Author Archives: Joe Pater

Handouts on ties in HS

The handouts on ties by John McCarthy and Kathryn Pruitt linked from the OT-Help 2 manual on p. 11 are now available from these links (the links in the manual are dead):

http://blogs.umass.edu/comphon/files/2019/09/Knotty-ties.pdf

http://blogs.umass.edu/comphon/files/2019/09/Ties-in-HS.pdf

http://blogs.umass.edu/comphon/files/2019/09/Remark-on-ties-in-HS.pdf

http://blogs.umass.edu/comphon/files/2019/09/Further-thoughts-on-ties.pdf

Did Frank Rosenblatt invent deep learning in 1962?

Deep learning (Le Cun et al. 2015: Nature) involves training neural networks with hidden layers, sometimes many levels deep. Frank Rosenblatt (1928-1971) is widely acknowledged as a pioneer in the training of neural networks, especially for his development of the perceptron update rule, a provably convergent procedure for training single layer feedforward networks. He is less widely acknowledged for his pioneering work with other network architectures, including multi-layer perceptrons, and models with connections “backwards” through the layers, as in recurrent neural nets. A colleague of Rosenblatt’s who prefers to remain anonymous points out that his “C-system” may even be a precursor to deep learning with convolutional networks (see esp. Rosenblatt 1967). Research on a range of perceptron architectures was presented in his 1962 book Principles of Neurodynamics, which was widely read by his contemporaries, and also by the next generation of neural network pioneers, who published the groundbreaking research of the 1980s. A useful concise overview of the work that Rosenblatt and his research group did can be found in Nagy (1991) (see also Tappert 2017). Useful accounts of the broader historical context can be found in Nilsson (2010) and Olazaran (1993, 1996).

In interviews, Yann Le Cun has noted the influence of Rosenblatt’s work, so I was surprised to find no citation of Rosenblatt (1962) in the Nature deep learning paper – it cites only Rosenblatt 1957, which has only single-layer nets. I was even more surprised to find perceptrons classified as single-layer architectures in Goodfellow et al.’s (2016) deep learning text (pp. 14-15, 27). Rosenblatt clearly regarded the single-layer model as just one kind of perceptron. The lack of citation for his work with multi-layer perceptrons seems to be quite widespread. Marcus’ (2012) New Yorker piece on deep learning classifies perceptrons as single-layer only, as does Wang and Raj’s (2017) history of deep learning. My reading of the current machine learning literature, and discussion with researchers in that area, suggests that the term “perceptron” is often taken to mean a single layer feedforward net.

I can think of three reasons that Rosenblatt’s work is sometimes not cited, and even miscited. The first is that Minsky and Papert’s (1969/1988) book is an analysis of single-layer perceptrons, and adopts the convention of referring to them as simply as perceptrons. The second is that the perceptron update rule is widely used under that name, and it applies only to single layer networks. The last is that Rosenblatt and his contemporaries were not very successful in their attempts at training multi-layer perceptrons. See Olazaran (1993, 1996) for in-depth discussion of the complicated and usually oversimplified history around the loss of interest in perceptrons in the later 1960s, and the subsequent development of backpropagation for the training of multilayer nets and resurgence of interest in the 1980s.

As for my question about whether Rosenblatt invented deep learning, that would depend on how one defines deep learning, and what one means by invention in this context. Tappert (2017), a student of Rosenblatt’s, makes a compelling case for naming him the father of deep learning based on an examination of the types of perceptron he was exploring, and comparison with modern practice. In the end, I’m less concerned with what we should call Rosenblatt with respect to deep learning, and more concerned with his work on multi-layer perceptrons and other architectures being cited appropriately and accurately. As an outsider to this field, I may well be making mistakes myself, and I would welcome any corrections.

Update August 25 2017: See Schmidhuber (2015) for an exhaustive technical history of Deep Learning. This is very useful, but it doesn’t look to me like he is appropriately citing Rosenblatt: see secs. 5.1 through 5.3. (as well as the refs. above, see Rosenblatt 1964 on the on the cat vision experiments).

Non-web available reference (ask me for a copy)

Olazaran, Mikel. 1993. A Sociological History of the Neural Network Controversy. Advances in Computers Vol. 37. Academic Press, Boston.

