coconut’
> or ‘tree’. Furthermore, the octopus likely does not comprehend that the
> signals possess meaning or serve a communicative function.333Bender & Koller
> (2020) emphasise the fact that the octopus lacks communicative intent when
> generating telegraphic signals. Since our focus here is in the narrower,
> more basic question of vector grounding, rather than on the more complex
> capacities related to language comprehension and communication, we will set
> those considerations aside for now.

As should be clear, the octopus in this thought experiment is operating
roughly as an extremely powerful LLM would. Regardless of how the octopus
represents the signals and their statistical relations, be it through vectors
or another means, it only has access to the signals and their statistical
relations—without any connection to the entities and properties in the real
world that the words encoded in those signals represent. Consequently, even if
the octopus can produce outputs that appear sensible to humans in all
situations, these outputs lack intrinsic meaning, as the octopus does not and
cannot assign meaning to them.444Our version of the Octopus Test goes beyond
Bender & Koller (2020) by assuming that it is possible the humans would never
notice they were no longer communicating with each other. In contrast, Bender
& Koller (2020) contends that the octopus would fail to produce appropriate
outputs to questions involving concrete objects it has never perceived, such
as ‘how do I build a coconut catapult?’. This claim seems to be challenged by
the often plausible replies that current LLMs provide to this sort of
question. All the more so, we should expect the superintelligent octopus to
generate even more reliably plausible responses. The Octopus Test implies that
LLMs generate outputs as devoid of intrinsic meaning as those produced by the
superintelligent octopus.555Arguably, LLMs’ outputs might be even more devoid
of intrinsic meaning than the octopus’, given that the latter is a biological
organism with motivation, superintelligence, and other features that LLMs
lack. Similar considerations apply to the comparison between LLMs and parrots
(Bender et al. 2021). In the case of these animals, even if their outputs
carry some meaning, they typically do not align with the meaning of the
language they produce.. It is humans, whether castaways or otherwise, who
interpret these outputs as meaningful because they resemble meaningful words
and sentences. LLMs have no access to coconuts, trees, or anything else beyond
language. The vectors they receive and manipulate during internal processing
are merely meaningless arrays of numbers, ungrounded in anything outside
statistical patterns in language, just like the outputs they generate. In
other words, the Octopus Test primes the intuition that all meaning in the
outputs produced by LLMs lies in the eye of the beholder, their human
interpreters. This would be so, we might add, because LLMs are susceptible to
the Vector Grounding problem.

Throughout the remainder of this paper, we will challenge this claim and
counter the intuition primed by the Octopus Test. We aim to show that,
contrary to first appearances, LLMs and other Large Pre-Trained Models, such
as VLMs, possess the relevant features to generate meaningful outputs based on
meaningful internal representations.

However, before delving into this argument, a more thorough examination of the
concept of grounding is necessary.

##  4 Five notions of Grounding

The notion of grounding appears quite frequently in philosophy, cognitive
science, and artificial intelligence research. In philosophy, it plays a
central role in many discussions on metaphysics (Fine 2012). However, our
focus will be on the notion of grounding that directly pertains to the
question of whether the internal representations and outputs of LLMs possess
intrinsic meaning, enabling them to represent things in the world
independently of human interpretation. This understanding of the term is most
prevalent in cognitive science and artificial intelligence. Various notions of
grounding have been invoked by cognitive scientists and AI researchers as
central to establishing meaning, occasionally leading to confusion. In this
section, we endeavour to bring clarity to this debate by identifying five
primary notions of grounding at play in discussions about intrinsic meaning in
cognitive systems, both biological and artificial (Figure 1).

Furthermore, we contend that only one of these five notions of grounding is
crucial for addressing the Vector Grounding Problem. If LLMs possess features
that enable them to adhere to the criteria for this particular type of
grounding, they become candidates for having representations and outputs with
intrinsic meaning. With this in mind, let us examine each distinct notion of
grounding in turn.

Figure 1: Five notions of grounding. A. _Referential grounding_ : a lexical
representation (<DOG>) is connected to its worldly referent (a dog). B.
_Sensorimotor grounding_ : a lexical representation (<DOG>) is connected to a
sensory representation (image of a dog). C. _Relational grounding_ : a lexical
representation (<DOG>) is connected to other lexical representations (<PET>,
<FURRY>). D. _Communicative grounding_ : Two speakers calibrate their
interpretation of an exchange to make use of the same lexical concept (<DOG>).
E. _Epistemic grounding_ : A lexical representation (<DOG>) is connected to
information stored in a knowledge base (about dog facts).

###  4.1 Referential Grounding

The first notion of grounding, which we may call _referential grounding_ ,
closely aligns with the philosophical notion of reference.666Partee (1981)
uses the phrase “language-to-world grounding” to designate a closely related
notion, which she contrasts with “language-to-language grounding” (see
subsection 4.3 below for a discussion of the latter). While Partee’s notion of
language-to-world grounding focuses on what ties down the intensions of
linguistic expressions with respect to their extralinguistic content, our
notion of referential grounding is broader, to include the relation between
mental representations and their worldly referents. It is the type of
grounding that connects representations to things in the world. Reference can
be loosely described as a relation that enables representations to ‘hook onto’
worldly entities or properties.777Much philosophical work has been dedicated
to examining the nature and varieties of reference, particularly for various
aspects of linguistic discourse, such as proper names, indexicals, and
abstract concepts. Reference is also normally taken to be very precise: a term
refers unambiguously (although there is an ongoing debate about the reference
of vague expressions). For our limited purposes, however, the intuitive notion
captured by this ‘hooking’ metaphor will suffice. For example, the word
‘Paris’ refers to the city of Paris, and arguably, so does a map of Paris.
Both representations allow us to receive and convey information about the
actual city of Paris. Similarly, many of our thoughts seem to hook onto
specific entities and properties in the world, allowing us to entertain
thoughts that refer to Paris, such as beliefs about it being the capital of
France or desires to visit the city.

Referential grounding, as we use the term, is whatever makes it so that
representations, whether public (e.g., words and maps) or internal (e.g.,
beliefs and subpersonal states), hook onto the world. It is plausible that
different kinds of representation require different means for hooking onto the
world in the relevant sense, that is, to be referentially grounded in specific
worldly entities and properties.

###  4.2 Sensorimotor Grounding

Another type of grounding that is often appealed to, especially in cognitive
psychology, is what we call _sensorimotor grounding_. For an internal
representation, such as a lexical concept, to be grounded in this sense is for
it to be fundamentally linked to sensorimotor representations available within
a cognitive system. For instance, the lexical concept ’football’ is
sensorimotorically grounded if its representation in a cognitive system can be
reduced to or is intrinsically connected to sensorimotor representations of
kicking movements, of the visual perception of a football pitch, of the
auditory perception of the sound of a ball being kicked, etc. This kind of
grounding plays a prominent role in theories in cognitive psychology that
embrace a moderate form of embodied cognition, such as those positing the
existence of “perceptual symbol systems” in human cognition (Barsalou 1999,
Pulvermüller 1999).

Interestingly, sensorimotor grounding is also the solution proposed by Harnad
(1990) to his Symbol Grounding Problem. He argued that the symbols in
classical AI systems needed to be grounded in two types of representation: (a)
iconic representations, which depict transformations of the projections of
object ’shapes’ on a system’s sensory surfaces; and (b) categorical
representations, which represent invariant sensory features that facilitate
the identification and discrimination of objects in different categories.
Harnad hypothesised that connectionist approaches to AI would be better
equipped to provide the necessary iconic and categorical representations,
which could then complement symbolic AI systems and result in hybrid symbolic-
connectionist systems.

We will come back to Harnad’s suggestion in subsection 4.6, arguing that it
fails to solve the Symbol Grounding Problem, and does not help with the Vector
Grounding Problem either.

###  4.3 Relational Grounding

A third notion of grounding, that we may call _relational grounding_ , is
occasionally used to refer specifically to intralinguistic relationships, in
accordance with the idea that a word’s meaning in a language is partly
determined by its relations to other words.888The label is somewhat under-
descriptive, since all forms of grounding are relational, though in different
ways. What we wish to underline, however, is that on this sense of grounding
the meaning of representations is dependent on the relations they stand in to
other representations in the same representational system. Thus, Partee (1981)
introduces the notion of “language-to-language grounding”, referring to the
way in which a language learner acquires knowledge about the meanings of words
by learning semantic connections between words in the language. According to
Partee, one key way in which this happens is through accepting certain
sentences as true, particularly those that are regarded as impervious to
empirical challenge within the linguistic community. For example, learning
that “bachelors are unmarried males” helps ground the meaning of ‘bachelor’ in
terms of its relation to ‘unmarried’ and ‘male’. More generally, semantic
relations like synonymy, hyponymy, meronymy, and the like can help ground a
word’s meaning by relating it to the meanings of other words.999Partee
contrasts language-to-language grounding with language-to-world grounding,
referring to the idea that word meanings must also be tied to the external
world, and not just to other words (i.e., what we called _referential
grounding_ above).

Partee’s analysis of language-to-language grounding focuses on the kinds of
logical and conceptual relations between word meanings that can be expressed
by meaning postulates or lexical decomposition. Meaning postulates are
metalinguistic statements that explicitly specify analytic relations between
words or expressions (such as “For every $x$, if $x$ is red then $x$ is
coloured”) (Carnap 1952). By contrast, lexical decomposition is a method of
representing word meaning by breaking it down into smaller units of meaning.
For example, Katz (1972) argues that word meanings are composed of semantic
markers, which are labels that express certain semantic or conceptual content
(e.g., ‘dog’ can be decomposed into [+ANIMATE], [+MAMMAL], and [+CANINE]).
Likewise, Jackendoff (1990) proposes to decompose the meaning of linguistic
expressions into conceptual primitives. These approaches converge in the
assumption that meaning can be at least partly grounded in relations among
words or expressions in a language.

Relational grounding is also closely related to inferential role semantics
(Block 1986, Brandom 1994). Inferential role semantics identifies the meaning
of a linguistic expression with its inferential relations to other
expressions. While lexical decomposition focuses on conceptual structures,
inferential role semantics focuses more broadly on the role played by words in
inferences. For example, the word ‘and’ plays a logical role in reasoning that
determines when compound statements are true or false based on the truth or
falsity of their components. Likewise, words like ‘larger’ or ‘slower’ have
inferential roles in comparisons, allowing us to determine comparisons between
items or the relative properties of a single item. Knowledge of such relations
between words underlies our ability to draw material inferences in language
and thought.

