Are Large Language Models Operationalizations of Saussurean Structure?

The title’s a bit ugly, but it captures the question I’m trying to ask: can various computational representations of language/meaning be usefully understood as “operationalizations” of what Ferdinand de Saussure describes as structure or langue in the Course in General Linguistics (1916). Given Saussure’s influence in literary theory and the humanities more broadly,I leave aside entirely Saussure’s impact in linguistics, though my sense is that Saussure was more put aside than superseded in linguistics. Insofar as computational approaches to language over the last twenty years represent something like a turn away from the dominance of Chomskyan grammar in the second half of the twentieth century, and towards something grounded in statistics, Saussure does seem a fitting figure. I think this would be a useful way of enabling thinking about computational representations of meaning, from word embeddings (about which I’ll say more) to “large language models” and related technologies that have been kind of amazing to watch develop over the last year (I’m thinking of GPT-3, of DALL-E… all those kind of jaw dropping pictures circulating on twitter over the past few months).

I’m writing to see if this observation 1) is true, and 2) is useful. (I’m more uncertain of the latter than the former.) It seems to me that Saussure’s account of language and meaning is a useful analogue to computational models of meaning because it describes meaning as essentially differential. (Or, in a Derridean vein, différantial? … I want LLMs to bring theory back! Which is what Ted Underwood predicted… nearly a decade ago!) For instance, in trying to explain models like DALL-E to someone the other day, I was asked: “So, does it [DALL-E] invent something new, or just recombine things from the internet?”Underwood captures a version of this in a mini-thread invoking Coleridge’s distinction between fancy and imagination from the Biographia Literaria. This question captures the challenge of thinking about, and thinking through, these models. I don’t think such models really do either; they don’t spontaneously create new images ex nihilo nor do they simply remix the already existing. But of course, this binary (creation/recombination) seems an impoverished way of thinking about how a human generates a text. The rather long and extensive, and now decades old, tradition of thinking about elements of culture through Saussure offers a valuable way out of this impasse. This very question was equally at stake in such (post)structuralist slogans as Roland Barthes’s insistence that “it is language which speaks, not the author” (Barthes 143) (a connection Underwood has also made [cite]). At the very least, thinking about these models as Saussurean structures (rather than as, say, intelligences) can forestall some of the worst ways of trying to understand what these models output.

The structuralist overtones of much computationally-driven cultural work has often come in a Lévi-Straussian flavor, mixed with a desire for a more empirically grounded work. But that is, I think, only one half (and, I think, the less influential half) of how structuralism, and the “theory moment,” shaped literary theory (to stick to the area with which I’m most familiar). Returning to Saussure gives an opportunity to enrich and complicate the structuralist/computational connection. I want to suggest that these models offer an opportunity to highlight the essentially quantitative element that underlies Saussure and, indeed, remains implicit in much post-Saussurean and poststructuralist thinking. This quantitative element is essential, but largely latent, in Saussure’s description of the arbitrary character of the sign.

I think the broad strokes (and perhaps even the narrow strokes) of the connections between computational models of language (including “large language models”) and structuralism seem like they’ve been in the ether for a while. For instance:

Sure, they didn't want to be proved right like this. But that's always true of prophecy. Poets and literary critics are still morally required to take a victory lap for predicting that "it is language which speaks, not the author." pic.twitter.com/Exw4VGXGZs

— Ted Underwood ((Ted_Underwood?)) June 14, 2022

"Lang." does seem better for current AI than "intelligence". But interesting how "lang." here closer to Saussure's "langue" (abstract signifying system) than "parole" (actual utterances). Isn't lang used as "foundation" model bc it provides a useful starterpack signifying system?

— Ryan Heuser ((quadrismegistus?)) May 16, 2022

structuralism is back baby!! https://t.co/60gRTTgBQc

— Robin Manley ((_robinmanley?)) April 26, 2022

These tweets all to some extent express the idea that there is something about language models/neural networks/“artificial intelligence” that recalls structuralism. Bernard Dionysus Geohegan’s work on cybernetics and structuralism and his forthcoming book Code: From Information Theory to French Theory promises to enrich the deeper history of this connection; but I want to focus on something far more modest.

Indeed, I started this post originally to talk about something much narrower—J. R. Firth, and the theorization of word embedding vectors.

On J. R. Firth as Theoretical Inspiration for Word Embedding Vectors

Word embeddings, or word embedding vectors (among other methods), are a way of representing the meaning of a word with a series of numbers. The basic idea of word embeddings is to treat a word as a point in (multidimensional) “space.”Listen, writing about these things means going out on a limb. If there is something grossly wrong this summary, let me know. A word’s position in space reflects, or represents, its meaning. Most simply: words with similar meanings should be grouped together in the same space. Schnauzers, bulldogs, and poodles might all be constellated around dog. A lovely idea, right? But how to do it? (Ryan Heuser’s posts on word vectors were an invaluable resource when I first read them.)