Slides

Tappert, Charles. 2017. Who is the father of deep learning? Slides from a presentation May 5th 2017 at PACE University, downloaded June 15th from the conference site.

Rosenblatt, with the image sensor of the Mark I Perceptron (Source: Arvin Calspan Advanced Technology Center; Hecht-Nielsen, R. Neurocomputing (Reading, Mass.: Addison-Wesley, 1990).)

The Mark 1 Perceptron (Source: Arvin Calspan Advanced Technology Center; Hecht-Nielsen, R. Neurocomputing (Reading, Mass.: Addison-Wesley, 1990).)

Conference on Computational Approaches to Linguistics?

A group of us have recently been discussing the possibility of a new conference on computational approaches to linguistics (group=Rajesh Bhatt, Brian Dillon, Gaja Jarosz, Giorgio Magri, Claire Moore-Cantwell, Joe Pater, Brian Smith, and Kristine Yu). We’ll provide some of the content of that discussion in a moment (we=Gaja and Joe), but the main question we’d like to get on the table is where the first meeting of that conference should be held. It’s so far agreed that it should be co-located with some other event to increase participation (at least for the first meeting), and the end of 2017 / beginning 2018 seems like the right time to do it. The ideas currently under discussion are:

  1. In conjunction with the Annual Meeting on Phonology in New York in early fall 2017. (We haven’t approached the organizers about this).
  2. In conjunction with a one-time workshop on computational modeling of language planned for fall of 2017 at UMass (invited speakers, pending funding, include Jacob Andreas, Emily Bender, Sam Bowman, Chris Dyer, Jason Eisner, Bob Frank, Matt Goldrick, Sharon Goldwater, and Paul Smolensky).
  3. As a “Sister Society” at the LSA general meeting 4-7 January in Salt Lake City (we have had preliminary discussions with the LSA and this seems very straightforward)

We’d very much appreciate your thoughts on the location or the substance of the conference as comments below, or use this google form to give a non-public response.

The original idea was to start a computational phonology conference, inspired by the success of the informal meetings that we’ve had as the North East Computational Phonology Circle, and by the central place that computational work has in phonology these days. But Giorgio pointed out that a broader meeting might well be of interest, and we seem to have come to a consensus that he’s likely right. It doesn’t seem like there is a general venue for computational linguistics of the non-engineering-focused kind, though we are aware of successful workshops that have been held at the ACL and elsewhere (e.g. Sigmorphon, MOL, CMCL). These workshops are in fact also part of the inspiration for this; however, the conference we envision would be broader in scope and co-located with a major linguistics conference to attract as many linguists as possible, minimize costs, and minimize additional conference travel.

We still think that a core contingent might well be the computational phonologists, especially at first, so we still think co-locating it with AMP might make sense (plus NYC is a good location). We’ve also had suggestions that we might in some years co-locate with other conferences, like NELS – the location of future meetings is something we could discuss in person at the first one.

We also seem to have come to a current consensus that we’d like to have reviewed short papers in the CS / CogSci tradition. This is an extremely efficient way to get research out. The one worry that was expressed was that this may create a barrier to later journal publication, but at least two journals with explicit policies on this (Cognitive Science and Phonology) allow publication of elaborated versions of earlier published conference papers.

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What’s Harmony?

From an e-mail from Paul Smolensky, March 28, 2015. Even though he wasn’t doing phonology in the mid-1980’s when he coined the term “Harmony Theory”, Paul had apparently taken a course on phonology with Jorge Hankamer and found vowel harmony fascinating.

 “Harmony” in “Harmony Theory” arises from the fact that the Harmony function is a measure of *compatibility*; the particular word was inspired by vowel harmony, and by the letter ‘H’ which is used in physics for the Hamiltonian or energy function, which plays in statistical mechanics the same mathematical role that the Harmony function plays in Harmony theory: i.e., the function F such that prob(x) = k*exp(F(x)/T).
(Although I took the liberty of changing the sign of the function; in physics, it’s p(x) = k*exp(–H(x)/T), in Harmony Theory, it’s p(x) = k*exp(H(x)/T). That’s because it drove me crazy working in statistical mechanics that that minus sign kept coming and going and coming and going from equation to equation, leading to countless errors; I just dispensed with it at the outset and cut all that nonsense off at the pass.)
From an e-mail from Mark Johnson Jan. 16th, 2016:
I always thought the reason why the physicists had a minus sign in the exponential was that otherwise temperatures would have to be negative.  But I guess you can push the negation into the Hamiltonian, which is perhaps what Paul did.
From an e-mail from Paul Smolensky, Feb. 10th, 2016:
Yes, that’s just what I did. Instead of minimizing badness I switched to maximizing goodness. I’m just that kind of guy.
From an e-mail from Mark Johnson, Feb. 10th, 2016:

Probabilities are never greater than one, so log probabilities are always less than or equal to zero.  So a negative log likelihood is always a positive quantity, and smaller negative log likelihood values are associated with more likely outcomes.  So one way to understand the minus sign in the Gibbs-Boltzmann distribution is that it makes H(x) correspond to a negative log likelihood.

But I think one can give a more detailed explanation.

In a Gibbs-Boltzmann distribution p(x) = k*exp(–H(x)/T), H(x) is the energy of a configuration x.

Because energies H(x) are non-negative (which follows from the definition of energy?), and given a couple of other assumptions (e.g., that there are an infinite number of configurations and energies are unbounded — maybe other assumptions will do?), it follows that probability must decrease with energy, otherwise the inverse partition function k would not exist (i.e., the probability distribution p(x) would not sum to 1).

So if the minus sign were not there, the temperature T (which relates energy and probability) would need to be negative.  There’s no mathematical reason why we couldn’t allow negative temperatures, but the minus sign makes the factor T in the formula correspond much closer with our conventional understanding of temperature.

In fact, I think it is amazing that the constant T in the Gibbs-Boltzmann formula denotes exactly the pre-statistical mechanics concept of temperature (well, absolute temperature in Kelvin).  In many other domains there’s a complex relationship between a physical quantity and our perception of it; what is the chance of a simple linear relationship like this for temperature?

But perhaps it’s not a huge coincidence.  Often our perceptual quantities are logarithmically related to physical quantities, so perhaps its no accident that T is inside the exp() rather than outside (where it would show up as an “exponential temperature” term).  And the concept of temperature we had before Gibbs and Boltzmann wasn’t just a naive perception of warmth; there had been several centuries of careful empirical work on properties of gases, heat engines, etc., which presumably lead scientists to the right notion of temperature well before the Gibbs-Boltzmann relationship was discovered.

From an e-mail from Paul Smolensky March 27, 2016:
Here are some quick thoughts.
0. Energy E in physics is positive. That’s what forces the minus sign in p(x) \propto exp(—E(x)/T), as Mark observes.

Assuming x ranges over an infinite state space, the probability distribution can only be normalized to sum to one if the exponent approaches zero as x -> infinity, and if E(x) > 0 and T > 0, this can only happen if E(x) -> infinity as x -> infinity and we have the minus sign in the exponent.

1. Why is physical E > 0?

2. Perhaps the most fundamental property of E is that it is conserved: E(x(t)) = constant, as the state of an isolated physical system x(t) evolves in time t. From that point of view there’s no reason that E > 0; any constant value would do.

3. For a mechanical system, E = K + V, the sum of the kinetic energy K derived from the motion of the massive bodies in the system and the potential energy V. Given Newton’s second law, F = ma = m dv/dt, E is conserved when F = — grad V and K = mv^2/2

then dE/dt = d(mv(t)^2/2)/dt + dV(x(t))/dt = mv dv/dt + dx/dt . grad V = v(ma) + v(—F) = 0; that’s where the — sign in —grad V comes from.

Everything in the equation E = K + V could be inverted, multiplied by —1, without change in the conservation law. But the commonsense meaning of “energy” is something that should increase with v, hence K = mv^2/2 rather than —mv^2/2.

4. Although K = mv^2/2 > 0, V is often negative.

E.g., for the gravitational force centered at x = 0, F(x) = —GmM x/|x|^3  = —grad V if V(x) = —GmM/|x| < 0
(any constant c can be added to this definition of V without consequence; but even so, for sufficiently small x, V(x) < 0)
Qualitatively: gravitational force is attractive, directed to the origin in this case, and this force is —grad V, so grad V must point away from the origin, so V must increase as x increases, i.e., must decrease as x decreases. V must fall as 1/|x| in order for F to fall as 1/|x|^2 so the decrease in V as x —> 0 must take V to minus infinity.