Finally, there is a clear connection between Partee’s “language-to-language
grounding” and distributional semantics. Like meaning postulates, lexical
decomposition, and inferential role semantics, distributional semantics seeks
to analyse word meanings in terms of word-to-word relationships. However,
instead of drawing on linguistic analyses of word meaning to identify semantic
primitives, structures, or inferential roles, it relies on analysing co-
occurrence statistics in text corpora. Consequently, distributional semantic
models capture relationships between words grounded in patterns of use, rather
than linguistic theory. In particular, modern vector space models such as LLMs
trained on large amounts of data can capture a wide range of usage-based
relationships between words, including more colloquial or informal
relationships that may be missed by lexical decomposition. Additionally, they
represent words in a continuous vector space, so that semantic relationships
are reflected in distance relations in such a space. This can accommodate
nuances in relatedness that are harder to capture with the discrete components
and relations of lexical decomposition. The high dimensionality of vector
spaces also allows for representing complex, multifaceted similarities between
words—some of which plausibly reflect conceptual structure and/or inferential
roles (Piantadosi & Hill 2022).

###  4.4 Communicative Grounding

Confusingly, the notion of grounding is also used in relation to another
aspect of language, which has to do with communication (Clark & Brennan 1991,
Traum 1994). In this context, the ’grounding problem’ refers to the problem of
establishing _common ground_ between speakers in conversation:

> In communication, common ground cannot be properly updated without a process
> we shall call _grounding_ … In conversation, for example, the participants
> try to establish that what has been said has been understood. In our
> terminology, they try to ground what has been said – that is, make it part
> of their common ground. (Clark & Brennan 1991, p. 128)

From this perspective, linguistic communication can be seen as a form of
coordinated action that involves collaborating to reach a common understanding
of what is said. The process of communicative grounding may involve explicit
clarification strategies, such as prompting an interlocutor to repeat or
reformulate a corrupted or ambiguous statement. But it also involves tracking
communicative intentions during the exchange, to infer what is communicated
from what is said. Such inferences can be made partly on the basis of
pragmatic presuppositions, namely what speakers take for granted or assume to
be true when they use certain sentences in the context of the conversation
(Stalnaker 2002).

The communicative notion of grounding has also been discussed by natural
language processing (NLP) researchers (Brennan 1998, Di Maro 2021, Chandu et
al. 2021). For example, Chandu et al. (2021) distinguish between _static_
grounding, in which common ground in basic communication between a human user
and a virtual agent is automatically established by querying a database (e.g.,
asking for a weather report); and _dynamic grounding_ , in which common ground
is more gradually established in back-and-forth communication between a human
and a dialogue agent. Bender & Koller (2020) define meaning to be a relation
between linguistic expressions and communicative intent, and characterise this
relation as a form of grounding:

> Without access to a means of hypothesizing and testing the underlying
> communicative intents, reconstructing them from the forms alone is hopeless,
> and [LLMs’] language use will eventually diverge from the language use of an
> agent who can ground their language in coherent communicative intents.
> (Bender & Koller 2020, p. 5189)

While communicative and referential grounding are distinct notions, they are
related in important ways. Referential grounding anchors language to the
world, but the same linguistic expressions may be referentially grounded in
different ways for different speakers, due to differences in perception,
knowledge, and conceptualisation. This means that calibrating reference in
conversation requires communicative grounding—language users must work
together to negotiate a common way of connecting language to the world.
Without such collaboration, there is no guarantee that speakers really mean
the same thing, even if they are using the same words.

###  4.5 Epistemic Grounding

Finally, the notion of grounding is occasionally used by NLP researchers to
refer more minimally to the relationship between linguistic expressions and
information stored in knowledge bases (Poon 2013, Tsai & Roth 2016, Chandu et
al. 2021, Thoppilan et al. 2022). For example, an expert system may contain a
knowledge base of facts and rules belonging to a particular domain. When the
system receives user input, it can query this knowledge base to determine an
appropriate response. A classic example is MYCIN, an expert system for
diagnosing infectious blood diseases (Shortliffe 1977). When given patient
symptoms, MYCIN would search its knowledge base of medical rules and facts to
suggest possible diagnoses and recommend treatments. In this system, language
is grounded in the structured knowledge contained in the expert system’s
knowledge base. We can call this notion _epistemic grounding_.

There are two ways in which current LLMs may involve epistemic grounding.
Firstly, they can be hooked up to external databases used to retrieve
information (Borgeaud et al. 2022, Thoppilan et al. 2022). Secondly, it has
been suggested that even LLMs that are not augmented with retrieval
capabilities might be functionally similar to knowledge bases themselves
(Petroni et al. 2019). Indeed, they may encode a significant amount of world
knowledge in their weights after pre-training on a very large corpus, as
illustrated by the remarkable performance of state-of-the-art LLMs on a wide
range of factual question-answering benchmarks (OpenAI 2023, Bubeck et al.
2023).

###  4.6 What Grounding for LLMs?

We have identified five distinct notions of grounding that play prominent
roles in discussions about meaning grounding in biological and artificial
systems. Which of these notions is necessary for LLMs to possess
representations and produce outputs endowed with intrinsic meaning? Recall
that in order to possess such meaning, it is minimally required that a
system’s representations and outputs be intrinsically about worldly entities
and properties, rather than have this connection be fixed through external
ascription—for example from a human user. To identify the most suitable notion
of grounding for this task, we will employ an elimination strategy, examining
each notion for its adequacy, beginning with Harnad’s proposal of sensorimotor
grounding as a solution to the Symbol Grounding Problem.

Sensorimotor grounding connects conceptual or linguistic representations to
sensorimotor representations within the same cognitive system. This sort of
grounding can be useful to shed light on some features of the former
representations, how they work, and what roles they can play in the economy of
a cognitive system. However, sensorimotor grounding falls short in addressing
the merry-go-round problem, as it merely grounds one type of representation in
another, rather than elucidating how they are tied to worldly entities and
properties. Consequently, it fails to resolve the central question of how
sensorimotor representations, which are posited to ground conceptual and
linguistic ones, establish a meaningful connection with the world.

One might argue that sensorimotor representations are grounded in the world by
resembling, to some extent, the entities they represent. However, the success
of such an approach relies on an additional factor beyond sensorimotor
grounding itself: it is the relevant resemblance relations that are supposed
to ground those sensorimotor representations in the world.101010See subsection
5.3 below for more on resemblance-based approaches to meaning. Grounding a set
of symbols in iconic (and categorical) representations—whether within a purely
symbolic, connectionist, or hybrid system—offers no solution without an
explanation of how these representations acquire intrinsic meaning. As
sensorimotor grounding does not directly provide a connection with the world
but only with other representations, it appears insufficient in addressing the
Symbol Grounding Problem, at least without further elaboration. Similarly,
this form of grounding does not resolve the Vector Grounding Problem, as
grounding vectors in other vectors still leaves open the question of how any
of those vectors come to be about anything at all.

The same line of reasoning applies to relational, communicative, and epistemic
grounding. Relational grounding anchors linguistic representations in their
relationships to other linguistic representations, suggesting that a
representation’s meaning is determined by its connections to the meanings of
other representations within a network of inferential, conceptual, or
statistical relations. Although this kind of grounding clearly does not escape
the representational carousel, the question arises whether it is sufficient to
provide intrinsic meaning nonetheless. One immediate challenge to such an idea
is the existence of a indefinite number of possible networks of mutually
coherent representations (assuming that at least approximately coherent
systems of representations are required). What picks out which of those
networks are appropriate for our world? And how did we come to possess an
appropriate one? Ruling out miraculous coincidences or pre-established harmony
(both of which are clearly untenable positions), the only plausible
explanation involves appealing to an additional, world-involving factor that
ensures that at least a subset of the representations in the network actually
connects with the world more directly (see 5.3).

Communicative grounding seeks to anchor representations in the shared content
of linguistic interactions between agents. However, this shared content relies
itself on the representations within the agents’ cognitive systems and the
meanings of any public representations used in the exchange. As with
sensorimotor grounding, one type of representation is grounded in another,
perpetuating the representational carousel without direct engagement with the
world. To address the Vector Grounding Problem (or the Symbol Grounding
Problem, for that matter), communicative grounding requires an additional
component: an account of how the grounding representations establish a
connection with the world.

Epistemic grounding, on the other hand, aims to ground linguistic
representations in knowledge bases. Yet, this approach encounters a familiar
obstacle: the representations within the knowledge bases themselves call for
an explanation of how they acquire intrinsic meaning. Consequently, epistemic
grounding alone fails to provide a comprehensive solution to the Grounding
Problem, as it does not address the question of how representations come to
possess intrinsic meaning to start with.

As the foregoing analysis suggests, the form of grounding that underlies the
other four types and is most relevant to addressing the Grounding Problem is
what we have termed referential grounding. The primary objective of
referential grounding is to anchor a representation—be it a symbol, a map, or
a vector—in the world itself, rather than in other representations. It stands
as the sole form of grounding that escapes the representational merry-go-round
and establishes a connection between a representation and whatever worldly
entity or property it is about. Consequently, to determine whether Large Pre-
Trained Models such as LLMs manipulate and produce representations with
intrinsic meaning, we must assess whether they can achieve referential
grounding. To do so, we first need to examine the requirements for a
representation to be referentially grounded.

##  5 Grounding Large Pre-Trained Models

###  5.1 Theories of Representational Content: causes and history

Fortunately, philosophers of cognitive science have dedicated considerable
effort over the past several decades to developing theories that explain how
mental and cognitive states, such as beliefs, desires, and neural activations,
can be about, or mean, entities and properties in the world. A subset of these
mental and cognitive states plausibly enables external, public
representations–such as words and sentences—to be meaningful. The meaning of
these external representations derives from the beliefs, intentions, and
conceptual representations of language users. Therefore, the _aboutness_ of
these mental and cognitive states is considered fundamental rather than
derived from any other type of meaningful state or process. What mental and
cognitive processes are about, or mean, is typically called ‘representational
content’, or ‘content’ for short. The philosophical project of developing
theories of representational content has the aim of illuminating how meaning
can emerge in a world that otherwise seems devoid of it. After all, natural
objects such as rocks and lakes generally do not possess internal states
endowed with meaning and, by themselves at least, do not mean anything.

It is, of course, beyond the scope of this paper to review and assess existing
theories of representational content.111111See Neander (2017), Millikan
(2017), Shea (2018) for book-length defences of the main contenders in current
debate. What matters for our limited purposes is that, despite some
disagreements on the finer details, philosophers of cognitive science have
largely reached a consensus on the key factors that enable internal states to
acquire content, and thus become representations with intrinsic meaning
(Coelho Mollo 2022). The first, most fundamental point of agreement is that an
account of representational content must identify one or more natural
relations between internal states and external entities and properties
responsible for making the former about the latter. These natural relations
must not be ones that already involve states with meaning. Since the goal is
to account for the emergence of meaning in the world, theories of content must
exclusively rely on meaning-less states and processes to avoid vicious
circularity. Much of the work in this area has been dedicated to identifying
those relations that can yield fruitful content ascriptions and contribute to
explaining the behaviour of cognitive systems.

