| Adam Wayment | |
| 3rd Year Graduate Student | |
| COGNITIVE SCIENCE DEPARTMENT | |
| The Johns Hopkins University | |
| Last updated Jan 18, 2006. |
Contact Info Research Interests Current Research Projects
|
office:
|
245 Krieger Hall |
|
email:
|
wayment@cogsci.jhu.edu |
|
phone:
|
(410)-???-??? |
| I read all email that reaches my inbox. |
(UNDER CONSTRUCTION PLEASE BE PATIENT)
Broadly, I am interested in humans' use of combinatorial symbol systems and their neural instantiation. In particular, I am interested in the best example of a naturally occurring combinatorial symbol system that I know of: human language. It should be clear that language is symbolic since sequences of sound stand for something; that [kæt] means cat and not boy, gerbil, or the color of a California mountain in June, indicates the symbolic nature of sound sequences. While any sound can be symbolic--the chiming of a grandfather clock means a certain time of day has arrived, the whirl of sirens means an emergency vehicle is coming through, etc--only human language sounds are combinatorial. A chime followed by a siren doesn't mean an emergency vehicle is coming by at a certain time of day, nor does it mean that a grandfather clock is about to pass by, so look out! However, when [kæt] is followed by [s] English speakers/hearers take it to mean something like, more than one four-legged, furry, feline, mammal. The "four-legged, furry, feline mammal" part, comes from [kaet] and the "more than one" part comes from the plural marker [s]. In fact, human language is combinatorial at all levels: phonemes combine to form different morphemes, which in turn combine to form words and utterances, which make up sentences and if the symbols combine just right out come jokes, newsreels, and epic poems.
Accepting a connectionist view of the human processing system, I want to know how the combinatorial language system can be instantiated in an artificial neural network. Now, I am not so audacious as to try and get a network to write epic poems, so at present, I am interested in the lowest level of symbols, the phonemes and syllables.
Phonemes: I am interested in understanding the forces at work in the formation of a phonological inventory. Now, from the point of view of symbol systems a phoneme is just a sound symbol: it is the minimal difference by which sounds may differ, but have different meanings. For example, [kæt] differs from [kæp] in meaning so the difference between [t] and [p] is phonemic in English, but [kæt] and [kæÿ] do not differ in meaning so [t] and [ÿ] are not phonemic (though they are phonemic in Hindi).
The first problem for symbols in networks is how can symbols emerge in a continuous acoustic/articulatory space? The acoustics are continuous since the human ear responds to all sounds in the range 2,000 to 20,000 Hz. The articulatory system has more featural dimensions, but it is certainly continuous along the place of articulation. Even doubting that individual speakers have the fine motor control for a truly continuous space, certainly across speakers, there is a continuous variation in vocal tract length, palate height, etc. Well, in summary, I think attraction and Harmony Theory (Smolensky 1986, 2005) has the answer to putting symbols in a continuous space (See Entailment Networks below) but there still remains the question of what is the right space over which phonemes are formed.
Not all phonemes are equal: it is an empirical fact that some phonemes are better than others. "Better" in the sense that they are preferred over other phonemes: they occur more broadly across the languages of the world and are used more frequently with-in languages. Acoustic salience, articulatory simplicity, and acoustic enhancement are all at work in determining why some feature combinations make for better phonemes than others. Using UPSID (Maddieson & Precoda 1989) I am currently working on measuring the forces from the phonological inventory corpus (See Measuring Markedness, below).
The second problem for networks is the constraints.
The third problem is the structure.
The fourth problem is the combinatorics.
By way of tensor algebra, the weights of a fully-connected semetric network may perform computations on fillers and roles whose representations are spread accross the whole network. Right now, I am developing a supervised learning procedure for a real-valued Boltzmann machine that operates on these fully-distributed representations.
When an OT grammar is encoded in a network, are there advantages (in terms of stability and learnability) to encoding a phenomenon via strictly ranked constraints? Right now, I am trying to get at the answer to this question by examing strict rankings from a perspective enriched by game theory:
Constraint Voting Game: Let the constraints be agents in a game, each having a total preference ordering over candidate outputs. Each agent (constraint) gets a weighted vote on the outcome. Strict ranking corresponds to an exponential weighting of the agents voting power. I think (yet can still not iron out the details of a proof) that an intransitive ordering of social preferences may be avoided by a strict ranking of the constraints. Since network states correspond to candidate outputs, an intransitive order would correspond to instability in a network.