5. In the cognitive context, it’s not clear there’s anything corresponding to the kinetic energy of massive bodies. So it’s not clear there’s anything to fix a part of E to be positive; flipping E by multiplication by —1 doesn’t seem to violate any intuitions. Then, assuming we keep T > 0, we can (must) drop the — in p(x) \propto exp(—E(x)/T) = exp(H(x)/T) where we define Harmony as H = —E. Now the probability of x increases with H(x); lower H is avoided, hence higher H is “better”, hence the commonsense meaning of “Harmony” has the right polarity.

E-mail from Mark Johnson March 27, 2016

Very nice!  I was thinking about kinetic energy, but yes, potential energy (such as gravitational energy) is typically conceived as negative (I remember my high school physics class, where we thought of gravitational fields as “wells”).  I never thought about how this is forced once kinetic energy is positive.

Continuing in this vein, there are a couple of other obvious questions once one thinks about the relationship between Harmony theory and exponential models in physics.

For example, does the temperature T have any cognitive interpretation?  That is, is there some macroscopic property of a cognitive system that T represents?

More generally, in statistical mechanics the number (or more precisely, the density) of possible states or configurations varies as a function of their energy, and there are so many more higher energy states than lower energy ones that the typical or expected value of a physical quantity like pressure is not that of the more probable low energy states, but instead determined by the more numerous, less probable higher energy states.

I’d be extremely interested to hear if Paul knows of any cases where this or something like it occurs in cognitive science.  I’ve been looking for convincing cases ever since I got interested in Bayesian learning!  The one case I know of has to do with “sparse Dirichlet priors”, and it’s not exactly overwhelming.

E-mail from Paul Smolensky, March 27, 2016

The absolute magnitude of T has no significance unless the absolute magnitude of H does, which I doubt. So I’d take Mark’s question about T to come down to something like: what’s the cognitive significance of T —> 0 or T —> infinity or T ~ O(1)?

And I’d look for answers in terms of the cognitive role of different types of inference. T —> 0 gives maximum-likelihood inference; T —> infinity gives uniform sampling; T ~ O(1) gives sampling from the distribution exp(H(x)).  Mark, you’re in a better position to interpret the cognitive significance of such inference patterns.

As for the question of density of states of different Harmony/energy, the (log) density of states is essentially the entropy, so any cognitive significance entropy may have — e.g., entropy reduction as predictor of incremental sentence processing difficulty à la Hale — qualifies as cognitive relevance of density of states. As for the average value of a quantity reflecting less-probable-but-more-numerous states more than more-probable states, I’m not sure what the cognitive significance of average values is in general.

Worst abstract review ever

“No data, yet combines two or more of the worst phonological theories, resulting in an account that is far more complicated and assumption-laden than the simple if typologically odd pseudo-example given.”

I received this review on an abstract I submitted recently. I’ve gotten plenty of bad reviews in the sense of them being negative, but I’ve never gotten one that was so unprofessional, and that made it so clear that the reviewer hadn’t engaged with the abstract in anything but the most superficial fashion. Because I didn’t think this reviewer was doing their job, I was moved to complain about it. I did so as follows:

“I’ve never complained about a conference review before, but this is one’s beyond the pale. I don’t want you to do anything about it, but I had to tell you I’m pretty shocked by it.”

The conference organizer reported that the program committee agreed that the review was unprofessional, and that this reviewer, along with another who had engaged in “soapboxing or axe-grinding”, would not be included in the list of reviewers passed on to the next year’s organizer.

I was pleased with this outcome, and I thought I’d tell this story because this seemed like a good way of improving the quality of reviewer pools that others might usefully adopt. I’d also be happy if this contributed to a general discussion of what the expectations are for reviews, and how we can make them better.

Moreton, Pater and Pertsova in Cognitive Science

The nearly final version of our Phonological Concept Learning paper, to appear in Cognitive Science, is now available here. The abstract is below, and we very much welcome further discussion, either by e-mail to the authors (addresses on the first page of the paper), or as comments to this post.

Abstract.

Linguistic and non-linguistic pattern learning have been studied separately, but we argue for a com- parative approach. Analogous inductive problems arise in phonological and visual pattern learning. Evidence from three experiments shows that human learners can solve them in analogous ways, and that human performance in both cases can be captured by the same models.