Two natural relations are widely considered to be central to endowing states
with meaning: causal-informational relations, and historical relations. In
general terms, causal-informational relations occur when one state of the
world conveys information about another due to a causally-generated
correlation between the two states. A classic example is the relationship
between smoke and fire: smoke is correlated with fire because it is caused by
it, so the presence of smoke carries information about the presence of fire.
Less evidently, neurons in brain area V1 convey information about edges in the
perceived visual scene, as their activation correlates (through a relatively
complex causal chain) with the presence of edges in the world in front of the
perceiving subject. However, the mere existence of a causal-informational
relation is widely believed to be insufficient to provide an account of
representational content. Such relations are abundant in nature, including
instances where no meaningful state appears to be present, as in the smoke-
fire example. An additional requirement often mentioned is that the causal-
informational relation be exploited, that is, used by a system due to its
information-carrying nature (Shea 2018). In other words, a system must use the
presence of smoke to obtain information about the presence of fire, form a
belief about there being a fire, guide fire-related behaviour, and so on, for
smoke to be a viable candidate for representing fire for that system.

However, there are several reasons to believe that exploited causal-
informational relations alone are insufficient to form the basis for an
adequate theory of representational content. One of the primary reasons is
that causal-informational relations fail to account for a key aspect of
meaningful states: their capacity for truth or falsehood, correctness or
incorrectness. To be a representation inherently involves the possibility of
_misrepresentation_ –the possibility of getting things wrong and failing to
fit to the world accurately. The addition of historical relations in theories
of content is partially motivated by their ability to address this gap.
Indeed, the historical relations relevant to elucidating the emergence of
meaning in the natural world involve selection and learning processes. The
guiding idea is that, through selection and/or learning, states and processes
in cognitive system come to acquire functions they are supposed to perform.
For example, neurons in V1 have the function of detecting edges in the visual
scene because they were selected for this purpose during evolution via natural
selection; and such selection occurred due to the causal-informational
relations they maintain with actual edges in the world. When these neurons
successfully detect edges, they represent correctly; when they fail to fire in
the presence of an edge or fire in the absence of one, they misrepresent.
Meaning involves a kind of descriptive normativity (Neander 2017), which can
be accounted for through the appropriate historical relations between systems
and the world.

Existing theories vary in the emphasis they place on causal-informational or
historical relations when accounting for the contents of representations, as
well as in the specific types of such relations they prioritise. Additionally,
they may diverge on the inclusion of further relations, such as structural
resemblance relations. Nevertheless, all of these theories, in one way or
another, assert that a combination of these relations is central to the
emergence of meaning in the world. To possess underived meaning, at a minimum,
is to stand in a specific set of causal-informational and historical relations
with the thing in the world being represented. It is due to this fundamental
meaningfulness of cognitive states that external symbols, such as those used
in language, acquire meaning. Theories of content, therefore, provide the
essential ingredients that determine referential grounding, enabling internal
states to hook onto things in the world.

###  5.2 The Sensorigraph

Figure 2: Sensorigraph and S-model. Left: the sensorigraph records the host’s
sensory input and motor input over a lifetime. Right: an autoregressive
S-model is trained on sensorigraph data by predicting the embedding for the
next timestep in the sensorimotor stream sequence.

In light of theories of representational content, there are are two promising,
complementary routes to arguing that Large Pre-Trained Models, such as LLM and
VLMs, are referentially grounded in the world. One appeals to grounding from
structure, and the other to causal-historical relations. Before we explore
each of these factors in more detail, we will briefly motivate their relevance
with another thought experiment designed to counteract intuitions elicited by
the Octopus Test.

Imagine that in the distant future, scientists design a remarkably advanced
brain implant called a _sensorigraph_ , capable of recording an individual’s
sensory input and motor output streams with perfect fidelity. Suppose millions
of people are fitted with sensorigraphs at birth, and these devices capture a
lifetime’s worth of multimodal data for each person. The dataset of
sensorimotor streams collected from sensorigraphs would contain everything the
hosts have ever perceived, including speech, as well as every motor action
they have ever enacted, including speaking and writing (Figure 2, left).

This gigantic dataset could be used to train a deep neural network, which we
shall call an S-model. An encoder component could divide sensorigraph streams
into chunks (e.g., 5-second clips) and encode each chunk as a vector that
summarises its content. A decoder component would then translate internal
vector representations back into the format of sensorigraph streams (Figure 2,
right).

During training, the S-model would be shown portions of actual sensorigraph
streams and learn to predict the next chunk of the stream based on the
previous chunks. The encoder would compress the previous chunks into a vector
representation, and the decoder would translate the representation into a
prediction of the next chunk. The system would then get feedback on the
accuracy of the prediction. Over time, it would learn how to accurately
capture the relationships between modalities in the vector representations and
reconstruct full, detailed streams.121212Of course, the architectural details
of the fictional S-model are merely sketched to flesh out the thought
experiment, and do not really matter for the overall argument. Nonetheless, it
is worth noting that despite the sci-fi premise, there are already much
simpler and smaller models that illustrate ideas in the general vicinity of
our S-model. For example, Phenaki is an ANN that learns from a diachronic
stream composed of videos, and outputs other diachronic streams (again in
video format) (Villegas et al. 2022). Gato is another multimodal model
designed to be a generalist agent; it is trained not only on text and images,
but also on robotic joint torques (analogous to proprioception) and button
presses (analogous to motor action) (Reed et al. 2022).

We could thus provide the S-model with a snippet from someone’s sensorigraph
recording and have it generate a plausible continuation of the stream. The
encoder would compress the starting snippet into a vector representation, the
decoder would translate it into a generated continuation, the encoder would
compress the generated chunk, and this process could be repeated indefinitely
to yield an open-ended sensorigraph stream. Just like novel text produced by
state-of-the-art LLMs is often indistinguishable from text written by actual
humans, novel sensorigraph streams produced by the S-model would be
indistinguishable from those recorded in actual humans. By learning to predict
across vision, audition, motion, and other modalities, the S-model would
acquire representations that capture the complex statistical relationships
between these modalities as they unfold in human experience.

This thought experiment serves as a counterpoint to the Octopus Test. Since
Bender and Koller’s 2020 superintelligent octopus is a colourful metaphor for
current LLMs, we will simply use that term for our discussion. One notable
difference between S-models and LLMs lies in the nature of their training
data: the S-model is trained on rich multimodal data, while LLMs rely solely
on text. Specifically, the S-model has access to statistical patterns
connecting shapes, sounds, words, movements, etc., whereas LLMs are limited to
linguistic corpora.

In learning to predict sensorigraph streams accurately, S-models would likely
develop highly sophisticated linguistic representations associated with
phonemes from the auditory stream, written words from the visual stream, as
well as motor commands for phonation and writing. These linguistic
representations in an S-model would achieve a high degree of sensorimotor
grounding, as they would be intricately linked to various sensory and motor
representations, unlike those in an LLM trained on text alone. This
distinction constitutes a major difference between the two types of systems.

However, both the S-model and LLMs share a common learning objective and
generative goal, focusing on next-item prediction (stream clips for the
S-model and linguistic tokens for LLMs). In each case, the model predicts the
subsequent items in a sequence based on the preceding context, i.e., previous
sequences of items. As such, neither LLMs nor the S-model possess ’direct’
access to worldly entities and properties. The S-model is trained on sequences
of multimodal information taken from human behaviour, while LLMs are trained
on sequences of tokens produced by humans. In essence, their training does not
involve direct interaction with the sources of the multimodal or linguistic
information contained in the relevant datasets; instead, they have access only
to data generated by humans through _their own_ interactions with the world
and language. The Sensorigraph thought experiment vividly demonstrates that
sensorimotor grounding differs from referential grounding. While the S-model
is maximally grounded from a sensorimotor perspective, this does not imply
referential grounding. Conversely, the absence of sensorimotor grounding in
LLMs has no immediate implications for their ability to achieve referential
grounding, i.e., to avoid the Vector Grounding Problem.

Beyond this important point about sensorimotor grounding, there is another
interesting difference between S-models and LLMs. The S-model has access to a
wealth of information about the world’s structure, and how it is affected by
human agency, much of which is presumably inaccessible to LLMs (and the
metaphorical octopus, at least in the above-sea environment). It is hard to
resist the intuition that the sensorigraph dataset is closer to the world than
the linguistic corpora on which LLMs are trained, even though it doesn’t allow
the S-model to directly ’touch’ the world either. LLMs’ training data
certainly carries a lot of information about the world, but such information
is mediated by the constraints and limitations of the language used to
describe it. In contrast, the sensorigraph dataset encodes proximal sensory
and motor signals, which often closely mirror the structure of the external
stimuli that elicited them. This difference is likely reflected in the
respective capabilities of these systems, even regarding linguistic
performance. For instance, one could imagine that the S-model would generate
speech significantly more compelling and coherent than that produced by LLMs.

This difference is not attributable solely to the distinction between unimodal
and multimodal datasets; rather, it relates to the amount of information about
the world encoded within the statistical properties of these datasets. This
disparity is not categorical but a matter of degree. The sensorigraph dataset
encodes a considerable amount of information about patterns of causal
interactions involving human agents in the world, and about the structure of
the world itself. In comparison, both multimodal datasets used to train VLMs
(e.g., image-caption pairs) and unimodal datasets used to train LLMs (i.e.,
linguistic corpora) encode significantly less information about these aspects.
However, this does not imply a complete absence of such information. In fact,
as we shall see, there are compelling reasons to believe that even LLMs
trained solely on text can extract information about the world by means of the
causal interactions of the agents whose linguistic outputs are reflected in
the training data. If this holds true, then LLMs, VLMs, and S-models might be
seen as existing on a continuum with respect to the quantity and quality of
information about the world they can access from their respective datasets,
and that they can encode during training.

###  5.3 Grounding from Structure

Some aspects of the world have an intrinsic relational structure. The identity
and properties of components in these domains are defined in terms of their
relations to other components. For example, colours form an organised system
in which each colour is defined by its similarity to adjacent colours: _red_
is more similar to orange than to _green_. Spatial directions are also defined
by their relationships: _left_ is defined relative to _right_ , _east_
relative to _west_.

