Some thoughts on Pater 2019

As you might imagine, a lot of my thoughts are covered by my commentary that we’re reading as one of the selections next time. But here’s the briefer version: I love seeing the fusion of linguistic representations with statistical methods. The real struggle for me as a cognitive modeler is when using RNNs is better than symbolic models that are more easily interpretable (e.g., hierarchical Bayesian models that allow overhypotheses to define a wider space of latent hypotheses).

At the very end of Pater’s article, I see a potentially exciting path forward with the advent of RNNs (or other models with distributed representations) that are interpretable. I’m definitely a fan of techniques that allow the learning of hidden structure without it being explicitly encoded — this is the same thing I see in hierarchical Bayesian overhypotheses. More on this below (and in my commentary for next time).

Specific thoughts:

(1) I couldn’t agree more with the importance of incorporating statistical approaches more thoroughly into learning/acquisition theories, but I remain to be sold on the neural networks side. It really depends on what kind of network: are they matching neurobiology (e.g., see Avery and Krichmar 2017, Beyeler, Rounds, Carlson, Dutt, & Krichmar 2017, Krichmar, Conrad, & Asada 2015; Neftci, Augustine, Paul, & Detorakis 2017, Neftci, Binas, Rutishauser, Chicca, Indiveri, & Douglas 2013) or are they a computational-level distributed representations approach (I think this is what most RNNs are), which seems hard to decipher, and so less useful for exploring symbolic theories more completely? Maybe the point is to explore non-symbolic theories.

Pater notes the following about non-symbolic approaches: “...it is hard to escape the conclusion that a successful theory of learning from realistic data will have a neural component.” If by neural, Pater means an implementational-level description, sure. But I’m not sold on distributed representations as being necessary for a successful theory of learning -- a theory can operate at the computational or algorithmic levels.

(2) I completely agree that structure-independent representations (statistical sequences that don’t involve phrases, etc.) can only get you so far. The interesting thing from an NLP standpoint, of course, is exactly how far they can get you — which often turns out to be surprisingly far. In fact, it’s often much further than I would have expected — e.g., n-grams over words (not even syntactic categories!!) work remarkably well as features for opinion spam detection, with near 90% classification accuracy: Ott et. al 2011, 2013. Though I guess n-grams do heuristically encode some local structure.

(3) RNNs seem to need to incorporate hierarchical representations to work (e.g., the Recurrent Neural Network Grammars of Dyer et al. 2016, and incorporating hierarchical structure into current neural network approaches in AI/NLP). But, sequence-to-sequence models do pretty well without explicit structure encoded in. So, if sequence-to-sequence models can handle aux-inversion (e.g., as in McCoy, Frank, & Linzen 2018...well, at least sort of -- it’s not clear they handle it the way humans do), what do we make of it from the linguistic cognition perspective?

This comes back to the question of model interpretation. With symbolic models, it’s usually clear what theory of representation is being evaluated. For RNNs, do we know what the distributed representations/continuous hypotheses are encoding? (This of course is less a problem from the engineering perspective -- we’re happy if we can get the machines to do it as well or better than humans.) As Pater noted, some read-out can be done with clever model comparisons, and some distributed representations (e.g., Palangi et al’s (2017) Tensor Product Recurrent Networks) may in fact encode syntactic structures we recognize. So then, the question is what we’re getting from the distributed representation.

Pater: “...it is given the building blocks of symbols and their roles, but must learn their configurations”. This starts to sound like the latent vs. explicit hypothesis space construction of Perfors (2012), which can be implemented in a variety of ways (e.g., variational learning as in Yang 2002). That is, RNNs allow the modeler to specify the building blocks but let the model construct the explicit hypotheses that get evaluated, based on its prior biases (RNN architecture, Bayesian overhypothesis hyperparameters, etc.). Something that could be interesting: the RNN version allows construction of explicit hypotheses from the building blocks that are outside what the modeler would have built in to the overhypothesis parameters; that is, they may be perfectly reasonable hypotheses from the given building blocks, but go against the natural overhypothesis-style parametric biases and so would get a low probability of being generated (and subsequently evaluated).

Since the RNN generates hypotheses with whatever architectural biases mold the explicit hypothesis construction, it may give higher probability to hypotheses that were lower-probability for a hierarchical Bayesian model.  That is, the Bayesian overhypotheses may be quite general (especially if we back off to over-over-hypotheses, and so on), but still require an explicit bias at some level for how hypotheses are generated from overhypotheses. That has to be specified by the modeler. This may cause Bayesian modelers to miss ways that certain building blocks can generate the kinds of linguistic hypotheses we want to generate.

