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Recursion • Something containing an instance of itself.
Recursion in Language The dog the cat the rat grabbed rode walked down the street. The dog the cat rode walked down the street. The dog walked down the street.
Recursion: “Stack” Memory The dog the cat the rat grabbed rode walked down the street. DOG CAT RAT GRAB RIDE WALK
Recursion: “Stack” Memory The dog the cat the rat grabbed rode walked down the street. GRAB RIDE WALK “Infinite competence…” RAT CAT DOG “Limited performance…”
SRN Simple Recurrent Network (Elman, 1990) • Some ability to use longer contexts • Incremental learning: no looking back • No “rules”: distributed representation
PCFG Probabilistic Context-Free Grammar • Easily handles recursive structure, long-range context • Hierarchical, “rule”-based representation • More computationally complex, non-incremental learning 0.8 0.65 0.35 0.1 … S NP VP N’ AdjP N’ N’ N Adjgreen …
Serial ReactionTime (SRT) Study • Buttons flash in short sequences • “press the button as quickly as possible when it lights up” • Dependent measure: RT • time from light on correct button pressed • Subjects seem to be making sequential predictions RT ∝ P(button|context) also: RT ∝ -log(P(button|context)) (“surprisal”, e.g. Hale, 2001; Levy, 2008)
Training the Humans • Eight subjects per experimental condition • Same sequences, different mappings • Broken into 16 blocks, with breaks • About an hour of button-pressing total • Emphasized speed, while minimizing errors
Training the Models • Trained on exactly the same sequences as the humans, but not fit to human data • Predictions at every point based solely on sequences seen prior to that • Results in sequence of probabilities • correlated with sequence of human RTs, through surprisal (negative log probability)
A Case Study in Recursion: Palindromes A C L Q L C A (Sequences of length 5 through 15; total of 3728 trials per subject)
“Did you notice any patterns?” PCFG PCFG SRN SRN Subjects with no awareness of pattern: “No”, “None”, “Not really” (n=5) Those with explicit awareness of pattern: “Circular pattern”, “Mirror pattern” (n=3) PCFG(explicit task performance) SRN(implicit task performance) Will this replicate?
Implicit, didn't notice (n=8) 0.6 PCFG SRN 0.5 0.4 0.3 Correlation (Surprisal vs RT) 0.2 0.1 0 -0.1 2 4 6 8 10 12 14 16 Block
Differences between individuals? • or actually between modes of processing? • What if we explicitly train subjects on the pattern? • First half implicit, second half explicit
Explicit Training Worksheet “This is the middle button in every sequence (and itonlyoccurs in the middle position, halfway through the sequence): This means that as soon as you see this button, you know that the sequence will start to reverse. Here are some example sequences of various lengths:
And Quiz Sheet “Now, complete these sequences using the same pattern (crossing out any unneeded boxes at the end of a sequence):
Fully explicit from middle (n=8) 0.6 PCFG 0.5 SRN 0.4 0.3 Correlation (Surprisal vs RT) 0.2 0.1 0 -0.1 2 4 6 8 10 12 14 16 Block (explicit instruction given here)
Context-free vs Context-sensitive A A B B C C D D 1 2 2 1 1 2 1 2
Explicit Instruction (after block 4) CFG: CSG:
Methods • Four conditions, with 8 subjects in each • Implicit context-free grammar (CFG) • Implicit context-sensitive grammar (CSG) • Explicit context-free grammar (CFG) • Explicit context-sensitive grammar (CSG) • Total of 640 sequences (4,120 trials) per subject • Sequences of length 4, 6, 8, and 10 • Around 1.5 hours of button-pressing • In blocks 9-16, 5% of the trials were “errors” A1 B1 C1 C2 B2 A2 D2
Blocks 1-4Blocks 5-8Blocks 9-12 (errors thicker)Blocks 13-16 (errors thicker)
** ** ** (6ms) (27ms) (2ms) (11ms) RT (ms)
Conclusions • Explicit/Implicit processing • Implicit performance correlated with the predictions made by an SRN (a connectionist model) • Explicit performance correlated with the predictions made by a PCFG (a rule-based model) • Grammatical complexity • Able to process context-free, recursive structures at a very rapid timescale • More limited ability to process context-sensitive structures
Future Directions • Longer training • More complex grammars • Determinism • Other response measures • EEG: more sensitive than RTs to initial stages of learning • Field studies in Switzerland or Brazil…?
Broader Goals • L2-learning pedagogy
Thankyous! MentorshipJeff ElmanRoger LevyMarta Kutas AdviceMicah Bregman Ben Cipollini Vicente Malave Nathaniel Smith Angela Yu Rachel Mayberry Tom Urbach Andrea, Seana and the 3rd Year Class! Research Assistants Frances Martin (2010) Ryan Cordova (2009) Wai Ho Chiu (2009)
AGL and Language Areas associated with syntax may be involved Bahlmann, Schubotz, and Friederici (2008). Hierarchical artificial grammar processing engages Broca's area. NeuroImage, 42(2):525-534. P600-like effects can be seen in AGL Christiansen, Conway, & Onnis (2007). Neural Responses to Structural Incongruencies in Language and Statistical Learning Point to Similar Underlying Mechanisms. “violations in an artificial grammar can elicit late positivities qualitatively and topographically comparable to the P600 seen with syntactic violations in natural language”
Context-free Grammar The dog the cat the rat grabbed rode walked. S NP VP NP NNP N S N the dogN the catN the rat VP grabbedVP rodeVP walked