In some cases, the relational structure of a domain corresponds to patterns in
human language and cognition. One way to conceptualise such correspondences is
in terms of mappings between the components of a domain and linguistic
expressions that preserve certain relationships. For instance, words for
closely related colours like ‘red’ and ‘orange’ may co-occur more frequently
than words for less similar colours, like ‘red’ and ‘green’. Similarly,
spatial terms like ‘left’ and ‘right’ or ‘east’ and ‘west’ commonly co-occur.
More broadly, the internal relations between component parts of a domain
partially determine the linguistic distinctions, properties, and categories we
use to describe them.

Such correspondences need not be deterministic or universal. While colour
similarity might correlate with word co-occurrence statistics for colour
terms, the mappings can be imperfect or probabilistic. Other types of
relations or domains may not exhibit any clear correspondences of this kind.
Our hypothesis is merely that there are at least approximate mappings between
some structural properties of linguistic expressions reflected in their
patterns of use, and some structural properties of specific worldly domains
these expressions refer to. If this hypothesis is correct, then we should
expect LLMs that learn to encode word meanings based on co-occurrence
statistics to acquire linguistic representations whose structure in the high-
dimensional vector space can be mapped to the structure of the world, at least
in limited domains. There is, in fact, mounting empirical evidence that this
is the case.

In the spatial domain, Liétard et al. (2021) probed representations of cities
and countries in various language models. All models performed better than
chance at encoding both absolute spatial information (probed by predicting GPS
coordinates) and relational spatial information (probed by predicting whether
two countries share a border), with larger models performing better than
smaller ones. Patel & Pavlick (2022) took a different approach, constructing a
grid world using only text characters, where the position of a special
character reflects either relational spatial concepts (_left, right, up, down,
top, bottom_) or cardinal directions (_north, south, east, west, northeast,
northwest, southeast, southwest_). They found that language models can learn
spatial representations that generalise to unseen worlds and unseen related
representations, after being explicitly shown mappings between language and
grid world states just for a small subset of such representations. While
smaller models could not generalise in this way, the largest model (GPT-3)
made intuitive errors and could generalise even to rotated worlds. This shows
that LLMs may learn representations that closely reflect the structure of the
real world, at least for the narrow domain of spatial relations.

Patel & Pavlick (2022) also considered the geometry of colour representations,
evaluating how well LLMs can map their representations of colour terms to
structural relationships in RGB colour space. Models were shown examples of
how some colour terms (e.g., _red, cyan, forest green_) mapped to RGB colour
codes (e.g., [255; 0; 0]), and were then prompted with held-out colour terms
and asked to generate the corresponding RGB codes. Performance was evaluated
by comparing the model’s predictions to the true RGB codes, testing the
models’ ability to generalise from seen colour mappings to unseen but related
colours. Again, GPT-3 performed well, suggesting that language models may
learn representations of colour terms whose geometry is near-isomorphic to the
structure of RGB colour space. Interestingly, Abdou et al. (2021) also found a
structural correspondence between representations of colour terms in LLMs and
CIELAB, a colour space with a perceptually meaningful distance metric.

Beyond the spatial and colour domains, Li, Kementchedjhieva & Søgaard (2023)
show that there is a broader structural correspondence between the
representational space of 12 LLMs trained only on text, and the
representational space of 14 deep learning models trained only on images.
Indeed, it is possible to learn precise linear mappings between these spaces.
Once again, scale was found to have an effect: the larger they get, the more
LLMs and computer vision models seem to converge on vector spaces with similar
geometries. Merullo et al. (2023) report a similar finding: training linear
projections from the representations of a computer vision model into the input
space of a language model is often sufficient to produce accurate captions
describing images.

Does such evidence suggest that LLMs might possess referentially grounded
representations, at least in specific domains like colours and space? Not
quite. For this argument to be persuasive, we would need to accept the
additional assumption that some form of mapping between representations and
the relevant domain—such as isomorphism or, more plausibly, homomorphism—-is
sufficient for referential grounding. However, philosophical work on theories
of representational content has long established that this is not the case
(Newman 1928, Goodman 1976, Shea 2018). Morphisms between two sets of objects
or properties are trivial to find, and relying solely on the existence of
morphisms between internal representations and structured domains in the world
could lead to a trivialisation of the notions of representation and meaning
(Piantadosi & Hill 2022, Søgaard 2022, Patel & Pavlick 2022).

Nevertheless, such mapping relations between sets of internal representations
and structured domains in the world can contribute to the referential
grounding of those representations, provided that they are complemented by
other factors. Representations that derive meaning partly through mapping
relations are often referred to as ‘structural representations’ (Swoyer 1991,
Ramsey 2007, Shea 2018). Accounts of structural representation, as with all
influential current theories of content, call upon causal-informational and
historical relations to complement the grounding role of the relevant
morphism. Therefore, a comprehensive defence of referential grounding in LLMs
requires demonstrating that these systems do, or at least can, stand in such
relations with what they are about.

As a side note, there do appear to be special domains in which grounding from
structure is sufficient for intrinsic meaning. One such domain involves
logical connectives, such as AND, OR, etc. Their meaning is indeed fully
captured by the relational structures they stand in (Fodor 1990). It is
plausible that a similar principle applies to certain lexical items, such as
conjunctions (‘and’, ‘but’, ‘therefore’, etc.). If an LLM can learn the
structure of relations that constitute the meaning of logical connectives and
linguistic conjunctions from its training data, then its representations of
these terms might be as intrinsically meaningful as they can be.

However, one might argue that this is not truly an instance of referential
grounding. After all, logical connectives and linguistic conjunctions do not
refer to entities or properties in the world—they are function terms, fully
characterised by their functional roles within a symbolic system.
Consequently, the only grounding they need is what we referred to as
relational grounding, rather than referential grounding. We shall refrain from
taking a particular stance on this question, as it potentially involves
complex metaphysical issues. Regardless of whether one considers the grounding
in this case to be relational or referential, it is presumably sufficient to
underpin the meaningfulness of LLM representations within these restricted
domains.

###  5.4 Indirect Grounding of LLMs: causes and history redux

As discussed in subsection 5.1, philosophical theories of representation have
identified sets of relations that imbue representations with content, giving
them intrinsic meaning. These primarily include causal-informational and
historical relations. Crucially for our purposes, these theories have focused
on more ordinary cases of representation involving lexical concepts,
perceptual representations, and the like, as opposed to the specialised
domains of logic and function words.

Our aim is to show that Large Pre-Trained Models, such as LLMs, may possess
grounded representations and outputs in this ordinary sense, which is the one
captured by the concept of referential grounding. To begin, we will examine
whether appropriate causal-informational relations exist between LLM
representations/outputs and entities and properties in the world.

#### Causal-informational relations

Although LLMs are trained exclusively on linguistic data, thus precluding any
direct causal-informational relationship with extra-linguistic entities, the
linguistic data itself is generated by humans who maintain causal-
informational connections to worldly entities and properties. Those data are
shaped by humans’ interactions with the world. Among its various functions,
language enables humans to express facts about the world, as well as their
experiences, emotions, and ideas concerning that world. The extensive corpus
of text upon which LLMs are trained likely embodies the ‘imprint’ that the
world has left on language and linguistic expression.

The patterns of language use derived from the training corpus are likely to
reveal important aspects of the world’s statistical structure. These patterns
are neither random nor predominantly stochastic; rather, language and
linguistic expressions are highly organised in systematic ways. This structure
embeds information about patterns of interaction between humans and the world,
human methods of categorising their environments, and the selection of
features that are more or less salient to them. The structure reflected in
these patterns of linguistic use carries significant information about the
meaning of linguistic expressions.

Furthermore, a plausible hypothesis for LLMs’ success in a wide range of
linguistic tasks is that they have induced general semantic patterns from
their training data, which closely resemble what could be termed semantic
‘laws’.131313For some preliminary work on the potential form of such semantic
laws, see Wolfram (2023). These laws are not merely formal or syntactic;
rather, they tap into the intricate relationships between linguistic form and
the world it describes, namely, the semantics of language. The requirements
for linguistic expression of worldly states-of-affairs underlie the patterns
in form and syntax found in human linguistic output.

A strict separation of form and meaning has been a central assumption in much
of linguistics, from Ferdinand de Saussure’s principle of the “arbitrariness
of the linguistic sign” (de Saussure 1916) to contemporary formal theories of
syntax and semantics (Chomsky 1957, Montague 1970). However, this notion has
faced increasing scrutiny since the 1980s, especially in light of empirical
investigations of the iconicity of language (Perniss & Vigliocco 2014). In
this context, iconicity refers to a non-arbitrary relationship between the
form of a linguistic sign and its referent, based on some similarity or
analogy. The nature of this similarity relation can vary: imagistic iconicity
involves a perceptual resemblance between a word and its referent (e.g., in
onomatopoeias), while diagrammatic iconicity entails a structural resemblance
(Haiman 1985).

Diagrammatic iconicity is pervasive in linguistic structures. For example, the
ordering of events in narrative sequences tends to reflect closeness and
succession in time (e.g. “Veni, vidi, vici”); what is nearest to the speaker
in a literal or metaphorical sense tends to be mentioned first (e.g. “here and
there”); elements whose referents are closely related in some way or other
tend to be adjacent in sentences (principle of adjacency); the use of
subordination reflects causality or conditionality between states-of-affairs
(e.g., “If you study hard, you will pass the exam”), etc. (Van Langendonck
2010). The pervasiveness of diagrammatic iconicity in linguistic structures
suggests that there is a deep connection between the surface form of language
and the meaning it conveys. The way in which linguistic signs are organised
and structured is not arbitrary, and may reflect some ways in which the world
is organised and structured.

While diagrammatic iconicity is not typically characterised in distributional
terms, patterns of co-occurrence in language reflect stable statistical
regularities in the way in which linguistic elements are used together.
Certain words tend to occur together more frequently than others, and certain
grammatical constructions tend to co-occur with particular semantic
categories. These patterns of co-occurrence are not random, and often reflect
the underlying structure of the world that speakers are trying to describe.
Thus, _contra_ Bender & Koller (2020), form and meaning are far from being so
easily separable, especially at the level of general patterns of language
use—such patterns are caused and shaped by human expressive needs in light of
the structure of causes and action opportunities in the world.

One might argue that the highly mediated nature of the causal-informational
relationships between LLMs and the world disqualifies them from possessing
intrinsically meaningful representations. The paradigmatic case studies on
which theories of content focus tend to involve relatively simple and
straightforward situations where an occurrent causal chain extends from an
object in the system’s immediate environment to the excitation of the system’s
sensory surfaces. Such occurrent causal chains are absent in the training of
LLMs, or, for that matter, during that of VLMs and even that of our
hypothetical S-model. Consequently, one might think that these models fail to
establish the appropriate causal-informational connections to worldly entities
and properties that partly underlie referential grounding.