An analogy: Genetic algorithms can be used to identify solutions that humans didn’t think of because they employ a much wider search of the latent hypothesis space; humans are fettered by their biases for what an optimal solution is going to look like.  Here: symbolic modelers may be fettered by ideas about how building blocks can be used to generate explicit hypotheses; RNNs may allow a wider search of the latent hypothesis space because they’re bound by different (implicit) ideas, via the RNN architecture. So, the solution an RNN comes up with (assuming you can interpret it) may provide a novel representational option, based on the building blocks given to it.

Bigger point: RNNs and distributed representations may provide a novel way of exploratory theorizing (especially for syntactic learning), to the extent that their innards are interpretable. For theory evaluation, on the other hand, it’s better to go with a symbolic model that’s already easy to understand….unless your theory is about the building blocks, leaving the explicit hypotheses they build and evaluate unspecified.

Some thoughts on Nordmeyer & Frank 2018

This is exactly the kind of behavioral work that serves as a good target of developmental modeling. (Thanks, N&F2018!) Moreover, the particular experiment lends itself very naturally to RSA modeling, given the importance of context manipulation (and then the RSA model allows us to be more concrete about what those contextual variables could be and what exactly they could do). 

More generally, this work also falls in a larger body of work that underscores the importance of pragmatic felicity when doing child language experiments. This was the basis for the Truth Value Judgment paradigm (Crain & Thornton 1998) -- it’s important to give supportive contexts if you want kids to show you their linguistic knowledge. They’re not as good as adults at “test-taking” -- i.e., compensating for a lack of supportive context by implicitly supplying their own. So, if kids aren’t behaving like they have adult-like linguistic knowledge, check if pragmatic (or processing) factors might be getting in the way.

Crain, S., & Thornton, R. (1998). The truth value judgment task: Fundamentals of design. University of Maryland working papers in linguistics, 6, 61-70.

Some other thoughts:

(1) The Kim (1985) child behavioral setup, which involved (for example) someone pointing at an apple and saying “This is not a banana”. The child would reply “wrong!”, but of course we don’t know why she’s saying it’s wrong. Is it the wrong meaning (semantic issue) or the wrong thing to say (pragmatic issue)? This reminds me of recent work on children’s (non-)endorsements when it comes to quantifier scope ambiguity (Viau & Lidz 2010, Savinelli et al. 2017). The key idea is that they weren’t saying no because they couldn’t get the interpretation; they were saying no because it wasn’t a very informative interpretation, given the prior context. This also seems to be a main factor in English children’s pronoun interpretation behavior being wonky (Conroy et al. 2009). Also similar to the Conroy et al. (2009) study is how N&F2018 are explicitly manipulating the context to show a replication of prior behavior and then how to fix it with supportive pragmatic context.

Savinelli, K. J., Scontras, G., & Pearl, L. (2017). Modeling scope ambiguity resolution as pragmatic inference: Formalizing differences in child and adult behavior. In CogSci.

Viau, J., Lidz, J., & Musolino, J. (2010). Priming of abstract logical representations in 4-year-olds. Language Acquisition, 17(1-2), 26-50.

Conroy, A., Takahashi, E., Lidz, J., & Phillips, C. (2009). Equal treatment for all antecedents: How children succeed with Principle B. Linguistic Inquiry, 40(3), 446-486.

(2) Varying the linguistic form: “has no X” vs. “doesn’t have an X”. Corpus analysis could tell you how often negation of different types appear in these forms since “has no X” is less good than “doesn’t have an X”. Then we would know if that’s just a frequency effect or if something more interesting is happening.

(3) With adults, “has no X” is better when everyone else has an X. The pragmatic reason for this is that there’s a more informative utterance when the referent has a Y instead of an X (i.e., “has a Y”) -- this seems like something that could be captured in an RSA model’s cost function. Basically, it costs more to say “has no X” compared with “has Y” when both are true.

(4) In general, kudos for getting kids to give ratings. This is super-hard to do well, since it requires young children to think metalinguistically. I also really appreciate seeing the histogram of responses in Figure 4. Here, we can see that there are still quite a number of kids who, in the unsupportive none context (where no one else has anything) think that “Abby doesn’t have an apple” is fine (>50); however, many more kids (>100) think it’s terrible. Similarly, there are >50 kids who think “Abby doesn’t have an apple” is terrible in the target context (where everyone else has an apple), though many more (>100) think it’s fine. Hello, child data messiness -- and bless your hearts, child behavioral researchers.

