Semantics
Compressed representations of reality for syntactic agents; which might be what meaning means
2014-12-29 — 2026-07-14
Wherein the Mapping of Words to Phenomena Is Treated as a Classification Problem, and Shared Human Experience Is Proposed as the Mechanism by Which Mutual Understanding Between Speakers Is Achieved.
The belly inside is beautiful, because the baby grows there,
because your sweet cock, all bright and jolly, thrusts there,
and good, tasty food descends there,
and for this reason the cavern, the grotto, the tunnel
are beautiful and important, and the labyrinth, too,
which is made in the image of our wonderful intestines.
When somebody wants to invent something beautiful and important,
it has to come from there,
because you also came from there the day you were born,
because fertility always comes from inside a cavity,
where first something rots and then, lo and behold,
there’s a little man, a date, a baobab.
And high is better than low,
because if you have your head down, the blood goes to your brain,
because feet stink and hair doesn’t stink as much,
because it’s better to climb a tree and pick fruit
than end up underground, food for worms,
and because you rarely hurt yourself hitting something above
— you really have to be in an attic —
while you often hurt yourself falling.
That’s why up is angelic and down devilish.”
— Umberto Eco. Foucault’s Pendulum.
On the mapping between linguistic tokens and what they denote.
If I had time I would learn about: Wierzbicka’s semantic primes, Wittgenstein, probably Mark Johnson if the over-egging doesn’t kill me. Logic-and-language philosophers, toy axiomatic worlds. Classic AI symbolic reasoning approaches. Drop in via game theory and neurolinguistics? Ignore most of it, mention plausible models based on statistical learnability.
1 Semantics is solved you guys
Have you had a talk with philosophers recently? Philosophers be all like
- Do machines have free will?
- Are machines conscious?
- Can I see the same colours as a mantis shrimp?
Great news guys, questions like this are all totally solved! In case you missed the memo, I will vouchsafe it to you here: the canonical solution to semantics.
Collectively, speakers of a given language have learned a mapping between words and their referents, by observing a lot of phenomena and talking about them. If you will forgive me bulldozing some interesting fine detail, I assert that a good enough model for the phenomena is a large fixed data set which comprises more-or-less everyday human experience (smells, tastes, scenes, proprioceptive twinges). Now, obviously there is a lot of going on when we learn to map from sensory experience to words. That is a whole thing which I will not attempt to solve here, but, you know, we are doing great at that.
The process of learning words we will approximate as a classifier.
Write \(\mathcal{X}\) for the space of phenomena and let each phenomenon have a frequency of occurrence in the world, \(p(x)\). We use \(V\) for a finite vocabulary to describe these. Not all things have names, and not all names are useful, so we will assume that \(|V|\) is much smaller than \(|\mathcal{X}|\), and “I dunno” is a perfectly valid label for a phenomenon. Suppose some stimuli occur often enough and are useful enough that humans name them. Everyday human experience is a joint distribution \(p(x, w)\) over \(\mathcal{X}\times V\), the propensity of a competent speaker subject to stimulus \(x\) to assign label \(w\) to it. \(w\) means \(x\) if \(p(w\mid x)\) is high.
In practice, a learner sees a finite sample \(\mathcal{D}=\{(x_i,w_i)\}_{i=1}^{n}\) of (stimulus, word) pairs, and fits a tractable model \(\hat p_{\mathcal{D}}(w\mid x)\) to it — the member of some family \(\mathcal{F}\) of candidate classifiers \(q(w\mid x)\) that maximizes the likelihood of the classifications of words actually heard,
\[\hat p_{\mathcal{D}} \;=\; \arg\max_{q\in\mathcal{F}}\;\sum_{(x_i,w_i)\in\mathcal{D}} \log q(w_i \mid x_i).\]
The meaning of a given word is the set of phenomena that are most likely to be assigned that word by the learned model,
\[[\![\,w\,]\!]_{\mathcal{D}} \;=\; \bigl\{\, x\in\mathcal{X} \;:\; w=\arg\max_{w'\in V}\,\hat p_{\mathcal{D}}(w'\mid x) \,\bigr\}.\]
Imagine you and I come from the same town and the main language spoken in the town is English. Your corpus \(\mathcal{D}'\) and mine \(\mathcal{D}\) are not identical, but a shared town and language means both are samples from the same \(p(x,w)\). My meaning for a given word is the region \([\![\,w\,]\!]_{\mathcal{D}}\) defined above; yours is \([\![\,w\,]\!]_{\mathcal{D}’}\), i.e. the same up to a difference in the training data we each sample from the world. We understand each other about \(w\) to the extent those two regions coincide, and we disagree on the phenomena that fall in one region but not the other, depending on the idiosyncrasies of our respective corpora.
