# Semantics

### compressed representations of reality for syntactic agents; also, what stuff means

“[…] archetypes don’t exist; the body exists.
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, Valiant’s PAC-learning, Wittgenstein, probably Mark Johnson if the over-writing 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.

## Learnability of terms

When do we need to use words? BGPL10 have a toy model for color words, which is a clever choice of domain.

StTe05: a connection to count model stochastics.

Also what embodiment means for this stuff.

## Neural models

What does the MRI tell us about denotation in the brain?

SNVV14 is worth it for the tagline alone: “experimental semiotics”

How can we understand each other during communicative interactions? An influential suggestion holds that communicators are primed by each other’s behaviors, 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 conceptualizations 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 synchronizes 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 favor the notion that meaning emerges from shared conceptualizations of a signal’s use.

## Meanings as probabilistic graphical classifiers

Eliezer Yudkowsky’s classic essay, How an algorithm feels from the inside.

Advanced-grade, semantics and discourse and values – Scott Alexander’s The whole city is centre.

## Word vector models

Nearly-reversible, distributed representations of semantics via entity embeddings. Do these actually tell us anything about semantics?

As invented by BDVJ03 and popularised/refined by Mikolov and Dean at Google, the skip-gram semantic vector spaces – definitely the hippest of the ways of defining String distances for natual language this season.

• Christopher Olah discusses it from a neural network perspective with diagrams and commends Bengio’s BDVJ03 for a rationale.
• Sanjeev Arora’s semantic word embeddings has an explanation of skipgrammish methods:

In all methods, the word vector is a succinct representation of the distribution of other words around this word. That this suffices to capture meaning is asserted by Firth’s hypothesis from 1957, “You shall know a word by the company it keeps.” To give an example, if I ask you to think of a word that tends to co-occur with cow, drink, babies, calcium, you would immediately answer: milk.

[…] Firth’s hypothesis does imply a very simple word embedding, albeit a very high-dimensional one.

Embedding 1: Suppose the dictionary has N distinct words (in practice, N=100,000). Take a very large text corpus (e.g., Wikipedia) and let Count5(w1,w2) be the number of times w1 and w2 occur within a distance 5 of each other in the corpus. Then the word embedding for a word w is a vector of dimension N, with one coordinate for each dictionary word. The coordinate corresponding to word w2 is Count5(w,w2). (Variants of this method involve considering cooccurence of w with various phrases or n-tuples.)

The obvious problem with Embedding 1 is that it uses extremely high-dimensional vectors. How can we compress them?

Embedding 2: Do dimension reduction by taking the rank-300 singular value decomposition (SVD) of the above vectors.

Using SVD to do dimension reduction seems an obvious idea these days but it actually is not. After all, it is unclear a priori why the above N×N matrix of cooccurance counts should be close to a rank-300 matrix. That this is the case was empirically discovered in the paper on Latent Semantic Indexing or LSI.

• For both descriptions below, we assume that the current word in a sentence is $$w_i.$$

CBOW: The input to the model could be $$w_{i-2}, w_{i-1}, w_{i+1}, w_{i+2},$$ the preceding and following words of the current word we are at. The output of the neural network will be $$w_i$$. Hence you can think of the task as “predicting the word given its context”. Note that the number of words we use depends on your setting for the window size.

Skip-gram: The input to the model is $$w_i$$, and the output could be $$w_{i-1}, w_{i-2}, w_{i+1}, w_{i+2}$$. So the task here is “predicting the context given a word”. Also, the context is not limited to its immediate context, training instances can be created by skipping a constant number of words in its context, so for example, $$w_{i-3}, w_{i-4}, w_{i+3}, w_{i+4}$$, hence the name skip-gram. Note that the window size determines how far forward and backward to look for context words to predict.

According to Mikolov:

Skip-gram: works well with small amount of the training data, represents well even rare words or phrases.

CBOW: several times faster to train than the skip-gram, slightly better accuracy for the frequent words.

This can get even a bit more complicated if you consider that there are two different ways how to train the models: the normalized hierarchical softmax, and the un-normalized negative sampling. Both work quite differently.

which makes sense since with skip gram, you can create a lot more training instances from limited amount of data, and for CBOW, you will need more since you are conditioning on context, which can get exponentially huge.

• Jeff Dean’s CIKM Keynote. (that’s “Conference on Information and Knowledge Management” to you and me.)

“Embedding vectors trained for the language modeling task have very interesting properties (especially the skip-gram model)”

$E(\text{hotter}) - E(\text{hot}) &≈ E(\text{bigger}) - E(\text{big}) \\ E(\text{Rome}) - E(\text{Italy}) &≈ E(\text{Berlin}) - E(\text{Germany})$

“Skip-gram model w/ 640 dimensions trained on 6B words of news text achieves 57% accuracy for analogy-solving test set.”

Sanjeev Aror aexplain that, more than that, the skip gram vectors for polysemic words are a weighted sum of their constituent meanings.

• We describe an approach for unsupervised learning of a generic, distributed sentence encoder. Using the continuity of text from books, we train an encoder/decoder model that tries to reconstruct the surrounding sentences of an encoded passage. Sentences that share semantic and syntactic properties are thus mapped to similar vector representations. […] The end result is an off-the-shelf encoder that can produce highly generic sentence representations that are robust and perform well in practice

Graph formulations, e.g. David McAllester, Deep Meaning Beyond Thought Vectors:

I want to complain at this point that you can’t cram the meaning of a bleeping sentence into a bleeping sequence of vectors. The graph structures on the positions in the sentence used in the above models should be exposed to the user of the semantic representation. I would take the position that the meaning should be an embedded knowledge graph — a graph on embedded entity nodes and typed relations (edges) between them. A node representing an event can be connected through edges to entities that fill the semantic roles of the event type

## Software

• word2vec

This tool provides an efficient implementation of the continuous bag-of-words and skip-gram architectures for computing vector representations of words. These representations can be subsequently used in many natural language processing applications and for further research.”

• fastText

fastText is a library for efficient learning of word representations and sentence classification.