I wish we could see an equivalent histogram for adults, though. I wonder how much of this messiness is because we’re dealing with kids vs. dealing with a felicity scale vs. dealing with a phenomenon that’s inherently messy in the target state.

Some thoughts on Tessler & Franke 2018

This is a great example of theoretically-motivated computational modeling coupled with behavioral experiments, here in the realm of negated antonyms (e.g.., "not unhappy"). My main qualm is with the paper length — there’s a lot of interesting stuff going on, and we just don’t get the space to see it fully discussed (more specifics on this below). This of course isn’t the authors’ fault — it just highlights the difficulty of explaining work like this in the space you normally get for conference proceedings.

Specific comments:

(1) The case study here with negated antonyms (which involve double negations like “not unhappy”) seems very relevant for sentiment analysis, where we still struggle to deal precisely with negated expressions. So, more generally, this is a particular case where I can see the NLP community paying closer attention and taking inspiration from cognitive work. For example, based on the results here for single utterances ("unhappy" = "not happy"), the antonym dictionary approach to negation (where "not happy" = "unhappy" or "sad") may not be a bad move in non-contrastive utterances.

(2) I love the clearcut hypothesis space, and the building blocks of contrary (tall vs. short) vs. contradictory (even vs. odd) adjectives. My own sense is that my prior experience is mostly comprised of contrary adjectives, but I wonder if that’s true. (Helloooo, corpus analysis. Also, what do we know about children’s development of these types of fine semantic distinctions?)

(3) I wish there had been a bit more space to explain why we see the modeling results we do. For the full uncertain negation, we get some mileage from a single utterance because it’s unnecessarily costly to say “not unhappy” unless it had a different meaning from "happy", which makes sense. When there are multiple utterances, we see a complete separation of all four options because...there are four different individuals who presumably have different states (or else why use different expressions)?

For the more restricted hypothesis of bonafide contraries that connects morphological negation explicitly to an opposite valence, we see separation for both single and multiple utterances, but much moreso for the multiple utterances. This is definitely a case of a more restricted hypothesis yielding stronger generalizations from ambiguous data, but I don’t quite see how we’re getting it. Certainly, “not unhappy” is more costly to produce than “happy”, so we get separation between those two terms, just as with the full uncertain negation hypothesis. But why, in the single utterance case, do we also get separation between “unhappy” and “not happy”?

For the most restricted hypothesis of logical negation, I get why we never get any separation — by definition, “unhappy” = “not happy” = not(happy), and so “not unhappy” = not(not(happy)) = “happy”.

Some thoughts on Fitz & Chang 2017 + Bonus thoughts on McCoy et al. 2018

(Just a quick note that I had a lot of thoughts about these papers, so this is a lengthy post.)

***F&C2017 general thoughts:

This paper tackles one of the cases commonly held up to argue for innate, language-specific knowledge: structure-dependent rules for syntax (and more specifically, complex yes/no questions that require such rules). The key: learn how to produce these question forms without ever seeing (m)any informative examples of them. There have been a variety of solutions to this problem, including recent Bayesian modeling work (Perfors et al. 2011) demonstrating how this knowledge can be inferred as long as the child has the ability to consider structure-dependent rules in her hypothesis space. Here, the approach is to broaden the relevant information from just the form of language (which is traditionally what syntactic learning focused on) and also include the meaning. This reminds me of CCG, which naturally links the form of something to its meaning during learning, and gets great bootstrapping power from that (see Abend et al. 2017 for an example and my forthcoming book chapter for a handy summary).

Perfors, A., Tenenbaum, J. B., & Regier, T. (2011). The learnability of abstract syntactic principles. Cognition, 118(3), 306-338.

Abend, O., Kwiatkowski, T., Smith, N. J., Goldwater, S., & Steedman, M. (2017). Bootstrapping language acquisition. Cognition, 164, 116-143.

Pearl, L. (forthcoming). Modeling syntactic acquisition. In J. Sprouse (ed.), Oxford Handbook of Experimental Syntax.

Interestingly enough with respect to what’s built into the child, it’s not clear to me that F&C2017 aren’t still advocating for innate, language-specific knowledge (which is what Universal Grammar is typically thought of). This knowledge just doesn’t happen to be *syntactic*. Instead, the required knowledge is about how concepts are structured. This reminds me of my comments in Pearl (2014) about exactly this point. It seems that non-generativist folks aren’t opposed to the idea of innate, language-specific knowledge -- they just prefer it not be syntactic (and preferably not labeled as Universal Grammar). Here, it seems that innate, language-specific knowledge about structured concepts is one way to accomplish the learning goal. More on this below in the specific thoughts section.