We test GMECCS, an implementation of the Configural Cue Model (Gluck & Bower, 1988a) in a Maximum Entropy phonotactic-learning framework (Goldwater & Johnson, 2003; Hayes & Wilson, 2008) with a single free parameter, against the alternative hypothesis that learners seek featurally- simple algebraic rules (“rule-seeking”). We study the full typology of patterns introduced by Shepard, Hovland, and Jenkins (1961) (“SHJ”), instantiated as both phonotactic patterns and visual analogues, using unsupervised training.

Unlike SHJ, Experiments 1 and 2 found that both phonotactic and visual patterns that depended on fewer features could be more difficult than those that depended on more features, as predicted by GMECCS but not by rule-seeking. GMECCS also correctly predicted performance differences between stimulus subclasses within each pattern. A third experiment tried supervised training (which can fa- cilitate rule-seeking in visual learning) to elicit simple-rule-seeking phonotactic learning, but cue-based behavior persisted.

We conclude that similar cue-based cognitive processes are available for phonological and visual concept learning, and hence that studying either kind of learning can lead to significant insights about the other.

Calamaro and Jarosz on Synthetic Learner blog

On the Synthetic Learner blog, Emmanuel Dupoux recently posted some comments on a paper co-authored by Gaja Jarosz and Shira Calamaro that recently appeared in Cognitive Science. Gaja has also written a reply. While you are there, take a peek around the blog, and the Bootphon website: Dupoux has a big and very interesting project on unsupervised learning of words and phonological categories from the speech stream.

Wellformedness = probability?

There are some old arguments against probabilistic models as models of language, but these do not seem to have much force anymore, especially because we now have models that can compute probabilities over the same representations that we use in generative linguistics (Andries Coetzee and I have an overview of probabilistic models of phonology in our Handbook chapter, Mark Johnson has a nice explanation of the development of MaxEnt models and how they differ from PCFG’s as well as other useful material on probabilistic models as models of language learning, Steve Abney has a provocative and useful piece about how the goals of statistical computational linguistics can be seen as the goals of generative linguistics; see more broadly the recent debate between Chomsky and Peter Norvig on probabilistic approaches to AI; see also the Probabilistic Linguistics book and Charles Yang’s review).

That’s not to say that there can’t be issues in formalizing probabilistic models of language. In a paper to appear in Phonology (available here) Robert Daland discusses issues that can arise in defining a probability distribution over the infinite set of possible words, in particular with Hayes and Wilson’s (2008) MaxEnt phonotactic grammar model. In the general case, for this to succeed, the probability of strings of increasing length must decrease sharply enough such that the sum of their probabilities never exceeds 1, and simply continues to approach it. Daland defines the conditions under which this will obtain in the Hayes and Wilson model in terms of the requirements on the weight of a *Struc constraint that assigns a penalty that increases as string length increases.

In the question period after Robert’s presentation of this material at the GLOW computational phonology workshop in Paris in April, Jeff Heinz raised an objection against the general notion of formalizing well-formedness in terms of probabilities, and he repeated this argument at the Manchester fringe workshop last week. Here’s my reconstruction of it (hopefully Jeff will correct me if I get it wrong – I also don’t have the references to the earlier work that made this argument). Take a (relatively) ill-formed short string. Give it some probability. Now take a (relatively) well-formed string. Give it some probability. Now concatenate the well-formed string enough times until the whole thing has probability lower than the ill-formed string, which it eventually will.

This is meant to be a paradox for the view that we can formalize well-formedness in terms of probabilities: the long well-formed string has probability lower than the short ill-formed string. It’s not clear to me, however, that there is a problem (and it wasn’t clear to Robert Daland either – the question period discussion lasted well into lunch, with Ewan Dunbar taking up Jeff’s position at our end of the table). Notice that Jeff’s argument is making an empirical claim that the concatenation of the well-formed strings does not result in a well-formedness decrease. When I talked to him last week, he claimed that this is clearer in syntax than phonology. Robert’s position (which I agree with) is that it likely does – though from his review of the literature on phonotactic well-formedness judgments we don’t seem to have empirical data on this point.