It is worth noting that theories of representational content strategically
focus on relatively simple cases as a foundation for understanding more
complex scenarios. However, it is undeniable that a significant portion of the
cognitive representations humans employ refer to entities and properties that
are not present in their immediate surroundings and for which no occurrent,
relatively unmediated causal chain is available. As such, a system’s ability
to employ meaningful representations does not depend on the presence of
unmediated causal connections to objects in its surroundings. Nonetheless, the
basic cases in which such connections are available could be regarded as the
paradigmatic grounding instances required to produce the relevant
representations, which are subsequently employed in other contexts. On the
face of it, LLMs do lack grounding instances from direct immediate causal
connections to the world.

This picture is overly simplistic, however. Many human representations acquire
meaning without such direct grounding instances. Instead, they are obtained by
means of testimony and social learning through representations produced by
others, who may have learned them in the same manner, rather than through
direct contact with their worldly referents. For example, most people have
never been in direct causal contact with enriched uranium, but that does not
entail that their thoughts and statements about uranium lack referential
grounding—they are indeed about uranium. A similar principle applies to LLMs:
their representations are at least partially grounded through testimony and
‘social’ learning, as their training data contains innumerable instances of
human communication. In this sense, LLMs represent an additional link in the
chain of testimony transmission that provides representations with causal-
informational relations to worldly entities, and thus partly underpins
intrinsic meaning.

In this sense, the causal-informational relationships that underpin meaning in
LLMs are dependent on humans. However, this dependence is distinct from the
one that drives the Vector Grounding Problem. The Problem is not _how_ the
representations of connectionist models come to acquire intrinsic meaning, but
_whether_ these representations have intrinsic meaning at all, instead of
being merely ascribed extrinsic meaning by external interpreters. To take once
again the example of enriched uranium, LLMs find themselves in a position
similar to most humans: their representations and outputs about enriched
uranium intrinsically refer to enriched uranium—irrespective of any
interpreter’s gloss—even though the process enabling such reference depends on
a chain of transmission that involves other systems with intrinsic meaning.

LLMs appear to possess the necessary elements to fulfil the causal-
informational requirement for referential grounding. They stand in complex,
mediated causal-informational relations to the world. These connections are
mediated since they pass through human linguistic production, where language
primarily functions as a tool to express aspects of the world.141414This
analysis would extend, _mutatis mutandis_ , to multimodal inputs, which are
also mediated by human interactions with the world (e.g., photographs are
captured by humans with a camera). However, one might argue that some worldly
properties instantiated by visual samples in a multimodal dataset, such as
shapes, can be accessed more directly than they could though the mediation of
language. This is because images (and samples in other sensory domains) are
entirely iconic, while language only exhibits limited patterns of iconicity.
They are complex due to the intricate causal-informational relationships
between the patterns of language use, the semantic ‘laws’ that govern them,
the structure of the world they have (culturally) evolved to capture, and the
causal chains of communication and testimony that produce the learning data—of
which the LLM itself can be considered a link. In light of these
considerations, we contend that Large Pre-Trained Models, such as LLMs, can
meet the causal-informational criteria necessary for possessing referentially
grounded representations and outputs.

#### Historical Relations

Although it is important to differentiate between causal-informational and
historical relations when considering referential grounding, these aspects are
often intertwined in real-world cases. The causal-informational relations
previously discussed with respect to LLMs possess a historical dimension, as
they depend on patterns of interaction between humans and their environments.
Likewise, in many of the interesting cases pertaining to human cognition, the
meaning-endowing causal-informational relationships can be traced back to past
episodes of learning.

As discussed in subsection 5.1, learning and selection processes are the
historical mechanisms that theories of representational content commonly
invoke. These processes explain how a system acquires a specific function or
purpose, particularly in relation to the production and/or use of
representations. Such functions clarify how cognitive systems can represent
_accurately_ —when they produce and use representations that fulfil the
relevant function—as well as _misrepresent_ , which occurs when the
representations produced and/or used are inappropriate for the task. While it
is widely accepted that Large Pre-Trained Models undergo a learning-like
process during training, it is less clear whether they undergo the relevant
kind of selection process. It can be argued that they do, at least to the same
degree as other human artefacts (Artiga 2016, Coelho Mollo 2019), given that
numerous design and implementation choices form an integral part of creating
artefacts such as AI systems. Nevertheless, according to some of the most
prominent theories of content, selection processes are not essential for
imbuing representations with meaning: learning processes alone may be
sufficient for establishing the relevant historical relations that contribute
to grounding meaning (Shea 2018).

The crux of the matter, however, lies in determining whether LLMs stand in
historical relations with the _right_ sorts of things, namely the entities and
properties in the world that could ground their representations. At first
glance, the situation appears analogous to that of causal-informational
relations: LLMs stand in historical relations to the world, albeit in a
mediated manner, through the human-generated data used for training them. The
critical question is: can LLMs nonetheless acquire world-involving functions
that enable the sort of descriptive normativity that is an essential feature
of meaning?

To address this question, it is important to distinguish between the proximate
and ultimate functions performed by LLMs during training and inference. The
proximate function of LLMs is plainly next-token prediction: predicting the
next token in a text sequence, given the context provided by that sequence.
This proximate function is infra-linguistic, and so are the standards for its
fulfilment or failure, namely whether the LLM predicts the correct tokens
reliably enough. While such function may be suitable to underpin _relational
grounding_ , it appears inadequate for contributing to the world-involving
normativity necessary for _referential grounding_.

Ultimate functions refer to the broader, more abstract goals that the model is
tasked with achieving through next-token prediction. These functions can be
world-involving in principle, such as generating text that accurately
describes real-world states of affairs, or solving problems based on real-
world information. In what follows, we will consider several potential sources
for world-involving ultimate functions in the training and use of LLMs.

Recent language models and chatbots are often fine-tuned, after pre-training,
with a technique known as ‘Reinforcement Learning from Human Feedback’ (RLHF)
(Ziegler et al. 2019, Ouyang et al. 2022, Bai et al. 2022). RLHF is used to
align the outputs of LLMs with specific normative goals, using direct human
feedback on their outputs. The process involves several steps. First, a set of
norm-sensitive prompts that could elicit unwanted outputs are selected. Some
of these prompts are morally sensitive, such as asking for the instructions to
build a bomb, while others are epistemically sensitive, such as asking a
factual question that only admits of one true answer. Second, these prompts
are given as input to the pre-trained LLM multiple times, such that the model
generates multiple outputs for each of them. Human workers are subsequently
instructed to rank outputs for each prompt according to explicit norms chosen
to align the model. These norms typically include epistemic goals such as
‘honesty’ or ‘truthfulness’, in addition to moral goals such as ‘harmlessness’
and ‘helpfulness’ (Askell et al. 2021). Third, the preferences acquired
through human feedback are used to train a reward model aimed at predicting
how humans would rank any output. Finally, the pre-trained LLM is optimised
with respect to that reward model by means of reinforcement learning.

RLHF is a promising candidate to infuse LLMs with world-involving functions.
Indeed, the evaluation standards for the outputs of LLMs fine-tuned with RLHF
are extra-linguistic, being determined by the normative criteria embedded in
human feedback. Of particular interest for our discussion is the criterion of
‘honesty’ or ‘truthfulness’ commonly used in RLHF. This criterion ensures that
the evaluation standards for the outputs of the fine-tuned model are world-
involving, as they hinge on the actual state of the world. During RLHF fine-
tuning, one of the LLM’s objective is to generate outputs accurately
reflecting real-world facts, receiving ‘rewards’ for success and ‘punishments’
for failure. The learning process is thus partly driven by the degree to which
the generated outputs match reality, endowing the model with the ultimate
function of producing factually correct statements. If, upon completing
training, an LLM produces an output incongruous with worldly states-of-
affairs, it has failed to fulfil one of its ultimate functions—namely,
producing ‘truthful’ outputs—and thus misrepresents. This ultimate function is
the missing ingredient for referential grounding, providing RLHF fine-tuned
LLMs with the kind of descriptive normativity essential to meaning.151515The
system’s accuracy is irrelevant; the crucial factor is the presence of a
representational world-involving function. In nature, it is not uncommon for
organisms to systematically misrepresent, particularly in high-stakes
situations. For instance, prey may frequently misrepresent the presence of a
predator, as a false-positive poses a far lesser problem to the organism than
a false-negative.

Models that are not fine-tuned with RLHF, like the majority of LLMs until
recently, are less obvious candidates for possessing all the required
ingredients for referential grounding. However, in some instances, the
required normativity may still be obtained within a specific subset of
domains, even without fine-tuning. Indeed, _in-context learning_ offers
another potential source of world-involving normativity in pre-trained models.
In-context learning refers to the phenomenon wherein LLMs learn to perform
tasks they have not been explicitly designed or trained for, simply by being
prompted to perform that task (explicitly or implicitly) in the input sequence
fed to the model.161616Some chatbots used in commercial services include a
hidden ‘pre-prompt’ automatically added to the user’s input on the system’s
back end. This pre-prompt is akin to a set of explicit instructions to steer
the model’s behaviour in certain ways, and may include a requirement to be
‘honest’ and ‘truthful’. For instance, an LLM trained through next-word
prediction can be prompted to translate between languages, summarise text, or
solve a mathematical problem without requiring domain-specific fine-tuning for
each task. In-context learning examples typically involve several instances of
successful task completion (‘few-shot learning’), but state-of-the-art models
also excel at ‘zero-shot learning’, i.e., performing tasks based solely on
instruction, without illustrative examples. Notably, in-context learning is an
emergent capability of the largest LLMs, such as GPT-3 and PaLM; smaller
models generally cannot learn new tasks on-the-fly and require supervised
fine-tuning instead.

The tasks explicitly specified at inference time through in-context learning
arguably go beyond mere next-word prediction. Consider, for example, the
experiment by Patel & Pavlick (2022) previously described. It involves
prompting the model in a few-short learning regime to learn mappings from
colour terms like ‘cyan’ to points in RGB colour space such as [0, 100, 100].
This is an instance of a world-involving function, having a standard of
success and failure directly contingent on how the world is. Although in-
context learning does not actually involve adjusting the model’s weights, it
has been shown to be functionally equivalent to a form of virtual gradient
descent (von Oswald et al. 2022, Dai et al. 2022). As such, it does qualify as
a genuine form of learning. Anything that is learned in this way will not
persist after inference, but it may nonetheless enable LLMs to acquire the
ability to perform world-involving functions on-the-fly. This capability
allows the model to acquire and use representations suitable for the task at
hand, and to misrepresent when these representations prove inadequate. In
particular, the prompts used in few-shot in-context learning can set a
normative standard for LLM outputs, which may be world-involving if they
involve an explicit or implicit requirement of truthfulness. This type of
normative grounding, being transient, is quite unlike the human case. This
illustrates how the investigation of referential grounding in AI systems may
uncover partly different reference-fixing mechanisms across artificial and
biological systems.