Pearl, L. (2014). Evaluating learning-strategy components: Being fair (Commentary on Ambridge, Pine, and Lieven). Language, 90(3), e107-e114.

***Bonus general thoughts on McCoy et al. 2018:

In contrast to F&C2017, M&al2018 are using only syntactic info to learn from. However, it seems like they’re similar to prior work in using smaller building blocks (i.e., indirect positive evidence) to generate hierarchical structure (i.e., structure-dependent representations) as the favored hypothesis. This is also similar to Perfors et al. (2011) - the main difference is that M&al2018 are using a non-symbolic model, while Perfors et al. (2011) are using a symbolic one. This then leads into the interpretation issue for M&al2018 -- when you find an RNN that works, why does it work? You have to do much more legwork to figure it out, compared to a symbolic model. However, F&C2017 had to do this too for their connectionist model, and I think they demonstrated how you can infer what may be going on quite well (in particular, which factors matter and how).

M&al2018 end up using machine learning classifiers to figure it out, and this seems like a great technique for trying to understand what’s going on in these distributed representations. It’s also something I’m seeing in the neuroscience realm when they try to interpret the distributed contents of, for instance, an fMRI scan.

**Specific thoughts on F&C2017:

(1) The key idea seems to be that nonlinguistic propositions are structured and this provides the crucial scaffolding that allows children to infer structure-dependent rules for the syntactic forms. Doesn’t this still rely on children having the ability to allow structure-dependence into their hypothesis space? Then, this propositional structure can push them towards the structure-dependent rules. But then, that’s no different than the Perfors et al. (2011) approach, where the syntactic forms from the language more broadly pointed towards structured representations that would naturally form the building blocks of structure-dependent rules.

The point that F&C2017 seem to want to make: The necessary information isn’t in the linguistic input at all, but rather in the non-linguistic input. So, this differs from linguistic nativists, who believe it’s not in the input (i.e., the necessary info is internal to the child) and from emergentists/constructionists, who believe it’s in the input (though I think they also allow it to not be the linguistic input specifically). But then, we come back to what prior knowledge/abilities the child needs to harness the information available if it’s in the input (of whatever kind) somewhere. How does the child know to view the input in the crucial way in order to be able to extract the relevant information? Isn’t that based on prior knowledge, which at some point has to be innate? (And where all the disagreement happens is how specific that innate knowledge is.)

Also related: In the discussion, F&C2017 say “Input is the oil that lubes the acquisition machinery, but it is not the machinery itself.” Exactly! And what everyone argues about is what the machinery consists of that uses that input. Here, F&C2017 say “the structure of meaning can constrain the way the language system interacts with experience and restrict the space of learnable grammar.” Great! So, now we just have to figure out where knowledge of that meaning structure originates.

(2) This description of the generativist take on structure dependence seemed odd to me: “consider only rules where auxiliaries do not move out of their S domains”. Well, sure, in this case we’re talking about (S)entences as the relevant structure. But the bias is more general than that (which is why it’s applicable to all kinds of structures and transformations, not just yes/no questions): only consider rules that use structures (like S) as building blocks/primitives. The reliance on linguistic structures, rather than other building blocks, is what makes this bias language-specific. (Though I could imagine an argument where the bias itself is actually a domain-general thing like “use the salient chunks in your system as building blocks for rules”, and that gets implemented in this domain with “salient chunks” = “linguistic structures like S”.)

(3) I quite liked Figure 1, with its visual representation of what a child’s hypothesis space looks like under each approach. I think it’s fair to say the linguistic nativist approach has traditionally ruled out structure-independent grammars from the hypothesis space, while the constructivist approach hasn’t. Of course, there are far more nuanced ways to implement the linguistic nativist idea (e.g., a low, but non-zero, prior on structure-independent grammars), but this certainly serves as the extreme endpoint.

(4) In 1.2, F&C2017 comment on the Perfors et al. 2011 Bayesian model, saying that it doesn’t “explain how grammars are acquired in the first place”. I think this must be referring to the fact that the hypothesis space of the Bayesian learner included possible grammars and the modeled learner was choosing among them. But how else is learning supposed to work? There’s a hypothesis space that’s defined implicitly, and the learner draws/constructs some explicit hypothesis from that implicit hypothesis space to evaluate (Perfors 2012 talks about this very helpfully). Maybe F&C2017 want a learner that constructs the building blocks of the implicit hypothesis space too? (In which case, sure, I’d love to have a model of conceptual change like that. But no one has that yet, as far as I’m aware.)