Key techniques for generating these vectors embed a word in this “semantic” space by looking at the terms that surround it. If you had a massive dataset and looked at the words that appear “near” (say, within 2 or 3 words) the terms for dog breeds I just mentioned, you would find terms for the sort of things dogs do—wag tails, fetch bones, mark territory, prick up their ears, get dewormed, and so on.¹ Now we can use those terms to generate the coordinates for each of our dog-related terms. Since words with similar meanings have similar collocates, this should get us our space, right? Carrying this intuition further, we would assume that cat as a term will not be closer in this space to bulldog or schaunzer than both of those terms will be to dog. But cat will be closer to dog (and any other words in that “neighborhood”) than it is to say “Constitution” or “fascism” (to pick two words chosen entirely without regard to contemporary events here in the summer of 2022).

From collocation of words to locations of vectors—that’s the idea.All fine for the English professor to say; but transforming collocation counts into a meaningful representation is going to involve some linear algebra. When people were first oohing and aahing over these things (back in 2015), one could use some relatively straightforward vector algebra to do things like querying for the resulting term if one started with the position of king, subtracted the embedding vector representing man, and added in the vector for woman. king - man + queen produced, queen, which is pretty impressive… or, it was in 2015. (Compared to the outputs of DALL-E and GPT-3, this all seems wonderfully quaint.)²

In reading the literature about word embedding vectors, the most frequently cited theoretical inspiration for this approach to meaning is the British linguistic J. R. Firth. He is quoted with great frequency for asserting that “You shall know a word by the company it keeps!” in “A Synopsis of Linguistic Theory” (179).This essay can be a bit tricky to track down. If you’d like a PDF, email/DM me. Firth insists that meaning be grounded in a “context of situation,” a concept that sounds vaguely related to the “company [a word] keeps,” but the former is a much broader idea. And for all the citations Firth gets as inspiration for semantic word vectors, they seem rather far afield of Firth’s central preoccupations in “A Synopsis.” Indeed, reading beyond this passage, one finds very little to help you reason about collocations quantitatively.³

Firth, in short, provides only the thinnest veneer of theoretical justification for what word embeddings are, and how they work. An essay by Mikael Brunila and Jack LaViolette (a May 2022 preprint) summarizes this situation well, discussing J. R. Firth alongside Zelig Harris as the theoretical inspirations for word embeddings. As they note, in the word embedding literature “despite an explosion of citations… this interest [in Firth] has not been very engaged.” Rather, Firth has been invoked in order to “lend theoretical authority to a field that struggles to lift its gaze from the latest state-of-the-art numbers” (Brunila and LaViolette). If you come to Firth from discussions of word embeddings (as I did), you may feel rather puzzled (as I did!), looking (in vain!) for collocation calculations among talk of “context of situation” and the occasional citation of Alfred North Whitehead (!).

The reason Firth’s thinking, or at least Firth’s slogan that meaning is related to the “company [a word] keeps,” is so often cited is because the technique used by word2vec, one of the most influential word embedding models, uses a small window of collocates to generate its vectors. But this window is more a detail of implementation, rather than an essential element in how one might imagine word embedding models (indeed, other word embeddings—including GloVe, unless I’m mistaken, don’t use this window). If the core insight of word vectors is to imagine meaning as a point in large dimensional space, then Firth may not be the most useful theoretical inspiration. The space these models create is generated by representing a term not simply in relation to its collocates, but also in relation to all the terms in the vocabulary. The collocates embed a term in a space that is generated (originally) by all the terms in the model’s vocabulary. It is the sum total of all the terms that are used, and then how they used in relation to one another, that really allows meaning to be represented and mapped in this spatial way.⁴

So, we’re not just talking about “the company [a word] keeps,” we’re talking about a method for generating a “space.” Yet even representing meaning as points in space is, to some degree a technical detail (or, perhaps, a metaphor). Trying to imagine what a 300-dimensional word embedding model “looks like” is, of course, impossible.I recall a rather funny comment somewhere: asked how to imagine, say, a twelve-dimensional space, a mathematician responded: “Imagine a three dimensional space. Now concentrate while saying 12 loudly.” While the algorithms and measures of distance used in such models have geometrical interpretations that make them easier to understand, what we’re really talking about is not “space” as we (non-mathematicians) visualize or imagine it. Or, we might say, it is very easy to imagine what a 300-dimensional word embedding looks like: it looks like a spreadsheet with 300 columns, and rows for each term in the vocabulary. What these models are quantifying and representing is not space, but the differences among the terms.

So this is my point: if these models are best understood as representing language (or meaning) as a system of differences, then it is Saussure, far more than Firth, who provides something like a theoretical description of this model. A set of word embedding vectors, or indeed most language models as I (in my inexpert way understand them) look very much like what Saussure calls “a system of pure values” (155).