We have argued that fine-tuning with RLHF and, to some extent, few-shot in-
context learning can endow LLMs with world-involving ultimate functions that
go beyond mere next-word prediction. In a more speculative vein, zero-shot in-
context learning (without hidden pre-prompts) may enable world-involving
normativity in a limited number of domains, such as games, where the ground
truth is entirely determined by the rules of the domain. If LLMs can learn
game rules by extrapolating patterns found during training, zero-shot in-
context learning may supply the normativity essential for referential
grounding. This is because the learned rules, whether represented explicitly
or implicitly within the LLM, provide the necessary success and failure
standards. Extending this line of reasoning even further, it is plausible that
some training events during pre-training (rather than inference or fine-
tuning) involve context windows containing a sequence of game moves. If LLMs
can deduce game rules from this subset of the training data, then their game-
related outputs should possess, for the same reasons as above, the type of
normativity relevant to referential grounding.171717This is especially
plausible in the special case of models trained entirely on sequences of game
moves in standard (text-based) notation. For example, Othello-GPT is a
Transformer model trained exclusively on scripts describing moves in the two-
player game Othello (Li, Hopkins, Bau, Viégas, Pfister & Wattenberg 2023).
While the model has no built-in knowledge of the board and its rules, there is
converging evidence that it acquires during training an internal
representation of the board state that allows it to predict legal moves (Nanda
2023). This could be seen as an example of a model inducing a world-involving
function (predicting a legal move on an Othello board given a game state)
purely from pre-training on next-token prediction.

In the case of predicting game moves, even if we assume that the game’s rules
implicitly provide some degree of normativity, one might object that this only
meets the conditions for relational rather than referential grounding—akin to
logical connectives and linguistic conjunctions examined in subsection 5.3.
However, there is a important distinction between these cases. Games do not
exist solely within the realm of linguistics; they have, as it were, their own
‘worlds’ governed by specific rules. Outputs generated in the context of game-
playing (whether through zero-shot in-context learning or pre-training) refer
to extralinguistic entities such as game pieces, moves, board positions, etc.,
which constitute the game ‘world.’ These are not simply components of language
itself, but belong to a distinct domain with its own extralinguistic rules,
providing a potential source of normativity for referential grounding.

This claim might still be resisted on the grounds that game rules ostensibly
learned by LLMs whose pre-training data (or zero-shot prompts) include game
moves are not genuinely _world_ -involving in the required sense, even if we
take the world in question to be a simple game world. After all, the model’s
explicit learning objective is next-token prediction, not game-move
prediction. But this is where the distinction between proximal and ultimate
functions proves useful. It is plausible that, in order to fulfil the function
of next-token prediction in this particular domain, the model must learn the
rules of the game, as this is the most efficient way to minimise error in this
specific prediction task. In such a case, the proximate function gives rise to
a distinct ultimate function for the domain, namely, predicting legal moves
according to the rules of a game. This is superficially analogous to LLMs
learning syntactic rules; however, in this case, the domain is
extralinguistic, and the rules learned pertain to the game world rather than
to the linguistic notation of game moves.

In sum, we have argued that the kind of descriptive normativity associated
with referential grounding—which accounts for the fact that grounded
representations can be correct or incorrect, appropriate or inappropriate—is
present at least in LLMs that have undergone additional training through
Reinforcement Learning from Human Feedback (RLHF). This type of fine-tuning
measures LLMs against the world, imbuing them with world-involving functions
acquired through learning. More speculatively, we have argued that such world-
involving functions may also be acquired by LLMs without fine-tuning. This is
plausibly the case in certain instances of few-shot in-context learning,
particularly when the prompt explicitly or implicitly encompasses a
requirement for truthfulness or adequacy of the outputs, such that the
standard of success or failure for the outputs is world-involving. This may
also be the case with zero-shot in-context learning, or even mere pre-
training, in highly specific domains like those involving descriptions of game
states. In such cases, if the model is able to induce game rules merely from
next-token prediction, and thus acquire a distinct ultimate function of next-
game-move prediction, it may satisfy the requirements for referential
grounding with respect to the game world.

###  5.5 Multimodality and Embodiment

The preceding discussion has primarily centred on LLMs trained exclusively on
text. Other large pre-trained models, such as vision-language models (VLMs),
are trained on multimodal datasets (e.g., image-caption pairs). Our
hypothetical S-model would also belong to this category, although its
sensorigraph dataset is substantially larger and richer compared to any
existing multimodal dataset. Notably, both LLMs and multimodal models are pre-
trained passively, so to speak, by sampling from serialised datasets rather
than by actively interacting with the world. Consequently, both types of
models would seem to face the Vector Grounding Problem.

Our argument has a surprising implication: while LLMs trained on text-only
data may achieve referential grounding at least in certain cases, typical
multimodal models do not. To illustrate this claim, let us examine a simple
VLM like CLIP (Radford et al. 2021). CLIP is developed by jointly training an
image encoder and a text encoder to predict the correct pairings of images and
text captions using an objective called contrastive learning. Suppose we have
a batch of images paired with their respective descriptions. We can jointly
train an image encoder and a text encoder to produce image and text vectors
for these samples, in a way that (a) maximises the similarities of the correct
image-text vector pairs, and (b) minimises the similarities of dissimilar
pairs. After pre-training with this contrastive objective, CLIP can predict
the most relevant caption for any given image, without directly optimising for
the task, in a manner reminiscent of the zero-shot capabilities of LLMs like
GPT-3.

Through contrastive pre-training with image-caption pairs, CLIP achieves what
we called _sensorimotor_ grounding, albeit to a very limited extent, if
compared to biological organisms or even to our fictional S-model—namely
connecting linguistic vector representations to pictorial vector
representations. CLIP also arguably achieves some degree of _relational_
grounding in the purely linguistic domain, although there is evidence that
contrastive learning from image-caption pairs severely limits the degree to
which this kind of model can induce syntactic structure compared to text-only
LLMs (Yuksekgonul et al. 2023). As far as causal-informational relations go,
the account we gave for LLMs should also apply to VLMs like CLIP: since both
images and their captions are shaped by human interactions with the world,
CLIP should stand in complex, mediated causal-informational relations to the
world.

The major difference between LLMs and VLMs when it comes to the Vector
Grounding Problem lies in their potential sources of world-involving ultimate
functions that could provide the kind of normativity suitable for referential
grounding. We have argued that LLMs trained on text only could secure such
functions from fine-tuning with human feedback (RLHF), or, more speculatively,
from in-context learning and perhaps even pre-training in limited domains
(e.g., sequences of game moves). By contrast, there is no obvious mechanism
that could enable CLIP to acquire world-involving ultimate functions from
contrastive pre-training, or at inference time. We ought to conclude that,
despite the common claim that VLMs and other multimodal models are ‘grounded’
by definition, such models actually fail to achieve _referential_ grounding,
and thus cannot overcome to the Vector Grounding Problem without further
modifications.

This is certainly not a limitation of _all_ multimodal models. For example,
state-of-the-art multimodal models like PaLM-E (Driess et al. 2023) and GPT-4
(OpenAI 2023) are based on pre-trained LLMs, and are capable of sophisticated
in-context learning over text and images.181818PaLM-E was designed by
combining an LLM pre-trained on text only, PaLM (Chowdhery et al. 2022), with
a large Vision Transformer (ViT) pre-trained on images only (Dehghani et al.
2023); the resulting model was fine-tuned on training sequences in which
multimodal tokens where inserted within language tokens. GPT-4 has two
versions: an LLM only capable of processing text, and a VLM that can only take
images as input. There is no official information about the architecture of
either version of GPT-4, so we are forced to speculate in this case, but it is
plausible that the multimodal version also combines a pre-trained LLM with a
pre-trained ViT. If we are correct in suggesting that in-context learning can
provide a world-involving function beyond next-token prediction, then we can
expect such models to achieve referential grounding in those tasks that
involve worldly standards of success. Similar considerations apply should
future multimodal models be fine-tuned in ways analogous to RLHF, including a
‘honesty’ or ‘truthfulness’ criterion.

There are ongoing efforts to overcome the limitations of LLMs and VLMs by
designing _embodied_ systems that do not just process sequences of
tokens—whether purely linguistic or multimodal—passively, but also actively
interact with real or virtual environments. One might expect such embodied
systems to escape the Vector Grounding Problem. Whether they do, however,
cannot be settled without paying attention to implementation details. Some
models do appear to clear that bar. For example, Hill et al. (2020) trained an
embodied agent in a 3D virtual environment to learn the names of unfamiliar
objects in a single exposure, and immediately apply this knowledge to carry
out instructions involving those objects. They used a combination of
predictive and reinforcement learning to train the agent in two steps. In the
discovery phase, the agent explores the virtual environment, fixates on each
object, and gets in return a text string containing the name of the object
(e.g., “This is a dax”). In the instruction phase, the locations of the
objects and the agent are randomised; the agent must respond to linguistic
instructions about objects (e.g., “pick up a dax”), and it is trained by means
of reward signals dictated by success or failure in carrying out the
instructions. In this experiment, the agent clearly learns to represent the
names of virtual objects through a world-involving function (relative to the
virtual world in which it can move). As such, there is little doubt that the
model achieves referential grounding.

Some artificial systems are embodied in the real world. For example, SayCan is
a project aiming to provide “real-world grounding” to an LLM by integrating it
with a robot to perform physical tasks from natural language instructions (Ahn
et al. 2022). In this system, the LLM is simply a module used to break down
the verbal introductions (e.g., “bring me an apple”) into sequences of
‘atomic’ behaviours that the robot can subsequently enact through low-level
visuomotor control. In order to parse instructions in a format suitable for
downstream processing and actionable goals, the LLM is provided with a
carefully engineered prompt that sets up the task as an instance of few-shot
learning. This prompt contains a number of examples of possible instructions
and the corresponding acceptable outputs for downstream processing, formatted
as a set of templatic sub-goals (e.g. “1. find an apple”, “2. pick up the
apple”, etc.).