Perfors, A. (2012). Bayesian models of cognition: what's built in after all?. Philosophy Compass, 7(2), 127-138.

F&C2017 also note in that same part that it’s problematic that children don’t seem to be as optimal as the computational-level Bayesian model. Again, sure, in the same way that any computational-level model needs to be translated to an algorithmic-level version that approximates the inference with child limitations. But this doesn’t seem such a big problem -- or rather, if it is, it’s *everyone’s* problem who works at the computational level of modeling.

(5) I really like the point F&C2017 make about the need to integrate meaning with these kind of learning problems. As they rightly note, what things mean is a very salient source of information. Traditionally, syntactic learning approaches in the generavist world have assumed the child only considers syntactic information when learning about syntactic knowledge. But precisely because syntax is a conduit for meaning to be expressed through and meaning transfer is the heart of communication, it seems exactly right that the child could care about information coming from meaning even when learning something syntactic. This again is where the Abend et al. (2017) model gets some of it bootstrapping power from. (Also, Pearl & Mis 2016 for anaphoric one -- another traditional example of poverty of the stimulus -- integrates meaning information when learning something ostensibly syntactic.)

Pearl, L. & Mis, B. (2016). The role of indirect positive evidence in syntactic acquisition: A look at anaphoric one. Language, 92(1), 1-30.

(6) The Dual-path connectionist model, which uses thematic role & tense info: Importantly, the need for this information is motivated by production in F&C’s model -- you’re trying to express some particular meaning with the form you choose, and that’s part of what’s motivating the form. In theory, this should also be relevant for comprehension, of course. But what’s nice about this approach is that it gets at one of the key criticisms generativists (e.g., Berwick et al. 2011) had of prior modeling approaches -- namely, the disconnect between the form and the meaning.

Berwick, R. C., Pietroski, P., Yankama, B., & Chomsky, N. (2011). Poverty of the stimulus revisited. Cognitive Science, 35(7), 1207-1242.

(7) The dual path architecture: It’s interesting to see the use of a compression layer here, which forces the model to abstract away from details -- i.e., to form internal categories like we believe humans do. (Here, this means abstracting away from individual words and forming syntactic categories of some kind). I think this forced abstraction is one of the key motivations for current autoencoder approaches in machine learning.

(8) Encoding complex utterances: If I’m understanding this correctly, here’s where we see the structure explicitly -- we have one complete proposition connected to the agent concept of another proposition. So, the structured representation is available to the learner a priori via the conceptual structure. So, we might reasonably call this domain-specific knowledge, just not domain-specific syntactic knowledge. Then, experience with the language input tells the child how to translate that structured concept into a sequence of words, in this case, via the use of relative clauses. In particular, the child needs to see relative clauses used for embedded conceptual structures like this.

(9) Input distribution: I really appreciate F&C2017’s attention to realistic input distributions for training their model. This makes their model connect more to the actual problem children face, and so it makes their modeling results more informative.

(10) I think it’s really informative to see these results where the model can recreate specific observed differences in the developmental trajectory, and explain it by means of how the input is viewed. That is, the power of the learning approach is basically in viewing the input the right way, with the right scaffolding knowledge (here, about links between structured concepts and syntactic forms). Once that input lens is on, the input much more transparently reflects the observed behavior patterns in children. And this is what good computational modeling can do: make a learning theory specific enough to evaluate (here, about how to use that input), and then evaluate it by giving it realistic input and seeing if it can generate realistic output.

(11) It seems like F&C2017’s characterization of the hypothesis space aligns with other prior approaches like Perfors et al. 2011: the prior knowledge is a soft constraint on possible grammars, rather than absolutely ruling out structure-independent grammars. (In fact, Perfors et al. 2011 went further and used a simplicity prior, which is biased against the more complex structure-dependent grammars.) But the basic point is that there’s no need to categorically restrict the hypothesis space a priori. Instead, children can use their input and prior knowledge to restrict their hypotheses appropriately over time to structure-dependent rules.