Saussure

So, let’s talk Saussure for a moment. My goal here is simply to highlight the (I think) often ignored quantitative element that is implicit in Saussure’s model of meaning, in order to ask whether contemporary, computational language models might be described as operationalized instances of a Saussurean model of meaning.

Central to Saussure’s description of language is a rejection of any attempt to treat it as a list-like aggregation of names paired with concepts/ideas. One instead had to treat the system as a whole: “A language is a system in which all the elements fit together, and in which the value of any one element depends on the simultaneous coexistence of all the others” (Saussure et al. 159). “Value” here is a slightly slippery term. Saussure calls the exchange of a word for an idea meaning, but the relationship a word has to the rest of the words in a language its value. A value is determined not in the relationship between a word and the object it names, but in relationship to the other words within a language/system.

Saussure offers an illuminating example of how value differs from meaning:

The French word mouton may have the same meaning as the English word sheep; but it does not have the same value. There are various reasons for this, but in particular the fact that the English word for the meat of this animal, as prepared and served for a meal, is not sheep but mutton. The difference in value between sheep and mouton hinges on the fact that in English there is also another word mutton for the meat, whereas mouton in French covers both.

In a given a language, all the words which express neighboring ideas help to define one another’s meaning. Each set of synonyms like redouter (‘to dread’), craindre (‘to fear’), avoir peur (‘to be afraid’) has its particular value only because they strand in contrast with one another. If redouter (‘to dread’) did not exist, its content would be shared out among its competitors… So the value of any given word is determined by what other words there are in that particular area of the vocabulary. (160)

Values don’t pre-exist the system, waiting to be labeled; they are, as we say, produced by the language. The key I want to highlight, however, is how strongly this description resonates with word vectors (and, I think, with computational models of language/meaning more broadly). Saussure’s language here—of a “neighborhood” of terms; of a “particular area of the vocabulary”—anticipates models of meaning as vector space. Saussure’s description here is, I think, a better description/theorization of word-embedding vectors (and similar models) than Firth’s “company it keeps” slogan.

After a discussion of differences in inflection systems and verb tenses across language (as another example, along the mutton/mouton distinction, of how values are produced by language), Saussure summarizes:

In all these cases what we find, instead of ideas given in advance, are values emanating from a linguistic system. If we say that these values correspond to certain concepts, it must be understood that the concepts in question are purely differential. That is to say they are concepts defined not positively, in terms of their content, but negatively by contrast with other items in the same system. What characterizes each most exactly is being whatever the others are not. (162).

This reflects what Saussure articulates as a “paradoxical principle”: the doubleness of all values. One: a value can be located within a system of like/comparable values; two, value can also be exchanged that for something dissimilar. Saussure’s example is money, which can be compared to other monetary values quantitatively, or exchanged for some object/commodity. In language a word can be compared to other like values (i.e. to other words)—but also “exchanged” for something dissimilar (a concept or an idea). When Saussure articulates this idea, he simply asserted that comparing words to other words is somehow akin to the quantitative comparison of one monetary value to another. Vector-space representations of language, I think we have a more direct model of what this could actually look like.

This crude image of signs relating to one another in a total system seems to show each term relating only to its neighbors—in a sort of one dimensional line. But the idea, I take it, is that each term is a single location within a much larger space, and is defined only by its difference from all the other terms. Some terms, of course, may be nearer and further—but the space is defined by all the terms, by the langue.

This understanding of meaning as differential, as produced by a value’s (quasi-quantitative) difference from other (quasi-quantiative) values, is at the heart of—indeed, I’m suggesting it is the heart of—the Saussurean model of meaning. Saussure, of course, doesn’t quantify his values, and doesn’t seem to imagine the uses or benefits of doing so. But the idea of meaning as essentially differential is, I think, a fundamentally quantitative (even if only implicitly so) concept.

In the context of intro lit theory classes (of the sort that I teach with some regularity), I think the stress is sometimes placed on Saussure’s insistence on the arbitrary character of the sign. From this arbitrariness stems the antifoundationalism that is a hallmark of poststructuralism. But, for my money (and, probably, Derrida’s), it is the claim that languagef is a system of differences without any positive values that is the genuinely interesting element of the Course in General Linguistics. After all, the observation that the signifier is “arbitrary” is neither novel to Saussure, nor particularly shocking. Saussure’s insight is that if, as seems incontestably obvious, there is no necessary relationship between what he calls signifier and signified (a fact well evidenced by the existence of different languages)Saussure does spend some a brief passage rejecting any attempt to ground meaning in onomatopoeia (101–02)., then arbitrary means differential: “the terms arbitrary and differential designate two correlative principles” (Saussure et al. 163). Large language models represent an operationalization of this idea, they lend calculations to what was always already (ahem) a quantitative concept.

