On the learnability of saltatory phonological alternations
James White
Department of Linguistics, UCLA
jameswhite@ucla.edu
1. Background and research questions
2. Case study: Saltatory alternations
•
•
Saltatory alternation: An alternation in which an
intermediate non-alternating sound is “jumped
over.”
•
E.g. Campidanian Sardinian:[6]
How do people learn the phonological alternations of their
language?
•
o
Is phonological learning the result of an unbiased search
for patterns?[1]
o
Or is learning guided by biases against certain patterns?
o
What types of patterns are dispreferred by learners?
o
What is the nature of these biases?
o
How can we account for them in learning models?
•
/pani/ 
[sːu βãi] ‘the bread’
/binu/ 
[sːu bĩu] ‘the wine’
2 feature
changes
p
b
β
-continuant
-continuant
+continuant
-voice
+voice
+voice
+labial
+labial
+labial
1 feature
1 feature
difference
difference
Why are they interesting?
Acknowledgments
o  Relatively uncommon.
o  It has long been argued that alternations between more similar sounds are
Much of the recent literature supports a soft bias approach:
certain patterns are dispreferred, but may be learned given
enough input.[2-5]
better than alternations between less similar.[7-8]
o  Accounting for them is not theoretically straightforward (e.g., classical
OT[9] cannot).
I would like to thank Bruce Hayes, Megha Sundara, Robert Daland, Kie Zuraw, Sharon
Peperkamp, Marc Garellek, Karen Campbell, Adam Albright, Jennifer Cole, audiences
at the UCLA phonology seminar and LSA, and anonymous LabPhon reviewers for
helpful comments on this project.
I would also like to thank undergraduate research assistants who have worked on
parts of this project: Kelly Ryan, Kelly Nakawatase, Ariel Quist, Emily Ho, Sarah Yiu,
Ben Longwill, and Maria Manukyan.
Any remaining errors are my own.
This work was funded in part by a UCLA Summer mentorship fellowship.
3. The experiments: Are learners biased against saltatory alternations?
Results in generalization phase
Method
Artificial language learning paradigm
--Repeat Exposure/Verification until 80% accuracy--
•
Participants: 20 UCLA undergrads per experiment.
o
Training input summary:
•
Exposure: Learn alternations by hearing pairs of
nonwords with a singular and plural picture.
o
Exp 1: Ambiguous
p
f
...
[kamap]
[kamavi]
How can we account for the dispreferred status, but
ultimate learnability, of saltatory alternations?
•
I use Maximum entropy grammar models.[10]
•
Implemented using the Maxent Grammar Tool (from Bruce
Hayes’s webpage).
•
Provide model:
•
•
•
v
f
b
p
v
f
p
v
b
f
v
Also included: analogous coronals [t, d, θ, ð].
5. The models
I. Traditional faithfulness[9], Unbiased
Faithfulness constraints:
IDENT(voice), IDENT(cont), IDENT(son)
For each input form, a set of candidates and the
observed probability of each candidate winning
Flat prior: For all constraints, µ = 0, σ2 = 0.5
o
A set of constraints and violations
Exp 2
60
40
20
0
•  Untrained sounds: Ps change intermediate sounds
when ambiguously saltatory (Exp 1) much more than
they do untrained non-intermediate sounds (Exp 2).
= dispreference for saltatory alternations!
Faithfulness constraints:
More expressive *MAP constraints[11]
for every pair of sounds
Overall r2 = .51
Exp 1
80
= how tightly a constraint weight is constrained
to its µ during learning
60
40
40
40
Training data: Same as experimental participants received.
0
o
Constraint weights
o
For each input form, the predicted probability of each
candidate
Same markedness constraints for all models:
o
*V[-voice]V = penalize intervocalic voiceless sounds
o
*V[-continuant]V = penalizes intervocalic stops
Language learners disprefer saltatory alternations, but
they are not unlearnable.
A MaxEnt grammar model can account for both of these
observations, provided that:
o
o
It has a more expressive set of constraints (such as the
*MAP variety).
It has a similarity bias, derived from confusion matrix
data, preferring alternations between similar sounds.
20
20
100
f, θ
✗ Predicts generalization to untrained
sounds in Exp 2
Fillers
b, d
f, θ
Exp 2
p, t
100
100
80
80
60
60
40
40
40
20
20
0
0
Exp 3
p, t
f, θ
100
80
80
60
60
Problem: the
constraint set doesn’t
allow saltation
40
20
0
p, t
Fillers
b, d
Fillers
p, t
f, θ
✓ Able to learn the
saltation!
✗ But doesn’t predict
that it is harder to
learn. Treated
just like
fillers.