**Bonus thoughts on M&al2018:

(B1) So, as cognitive scientists, should we spend more research time on the architecture that worked (i.e., the GRU with attention)? It does a very non-human thing, while also doing human things. And we don’t know why it’s doing either of those things, compared with other similar-seeming architectures that don’t. I should note that this is my existential issue with non-symbolic models, not a criticism specifically for M&al2018. I think they did a great job for a first pass at this question. Also, I really appreciate how careful they were about giving caveats when it comes to interpreting their results.

Some thoughts on Hahn et al. 2018

It’s really cool to see how adding processing considerations to an idealized (i.e., rational) model yields observable behavior. It reminds me of the importance of the different Marr explanation levels, where the algorithmic level is where processing considerations often get added (since these affect the algorithm humans use). A lot of work we’ve read about so far has been at the computational level (where, for example, the Rational Speech Act model typically lives). But in the back in my mind, I’m always thinking about what key differences might emerge once we have the bottleneck of human cognitive constraints.

Some other thoughts:

(1) Introduction, “As they occur in languages with widely different grammatical structures, we can expect that such an explanation will make reference to general principles of human communication and cognition” - I’m completely sympathetic to this approach, though it strikes me as funny that this is the same empirical fact that generativists use to appeal to innate, language-specific mechanisms (i.e., Universal Grammar). That is, the appearance of a pattern like this across the world’s languages is a signal to generativists that a universal language-specific principle is at work. Of course, as Hahn et al. (2018) note, it could well be that the universal principle has an effect on language (here, as adjective ordering constraints) but in fact the principle itself could be domain-general (e.g., something having to do with memory limitations, etc.).

(2) The Function of Subjective Adjectives:  I love seeing how to operationalize intuitions formally -- this is a great example. We have a somewhat squishy notion of subjectivity that gets formalized as judgments whose truth is relative to individuals, which subsequently gets implemented as the listener inferring the speaker’s judgment.

(3) A Model of Adjective Use, where the listener infers a full word state that includes multiple people: This seems equivalent to inferring that the adjective is in fact subjective. Developmentally, that’s definitely a step kids have to figure out, i.e., is adjective A likely to be something everyone agrees on or not?

(4) Communication: Rational Listeners and Speakers, an RSA model with just L0 and S. So this is just a model of why a speaker chooses to say something, rather than how a pragmatic listener (L1) chooses to interpret it? I wonder why we stop at this level rather than going another layer to a pragmatic speaker (S1) who chooses to say something, based on how a pragmatic listener will interpret it. That’s what we have to do when modeling Truth Value Judgment Tasks (TVJTs), for example. Maybe that’s because TVJTs aren’t normal speech events, but instead involve participants judging what they themselves would say?

(5) Communication: Rational Listeners and Speakers, where a speaker’s utility function is adjusted (from just basic negative surprisal) because she realizes other people’s judgments may be different than others: This part where the expected utility isn’t just negative surprisal may be a developmental step kids would have to complete. That is, if kids realize adjectives can be subjective and other people may disagree, then they’d behave like what’s modeled here. On the other hand, if kids don’t realize adjectives can be subjective, they may simply go with negative surprisal.

(6) Communication: Rational Listeners and Speakers, where the cost is the surprise of utterance u across the community’s language use: This is interesting too -- usually we see cost having to do with individual production costs such as longer utterances being more costly than shorter ones. But of course here, all the utterances are the same length. Instead, what could differ is the frequency of that combination. This seems like a useful aspect to incorporate into speaker models more generally, since frequency in the input can certainly affect ease of production.

(7) Adding Noise: I love seeing how this explanation works, with words further back being more likely to be deleted before the whole phrase can be interpreted. It’s nicely intuitive that more subjective words would be preferred further back, since they lead to more disagreement across listeners. But I wonder how this story would work for languages where the adjectives comes after. In that case, the more subjective adjective is still further away, but this time it’s the one the listener would have heard most recently. So, I think that means the one further in the past would be deleted more often -- in this case, the less subjective one -- and the more subjective one would be likely to survive. And then it becomes weird, because now we get the reverse situation, where the surviving adjective is the one that listeners don’t agree on as much. It seems like this account would predict languages with adjectives occurring after the noun to have the more subjective ones closer to the noun, since they’d be more likely to be forgotten. But that’s not what we see.

There’s a specific note about this in the discussion: “Our account seems to make the correct prediction. In such languages, the noun is more likely to be lost when the second (subjective, in this case) adjective is reached.” -- So is the idea that the listener is just left with the two adjectives and no noun? Why does that lead to the correct order of noun-less_subjective_adj-more_subjective_adj, from a communicative standpoint?