So what?

I’ve contended that Saussure offers a better/richer/more descriptive theoretical account of word embeddings rather than Firth. But I’ve insisted on this point at such length because Saussure also offers a more recognizable point of reference a wide range of things in the humanities influenced by structuralism and poststructuralism (the sort things that folks encounter in humanities classes like “literary theory”). If we can recognize large language models are an odd combination of Saussurean langue/parole, it seems an opportunity to leverage a long history of theory in the humanities. Does Saussure offers a richer point of transit between contemporary discussions about large language models and the history of theory?

Or, to approach the problem from something like the other dimension: Does seeing large language models as Saussurean structures reveal a tacit, quantitative dimension to much structuralist influenced work. Consider Judith Butler’s Gender Trouble—certainly one of the most influential “theory” texts. In Gender Trouble, Butler draws a distinction between their own position and structuralism. Butler writes:

The totality and closure of language is both presumed and contested within structuralism. Although Saussure understands the relationship of signifier and signified to be arbitrary, he places the arbitrary relation within a necessarily complete linguistic system. All linguistic terms presuppose a linguistic totality of structures, the entirety of which is presupposed and implicitly recalled for any one term to bear meaning. This quasi-Liebnizian view, in which language figures as a systemic totality, effectively suppresses the moment of difference between signifier and signified, relating and unifying that moment of arbitrariness within a totalizing field. The poststructuralist break with Saussure… refutes the claim of totality and universality and the presumption of binary structural oppositions that implicitly operate to quell the insistent ambiguity and openness of linguistic and cultural signification. (40)

This distinction could offer interesting complications to the very of Saussure I’ve presented. But what I want to stress is what Butler here shares with Saussure: a commitment to the arbitrariness of the sign. The “insistent ambiguity and openness of linguistic cultural signification” that is so essential to Butler’s larger description of gender’s performativity, is not less quantitative/differential than Saussure’s description of langue. Such signifying phenomena—defined by iterability, by arbitrariness, by difference (or différance)—imply a differential “matrix” (a term used by poststructuralists and machine learning enthusiasts alike), and so are in some sense quantitative. I’m emphatically not interested in trying to actually operationalize Butler’s account of gender—to attach numbers to particular gendered signifiers, say—but it seems that Butler’s notion of gender, in desubstantializing gender, makes it instead an essentially stochastic concept. Perhaps some find that unsurprising—but this is certainly not the way I’m used to thinking about gender.

I also think the differences between Saussurean structure and large language models can be potentially revealing. Saussure infamously insists on a rigid distinction between the abstract system that a language constitutes (langue) and any particular use/event of that system (speech or parole). The structuralist, in Saussure’s description, studies langue, a synchronic system imagined outside of its history, rather than any particular use or parole. While a vector-space model of meaning (like word embeddings) operates like langue, it is built entirely out of parole. These models scoop up massive amounts of text in order to transform what Saussure calls values into actual numeric values. How should we understand the implications of this difference? Can we understand issues of embedded bias described by Safiya Noble, for instance, as a consequence of treating parole as langue? Does such a redescription enable our thinking in any productive way?

Finally, Saussure reminds us of the inherently social location of the “intelligence” these models are able to achieve. If these models present us with uncanny images of apparent intelligence, it is useful to recall that the very “structure” that these models manage to boil down and concentrate from so many instances of parole is an intelligence that we have collectively put there. David Weinberger famously insisted, in what became a sort of slogan for mid 2010s-among social network enthusiasm, that “the smartest person in the room is the room.” It’s a description of the power of networked culture. But, of course, a room is never “the smartest person” “in the room”; a room is neither smart nor a person. Weinberger’s eminently reasonable point—(crudely: that people working together have more intelligence than any individual and that networks enrich/enable this)—is fair enough, and well taken! The danger is to localize and attribute this outcome of social organization to a particular technology (here, “the room”).(See also Jerome McGann, A New Republic of Letters, pg. 43). In discussions of language models, I think we sometimes see something similar—a misattribution of collective, cultural “knowledge”/“intelligence” (of the sort that is embedded in language use) to the particular mechanism/technology for extracting/re-presenting that intelligence. A crude analogy: a pressure cook can make a mighty stock, but the flavor comes from the ingredients, not the pressure cooker. I’m inclined to see Saussure’s model of meaning as helping to remind us that what looks like “intelligence” in these models is a system of relationships that inheres in the material they’re trained on. It is the position of the points that is the source of the word embeddings power, and that position reflects how the words are used. The embeddings, or other technologies, can reveal some surprising and shocking and impressive things; they are truly remarkable. But it is the system of differences—or the odd pieces of it that are carved off and thrown into the flow of GPU-powered tensors—which is the location of the “intelligence” such models achieve, far more than than the models themselves.

Works Cited