Aggregating over the vocabulary, our miscommunication rate is the probability that we assign different labels to the same phenomenon,
\[\Pr_{x\sim p(x)}\!\left[\,\hat w_{\mathcal{D}}(x)\neq\hat w_{\mathcal{D}'}(x)\,\right],\qquad \hat w_{\mathcal{D}}(x)=\arg\max_{w'\in V}\hat p_{\mathcal{D}}(w'\mid x).\]
Since \(\mathcal{D}\) and \(\mathcal{D}'\) are drawn from the same \(p(x,w)\), that probability is small: we typically assign the same words to the same phenomena. The disagreements that remain are the rare phenomena, where neither corpus held enough examples to settle which word applies, or maybe where the usage itself is ambiguous. So I might think a whale is not a fish because it is a mammal, and you might think it is a fish because it lives in the water.
Generally our vocabularies nearly agree because our corpora nearly do, because we learned words from similar experiences from being in the same time and place.
I have a hard one for you now:
- Does a dog have Buddha nature?
OK, I didn’t say what nameable phenomena were. In practice, labelling phenomena in the world is a social and sensory process. The label is stuff that we usually agree on, and the phenomenon itself is something that we can readily agree on, like “furry things that like sardines and purr” are “cats”.
2 Symbol grounding
Piantadosi and Hill (2022) on the Symbol grounding problem in transformers. This is now charmingly referred to as the “vector grounding problem” (Mollo and Millière 2023).
3 As a classification problem
Eliezer Yudkowsky’s essay, How an algorithm feels from the inside, which inspired Scott Alexander’s The Categories Were Made For Man, Not Man For The Categories.
From a different direction, Microsoft argues that objects are a kind of anchor point in training cross-modal AI systems. (Li et al. 2020)
…objects can be naturally used as anchor points to ease the learning of semantic alignments between images and texts. This discovery leads to a novel VLP framework that creates new state-of-the-art performance on six well-established vision-and-language tasks. …. Though the observed data varies among different channels (modalities), we hypothesize that important factors tend to be shared among multiple channels (for example, dogs can be described visually and verbally), capturing channel-invariant (or modality-invariant) factors at the semantic level. In vision-and-language tasks, salient objects in an image can be mostly detected by modern object detectors, and such objects are often mentioned in the paired text.
Also, what does embodiment mean for this stuff, in terms of priors?
4 As an evolutionary phenomenon
Moved to Language games.
5 Simulacra
See simulacra.
6 Neurology of
What does the MRI tell us about denotation in the brain?
(Stolk et al. 2014) is worth it for the tagline: “experimental semiotics”
How can we understand each other during communicative interactions? An influential suggestion holds that communicators are primed by each other’s behaviours, with associative mechanisms automatically coordinating the production of communicative signals and the comprehension of their meanings. An alternative suggestion posits that mutual understanding requires shared conceptualisations of a signal’s use, i.e., “conceptual pacts” that are abstracted away from specific experiences. Both accounts predict coherent neural dynamics across communicators, aligned either to the occurrence of a signal or to the dynamics of conceptual pacts. Using coherence spectral-density analysis of cerebral activity simultaneously measured in pairs of communicators, this study shows that establishing mutual understanding of novel signals synchronises cerebral dynamics across communicators’ right temporal lobes. This interpersonal cerebral coherence occurred only within pairs with a shared communicative history, and at temporal scales independent from signals’ occurrences. These findings favour the notion that meaning emerges from shared conceptualisations of a signal’s use.
7 Word vector models
Where the action is at. See vector embeddings.