40
f, θ
✓ No overgeneralization in Exp 2!
b, d
Fillers
p, t
f, θ
✓ Able to learn the saltation, but
still some errors relative to fillers
(just like participants)!
Exp 3
100
80
60
40
20
20
0
0
f, θ
b, d
0
Exp 3
100
Fillers
20
b, d
✗ Totally unable to learn the saltation
✓ Difference in stops
and fricatives!
Exp 2
60
Fillers
Strikingly good fit,
with no manipulation
of weights by hand!
0
p, t
80
b, d
Intermediate
frics
20
0
Exp 2
Intermediate
stops
Participants learn saltatory alternations, but
they are harder to learn—they continue to
make errors that they don’t make for fillers.
Overall r2 = .95
100
Model output:
Fillers
Exp 1
60
b, d
Trained stops
Similarity bias prior – similar to Steriade’s P-map[8]:
Step 1: Use confusion matrix probabilities[12] as
input to a separate Maxent model with *MAP constraints.
E.g., *MAP(p, v) = Don’t map underlying /p/
Result: *MAP constraints receive weights based on
to surface [v]
confusability; Constraints penalizing more confusable
(i.e., more similar) sounds get lower weights.
E.g., *MAP(b, v) has lower weight than *MAP(p, v).
Flat prior: For all constraints, µ = 0, σ2 = 0.5
Step 2: These weights become preferred weights (µ) in
the main model. For all constraints, σ2 = 0.5.
✗ No difference in stops
vs. fricatives
Fillers
20
Faithfulness constraints: *MAP constraints
80
p, t
40
III. *MAP constraints, Similarity bias
100
•
Exp 4
60
Untrained stops Untrained frics
60
σ2
Exp 3
80
0
Fillers
80
µ = preferred weight for a constraint
100
Final sound of singular word
Overall r2 = .48
Exp 1
Exp 1
100
•
•  Explicitly saltatory cases: some
learning, but a lot more errors than on
fillers, despite training (compare faded
bars to Fillers).
80
II. *MAP constraints, Unbiased
Exp Results
Model Predictions
Best Possible Fit (Model directly
trained on experimental results)
Experiments 3 & 4
•  Preference for
changing
untrained stops
more than
fricatives.
100
Trained stops
Equal number of non-alternating fillers (mostly
sonorants) in training.
E.g. [luman]  [lumani]
A set of input forms
Prior (soft bias), 2 settings for each constraint:
b
•
o
6. Conclusions
•
p
o
o
•
b
Exp 4: Explicit
fricative saltation
Tested in Generalization phase on nonwords ending in
[p, b, f] for each experiment.
e.g. [kamap] ... [kamavi] -or- [kamapi]
•
Exp 3: Explicit
stop saltation
Exp 2: No saltation
•
o  Verification: Tested on subset of exposure pairs.
Participants choose between changing and non-changing •
auditory plural options (order counterbalanced).
4. Modeling overview
•  Trained pattern:
Good generalization
to novel nonwords.
% changing plural option chosen
Procedure – 3 phases:
•
Experiments 1 & 2
Generalization: Same test on novel nonwords,
including some ending in untrained sounds.
% changing plural option chosen
•
p, t
Fillers
b, d
f, θ
p, t
Fillers
b, d
f, θ
7. References
{6] Bolognesi, R. (1998). The phonology of Campidanian Sardinian: A unitary account of self-organizing structure. Holland Academics.
{1] Blevins, J. (2004). Evolutionary phonology: The emergence of sound patterns. Cambridge Univ. Press.
[8] Steriade, D. (2001/2008). The phonology of perceptibility effects: the P-map and its consequences for constraint organization.
[2] Hayes, B., et al. (2009). Natural and unnatural constraints in Hungarian vowel harmony. Language.
[9] Prince, A., & Smolensky, P. (1993/2004). Optimality theory: Constraint interaction in generative grammar. Blackwell.
[3] Hayes, B., & White, J. (in press). Phonological naturalness and phonotactic learning. Linguistic Inquiry.
[10] Hayes, B, & Wilson, C. 2008. A maximum entropy model of phonotactics and phonotactic learning. Linguistic Inquiry.
[4] Wilson, C. (2006). Learning phonology with substantive bias: An experimental and computational study of velar palatalization. Cog. Sci.
[11] Zuraw, K. (2007). The role of phonetic knowledge in phonological patterning: Corpus and survey evidence from Tagalog. Language.
[5] Finley, S., & Badecker, W. (2008). Substantive biases for vowel harmony languages. WCCFL 27.
[12] Wang, M. D., & Bilger, R. C. (1973). Consonant confusions in noise: a study of perceptual features. JASA.
[7] Trubetzkoy, N. S. (1939). Principles of Phonology.
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