Robert asked us to work with him in designing the experiment, and at the time I wasn’t sure that this was the best use of our lunch time, but I think he has a point. If this is in fact an empirical issue, and we can agree beforehand on how to test it, then this would save a lot of time compared with the usual process of the advocates of one position designing an experiment, which even if it turns out the way they hope, can then be criticized by the advocates of the other position as not having operationalized their claim properly, and so on…

It’s also of course possible that this is not an empirical issue: that there is a concept of perfect well-formedness that probabilistic models cannot capture. This reminds me of a comment on a talk I got once from a prominent syntactician when I discussed probabilistic models that can give probability vanishingly close to zero to ill-formed structures: “but there are sentences that I judge as completely out for English – they should have probability zero”. My response was to simply repeat the phrase vanishingly close to zero, and check to make sure he knew what I meant.

Representations in OT

I’ve recently had some useful discussion with people about the nature of representations in OT, and how they did or did not (or should or should not) change from a theory with inviolable constraints (= principles and parameters theory). I’d like to summarize my thoughts, and would very much welcome further discussion.

In our discussion following Tobias Scheer’s mfm fringe presentation, I brought up the point that when one switches to violable constraints, it’s not obvious that the representations should stay the same. Tobias asked for an example, and I didn’t have a good one right away, but then realized that a particularly clear and worked out one is in the discussion of extrametricality vs. nonfinality in Prince and Smolensky 1993/2004. Gaja Jarosz also reminded me of underspecification: since markedness is expressed in output constraints in OT, it’s not obvious that one also requires a theory of input underspecification for that purpose.

I think my own experience of working on my *NC project in the mid nineties illustrates some more aspects of what happened to representations as OT was being extended to segmental phonology, and brings up some further issues. When I started that project, I was looking for an explanation for the facts in terms of feature markedness and positional licensing. I wanted to get the directionality of postnasal voicing, which unlike most other local assimilation processes is L-to-R, instead R-to-L. I also wanted to get conspiracies amongst processes that resolve nasal-voiceless obstruent clusters. I tried hard and failed, and eventually “gave up” and used the formally stipulative but phonetically grounded *NC constraint. I later realized that this failure was part of a more general issue: it doesn’t seem to be the case that positional markedness can always be derived from the combination of general context-free markedness constraints and general positional licensing constraints. The best I could do in terms of those assumptions was to say that the coda nasal [voice] wanted to be licensed in onset position and hence spread, but that didn’t explain why it was just nasals that did this, nor did it deal sufficiently well with directionality. I have some more discussion of the general problems with deriving positional markedness from prosodic licensing, and further references, in a discussion of local conjunction on p. 10 of this paper (also in my review of the Harmonic Mind).

Taking the approach to segmental phonology in the *NC proposal, we can ask what that commits us to in terms of a theory of representations. It looks to me like what we would need is a feature set that is sufficiently expressive to formalize our constraints, but that’s it. Phonetic grounding is expressed as restrictions on the universal set of constraints (or as restrictions on possible rankings, in work like Steriade’s on perceptual grounding). And this set of features could be universal, with no language-specific choices (thanks to Pavel Iosad for a question on this) – contrast and its absence can be captured by ranking alone. Furthermore, I don’t think there is any sense in which this theory has the concept of a natural class (thanks to Kristine Yu for a question on that). So this perhaps at least partially explains why the nature of segmental representations has not been a big topic in at least some variants of OT.

Now I should say that I can see lots of reasons why you would want to say that features do differ from language to language, and why the particular feature set you choose could have consequences for predictions about learning and generalization. But in terms of the particular theory I’ve just described, I don’t see any arguments for language-specific differences in feature specification. I should probably also say that I see reasons why one might not want to model the role of phonetics in phonology as just stipulations about the constraint set with some armchair phonetic justification – there are clearly plenty of alternatives. But the proposal is a natural extension to general approach to encoding of substance in OT as stipulations about constraints: e.g. that there is Onset and NoCoda, but not NoOnset and Coda.

Finally, let me emphasize that what I’ve said about a lack of interest in the nature of segmental representations based on my *NC work should not be taken as representative of a lack of interest in segmental features in OT as a whole (or even in my mind!). For example, there are extremely interesting questions about the nature of the representations needed for `spreading’: Bakovic (2000: diss.) takes the position that there is no spreading, while others have defended autosegmental representations or adopted gestural representations, and yet others (e.g. Cole and Kisseberth) have proposed domain-based representations.