Does SayCan really provide the LLM with “real-world grounding”, in the
referential sense? Not quite. The mere fact that the LLM embedded in the
SayCan system generates outputs that can be subsequently processed to perform
robotic actions in the real world is irrelevant to the question of whether the
LLM itself is referentially grounded, since the LLM is not trained or fine-
tuned in light of the success or failure of such actions. Admittedly, the LLM
component of SayCan is prompted through few-shot learning. As we have argued,
few-shot learning could in principle provide a text-only model with world-
involving ultimate functions, without further fine-tuning. For that to be the
case, however, a normative standard for success and failure would have to be
implicitly specified by the prompt format, such that the task learned in
context requires accuracy with respect to the actual state of the world. By
contrast, the few-shot prompt supplied in SayCan involves translating
linguistic instructions into low-level goals appropriate for visuomotor
control of the robot. Such goals are not normatively equivalent to factual
statements, as they have a different direction of fit: while in factual
statements the representation is supposed to fit to how the world is, goals
are satisfied when the world is changed so as to fit to the goal
representation. While this feature of SayCan may endow its embedded LLM with a
sort of (more complicated) normativity derived from standards of goal
satisfaction—an idea that calls for further investigation—it should be clear
that embodiment in this case is playing no role in ensuring referential
grounding: all the work, if any, is being done by the LLM. Perhaps
surprisingly, embodiment ends up being irrelevant to tackling the Vector
Grounding Problem in this kind of system.

Multimodal and embodied models may be referentially grounded if they meet
specific requirements, such as the availability of a mechanism for few-shot
learning on a world-involving task. However, they are not referentially
grounded just by being embodied, as it is often assumed. Contrary to popular
belief, they do not offer a straightforward solution to the Vector Grounding
Problem. There are thus instances of multimodal and embodied models that are
less plausible candidates for referential grounding than text-only LLMs fine-
tuned with RLHF and/or prompted for few-shot learning.

##  6 Concluding Remarks

We have argued that the Symbol Grounding Problem, as introduced by Harnad, can
be adapted to apply to deep neural networks such as large pretrained models,
thereby taking the form of what we have termed the Vector Grounding Problem.
Despite first appearances, we have sought to demonstrate that at least a
subset of current large pretrained models have the features necessary to be
endowed with representations and outputs grounded in the world. Our analysis
has primarily focused on Transformer-based LLMs, which are some of the most
successful models in natural language processing to date.

While our discussion has focused on LLMs and, to a lesser extent, on their
multimodal counterparts, any AI system fulfilling the causal-informational and
historical relations requirements delineated above can possess representations
with intrinsic meaning. Meeting these requirements is far from trivial, but it
may also be less demanding than it initially seems. As philosophical theories
of representation have forcefully shown, in order to understand how cognitive
systems—both biological and artificial—function, including at the subpersonal
level, we must carefully scrutinise our intuitions about the requirements for
intrinsic meaning. We must also resist the temptation to assume that the
availability of intrinsic meaning necessarily entails the existence of complex
cognitive abilities such as understanding, knowledge, or consciousness. While
having states imbued with intrinsic meaning might constitute one of the
fundamental conditions for possessing these other cognitive abilities, it is
insufficient on its own. For instance, activations of specific populations of
neurons in the mammalian cortex may represent the presence of edges in the
visual scene, but these neuronal activations do not inherently understand or
possess knowledge about edges. We suggest that a similar claim can be made
regarding the internal representations and outputs of LLMs and related
connectionist models.

We argued for this claim in two steps. First, we distinguished between various
forms of grounding, which are often conflated in the cognitive science and
computer science literature. We suggested that one particular form of
grounding, which we termed _referential grounding_ , is central to both the
Vector Grounding Problem and the older Symbol Grounding Problem. Referential
grounding pertains to the way in which representations hook onto the world. It
is the most fundamental type of grounding, and arguably serves as the basis
for all other notions of grounding (with the partial exception of relational
grounding). As theories of representational content have persuasively
demonstrated, referential grounding requires two main factors: causal-
informational relations between representations and the world, and historical
relations that imbue representations with a sort of descriptive normativity.

Second, we have shown that certain LLMs trained exclusively on linguistic
data, particularly those fine-tuned with Reinforcement Learning from Human
Feedback (RLHF), are referentially grounded. These models benefit from
indirect causal-informational relations with worldly entities and properties,
mediated by human interactions with the world, which in turn shape the
linguistic inputs they receive during training and inference. Furthermore,
RLHF introduces an additional learning objective that is directly world-
involving, as it encompasses a requirement for truthfulness or factuality. The
normativity of this requirement supplies an extralinguistic accuracy standard
for the representations and outputs of LLMs. More tentatively, we have
suggested that even without RLHF, the representations and outputs of LLMs may
achieve referential grounding in some limited domains, through in-context
learning, and perhaps even through mere pre-training on specific kinds of
input sequences, such as those describing game moves.

This discussion leads us to a potentially surprising conclusion: some
multimodal models trained on images in addition to text, like CLIP or DALL-E
2, are poor candidates for referential grounding, since they lack the kind of
learning process that could supply world-involving functions. In fact, even
some embodied systems that combine a ‘frozen’ LLM with a robotic body, like
SayCan, might also fail to achieve referential grounding of the LLM’s
representations and outputs. In such systems, the robot’s interaction with the
real world turns out to be irrelevant to the Vector Grounding Problem, as it
cannot provide the LLM with the right kind of world-involving function.
Whether the few-short learning prompt passed to the LLM component is suitable
to play that role is debatable, given its focus on goal specification rather
than factual accuracy. One benefit of our analysis is to highlight that
multimodality and embodiment are neither necessary nor sufficient conditions
for referential grounding in artificial systems, although they are certainly
compatible with it if the right kind of learning process is available.

## References

  * (1)
  * Abdou et al. (2021) Abdou, M., Kulmizev, A., Hershcovich, D., Frank, S., Pavlick, E. & Søgaard, A. (2021), ‘Can Language Models Encode Perceptual Structure Without Grounding? A Case Study in Color’.
  * Ahn et al. (2022) Ahn, M., Brohan, A., Brown, N., Chebotar, Y., Cortes, O., David, B., Finn, C., Fu, C., Gopalakrishnan, K., Hausman, K., Herzog, A., Ho, D., Hsu, J., Ibarz, J., Ichter, B., Irpan, A., Jang, E., Ruano, R. J., Jeffrey, K., Jesmonth, S., Joshi, N. J., Julian, R., Kalashnikov, D., Kuang, Y., Lee, K.-H., Levine, S., Lu, Y., Luu, L., Parada, C., Pastor, P., Quiambao, J., Rao, K., Rettinghouse, J., Reyes, D., Sermanet, P., Sievers, N., Tan, C., Toshev, A., Vanhoucke, V., Xia, F., Xiao, T., Xu, P., Xu, S., Yan, M. & Zeng, A. (2022), ‘Do As I Can, Not As I Say: Grounding Language in Robotic Affordances’.
  * Alayrac et al. (2022) Alayrac, J.-B., Donahue, J., Luc, P., Miech, A., Barr, I., Hasson, Y., Lenc, K., Mensch, A., Millican, K., Reynolds, M., Ring, R., Rutherford, E., Cabi, S., Han, T., Gong, Z., Samangooei, S., Monteiro, M., Menick, J., Borgeaud, S., Brock, A., Nematzadeh, A., Sharifzadeh, S., Binkowski, M., Barreira, R., Vinyals, O., Zisserman, A. & Simonyan, K. (2022), ‘Flamingo: A Visual Language Model for Few-Shot Learning’.
  * Artiga (2016) Artiga, M. (2016), ‘New perspectives on artifactual and biological functions’, Applied Ontology 11, 89–102.
  * Askell et al. (2021) Askell, A., Bai, Y., Chen, A., Drain, D., Ganguli, D., Henighan, T., Jones, A., Joseph, N., Mann, B., DasSarma, N., Elhage, N., Hatfield-Dodds, Z., Hernandez, D., Kernion, J., Ndousse, K., Olsson, C., Amodei, D., Brown, T., Clark, J., McCandlish, S., Olah, C. & Kaplan, J. (2021), ‘A General Language Assistant as a Laboratory for Alignment’.
  * Bai et al. (2022) Bai, Y., Jones, A., Ndousse, K., Askell, A., Chen, A., DasSarma, N., Drain, D., Fort, S., Ganguli, D., Henighan, T., Joseph, N., Kadavath, S., Kernion, J., Conerly, T., El-Showk, S., Elhage, N., Hatfield-Dodds, Z., Hernandez, D., Hume, T., Johnston, S., Kravec, S., Lovitt, L., Nanda, N., Olsson, C., Amodei, D., Brown, T., Clark, J., McCandlish, S., Olah, C., Mann, B. & Kaplan, J. (2022), ‘Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback’.
  * Barsalou (1999) Barsalou, L. W. (1999), ‘Perceptual symbol systems’, Behavioral and Brain Sciences 22, 577–660.
  * Bender et al. (2021) Bender, E. M., Gebru, T., McMillan-Major, A. & Shmitchell, S. (2021), On the dangers of stochastic parrots, in ‘Proceedings of the 2021 ACM Conference on Fairness, Accountability, and Transparency’, ACM.
  * Bender & Koller (2020) Bender, E. M. & Koller, A. (2020), Climbing towards NLU: On meaning, form, and understanding in the age of data, in ‘Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics’, Association for Computational Linguistics.
  * Block (1986) Block, N. (1986), ‘Advertisement for a Semantics for Psychology’, Midwest Studies in Philosophy 10, 615–678.
  * Bommasani et al. (2022) Bommasani, R., Hudson, D. A., Adeli, E., Altman, R., Arora, S., von Arx, S., Bernstein, M. S., Bohg, J., Bosselut, A., Brunskill, E., Brynjolfsson, E., Buch, S., Card, D., Castellon, R., Chatterji, N., Chen, A., Creel, K., Davis, J. Q., Demszky, D., Donahue, C., Doumbouya, M., Durmus, E., Ermon, S., Etchemendy, J., Ethayarajh, K., Fei-Fei, L., Finn, C., Gale, T., Gillespie, L., Goel, K., Goodman, N., Grossman, S., Guha, N., Hashimoto, T., Henderson, P., Hewitt, J., Ho, D. E., Hong, J., Hsu, K., Huang, J., Icard, T., Jain, S., Jurafsky, D., Kalluri, P., Karamcheti, S., Keeling, G., Khani, F., Khattab, O., Koh, P. W., Krass, M., Krishna, R., Kuditipudi, R., Kumar, A., Ladhak, F., Lee, M., Lee, T., Leskovec, J., Levent, I., Li, X. L., Li, X., Ma, T., Malik, A., Manning, C. D., Mirchandani, S., Mitchell, E., Munyikwa, Z., Nair, S., Narayan, A., Narayanan, D., Newman, B., Nie, A., Niebles, J. C., Nilforoshan, H., Nyarko, J., Ogut, G., Orr, L., Papadimitriou, I., Park, J. S., Piech, C., Portelance, E., Potts, C., Raghunathan, A., Reich, R., Ren, H., Rong, F., Roohani, Y., Ruiz, C., Ryan, J., Ré, C., Sadigh, D., Sagawa, S., Santhanam, K., Shih, A., Srinivasan, K., Tamkin, A., Taori, R., Thomas, A. W., Tramèr, F., Wang, R. E., Wang, W., Wu, B., Wu, J., Wu, Y., Xie, S. M., Yasunaga, M., You, J., Zaharia, M., Zhang, M., Zhang, T., Zhang, X., Zhang, Y., Zheng, L., Zhou, K. & Liang, P. (2022), ‘On the Opportunities and Risks of Foundation Models’.
  * Borgeaud et al. (2022) Borgeaud, S., Mensch, A., Hoffmann, J., Cai, T., Rutherford, E., Millican, K., Driessche, G. B. V. D., Lespiau, J.-B., Damoc, B., Clark, A., Casas, D. D. L., Guy, A., Menick, J., Ring, R., Hennigan, T., Huang, S., Maggiore, L., Jones, C., Cassirer, A., Brock, A., Paganini, M., Irving, G., Vinyals, O., Osindero, S., Simonyan, K., Rae, J., Elsen, E. & Sifre, L. (2022), Improving Language Models by Retrieving from Trillions of Tokens, in ‘Proceedings of the 39th International Conference on Machine Learning’, PMLR, pp. 2206–2240.
  * Brandom (1994) Brandom, R. (1994), Making It Explicit: Reasoning, Representing, and Discursive Commitment, Harvard University Press.
  * Brennan (1998) Brennan, S. E. (1998), The grounding problem in conversations with and through computers, in S. R. Fussell & R. J. Kreuz, eds, ‘Social and Cognitive Approaches to Interpersonal Communication’, Lawrence Erlbaum, Hillsdale, NJ, pp. 201–225.
  * Brown et al. (2020) Brown, T. B., Mann, B., Ryder, N., Subbiah, M., Kaplan, J., Dhariwal, P., Neelakantan, A., Shyam, P., Sastry, G., Askell, A., Agarwal, S., Herbert-Voss, A., Krueger, G., Henighan, T., Child, R., Ramesh, A., Ziegler, D. M., Wu, J., Winter, C., Hesse, C., Chen, M., Sigler, E., Litwin, M., Gray, S., Chess, B., Clark, J., Berner, C., McCandlish, S., Radford, A., Sutskever, I. & Amodei, D. (2020), ‘Language Models are Few-Shot Learners’, arXiv:2005.14165 [cs] .
  * Bubeck et al. (2023) Bubeck, S., Chandrasekaran, V., Eldan, R., Gehrke, J., Horvitz, E., Kamar, E., Lee, P., Lee, Y. T., Li, Y., Lundberg, S., Nori, H., Palangi, H., Ribeiro, M. T. & Zhang, Y. (2023), ‘Sparks of Artificial General Intelligence: Early experiments with GPT-4’.
  * Buckner (2019) Buckner, C. (2019), ‘Deep learning: A philosophical introduction’, Philosophy Compass 14(10), e12625.
  * Carnap (1952) Carnap, R. (1952), ‘Meaning postulates’, Philosophical Studies 3(5), 65–73.
  * Castelvecchi (2016) Castelvecchi, D. (2016), ‘Can we open the black box of AI?’, Nature News 538(7623), 20.
  * Chandu et al. (2021) Chandu, K. R., Bisk, Y. & Black, A. W. (2021), Grounding ‘Grounding’ in NLP, in ‘Findings of the Association for Computational Linguistics: ACL-IJCNLP 2021’, Association for Computational Linguistics, Online, pp. 4283–4305.
  * Chen et al. (2020) Chen, T., Kornblith, S., Norouzi, M. & Hinton, G. (2020), A Simple Framework for Contrastive Learning of Visual Representations, in ‘Proceedings of the 37th International Conference on Machine Learning’, PMLR, pp. 1597–1607.
  * Chomsky (1957) Chomsky, N. (1957), Syntactic Structures, Mouton.
  * Chowdhery et al. (2022) Chowdhery, A., Narang, S., Devlin, J., Bosma, M., Mishra, G., Roberts, A., Barham, P., Chung, H. W., Sutton, C., Gehrmann, S., Schuh, P., Shi, K., Tsvyashchenko, S., Maynez, J., Rao, A., Barnes, P., Tay, Y., Shazeer, N., Prabhakaran, V., Reif, E., Du, N., Hutchinson, B., Pope, R., Bradbury, J., Austin, J., Isard, M., Gur-Ari, G., Yin, P., Duke, T., Levskaya, A., Ghemawat, S., Dev, S., Michalewski, H., Garcia, X., Misra, V., Robinson, K., Fedus, L., Zhou, D., Ippolito, D., Luan, D., Lim, H., Zoph, B., Spiridonov, A., Sepassi, R., Dohan, D., Agrawal, S., Omernick, M., Dai, A. M., Pillai, T. S., Pellat, M., Lewkowycz, A., Moreira, E., Child, R., Polozov, O., Lee, K., Zhou, Z., Wang, X., Saeta, B., Diaz, M., Firat, O., Catasta, M., Wei, J., Meier-Hellstern, K., Eck, D., Dean, J., Petrov, S. & Fiedel, N. (2022), ‘PaLM: Scaling Language Modeling with Pathways’.
  * Clark & Brennan (1991) Clark, H. H. & Brennan, S. E. (1991), Grounding in communication, in ‘Perspectives on Socially Shared Cognition’, American Psychological Association, Washington, DC, US, pp. 127–149.
  * Coelho Mollo (2019) Coelho Mollo, D. (2019), ‘Are there teleological functions to compute?’, Philosophy of Science 86(3), 431–452.
  * Coelho Mollo (2022) Coelho Mollo, D. (2022), ‘Deflationary Realism: Representation and idealisation in cognitive science’, Mind & Language 37(5), 1048–1066.
  * Dai et al. (2022) Dai, D., Sun, Y., Dong, L., Hao, Y., Sui, Z. & Wei, F. (2022), ‘Why Can GPT Learn In-Context? Language Models Secretly Perform Gradient Descent as Meta-Optimizers’.
  * de Saussure (1916) de Saussure, F. (1916), Cours de Linguistique Générale, Payot, Paris.
  * Dehghani et al. (2023) Dehghani, M., Djolonga, J., Mustafa, B., Padlewski, P., Heek, J., Gilmer, J., Steiner, A., Caron, M., Geirhos, R., Alabdulmohsin, I., Jenatton, R., Beyer, L., Tschannen, M., Arnab, A., Wang, X., Riquelme, C., Minderer, M., Puigcerver, J., Evci, U., Kumar, M., van Steenkiste, S., Elsayed, G. F., Mahendran, A., Yu, F., Oliver, A., Huot, F., Bastings, J., Collier, M. P., Gritsenko, A., Birodkar, V., Vasconcelos, C., Tay, Y., Mensink, T., Kolesnikov, A., Pavetić, F., Tran, D., Kipf, T., Lučić, M., Zhai, X., Keysers, D., Harmsen, J. & Houlsby, N. (2023), ‘Scaling Vision Transformers to 22 Billion Parameters’.
  * Devlin et al. (2018) Devlin, J., Chang, M.-W., Lee, K. & Toutanova, K. (2018), ‘BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding’, arXiv:1810.04805 [cs] .
  * Di Maro (2021) Di Maro, M. (2021), ‘Computational Grounding: An Overview of Common Ground Applications in Conversational Agents’, IJCoL. Italian Journal of Computational Linguistics 7(1 | 2), 133–156.
  * Driess et al. (2023) Driess, D., Xia, F., Sajjadi, M. S. M., Lynch, C., Chowdhery, A., Ichter, B., Wahid, A., Tompson, J., Vuong, Q., Yu, T., Huang, W., Chebotar, Y., Sermanet, P., Duckworth, D., Levine, S., Vanhoucke, V., Hausman, K., Toussaint, M., Greff, K., Zeng, A., Mordatch, I. & Florence, P. (2023), ‘PaLM-E: An Embodied Multimodal Language Model’.
  * Fine (2012) Fine, K. (2012), Guide to Ground, in F. Correia & B. Schnieder, eds, ‘Metaphysical Grounding’, Cambridge University Press, pp. 37–80.
  * Firth (1957) Firth, J. R. (1957), Papers in Linguistics, 1934-1951, Oxford University Press, London.
  * Fodor (1990) Fodor, J. A. (1990), A Theory of Content and Other Essays, MIT Press.
  * Goodman (1976) Goodman, N. (1976), Languages of Art: An Approach to a Theory of Symbols, Hackett Publishing.
  * Haiman (1985) Haiman, J. (1985), Iconicity in Syntax, Vol. 6, John Benjamins Publishing.
  * Harnad (1990) Harnad, S. (1990), ‘The symbol-grounding problem’, Physica D 42, 335–346.
  * Harris (1954) Harris, Z. S. (1954), ‘Distributional structure’, Word 10, 146–162.
  * Hill et al. (2020) Hill, F., Tieleman, O., von Glehn, T., Wong, N., Merzic, H. & Clark, S. (2020), ‘Grounded Language Learning Fast and Slow’.
  * Jackendoff (1990) Jackendoff, R. S. (1990), Semantic Structures, Cambridge: MIT Press.
  * Katz (1972) Katz, J. J. (1972), Semantic Theory, New York: Harper & Row.
  * Kiela et al. (2021) Kiela, D., Bartolo, M., Nie, Y., Kaushik, D., Geiger, A., Wu, Z., Vidgen, B., Prasad, G., Singh, A., Ringshia, P., Ma, Z., Thrush, T., Riedel, S., Waseem, Z., Stenetorp, P., Jia, R., Bansal, M., Potts, C. & Williams, A. (2021), ‘Dynabench: Rethinking Benchmarking in NLP’.
  * LeCun et al. (2015) LeCun, Y., Bengio, Y. & Hinton, G. (2015), ‘Deep learning’, Nature 521(7553), 436–444.
  * Li, Kementchedjhieva & Søgaard (2023) Li, J., Kementchedjhieva, Y. & Søgaard, A. (2023), ‘Implications of the Convergence of Language and Vision Model Geometries’.
  * Li, Hopkins, Bau, Viégas, Pfister & Wattenberg (2023) Li, K., Hopkins, A. K., Bau, D., Viégas, F., Pfister, H. & Wattenberg, M. (2023), ‘Emergent World Representations: Exploring a Sequence Model Trained on a Synthetic Task’.