LING 696B: Categorical perception, perceptual magnets and neural nets

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LING 696B: Categorical perception, perceptual magnets and neural nets

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From last time: quick overview of phonological acquisition Prenatal to newborn

4-day-old French babies prefer listening to French over Russian (Mehler et al, 1988)

Prepared to learn any phonetic contrast in human languages (Eimas, 71)

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A quick overview of phonological acquisition 6 months: Effect of experience

begin to surface (Kuhl, 92)

6 - 12 months: from a universal perceiver to a language-specific one (Werker & Tees, 84)

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A quick overview of phonological acquisition 6 - 9 months: knows the sequential

patterns of their language English v.s. Dutch (Jusczyk, 93)

“avoid” v.s. “waardig” Weird English v.s. better English

(Jusczyk, 94) “mim” v.s. “thob”

Impossible Dutch v.s. Dutch (Friederici, 93)

“bref” v.s. “febr”

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A quick overview of phonological acquisition 6 months: segment words out of

speech stream based on transition probabilities (Saffran et al, 96) pabikutibudogolatupabikudaropi…

8 months: remembering words heard in stories read to them by graduate students (Jusczyk and Hohne, 97)

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A quick overview of phonological acquisition From 12-18 months and above:

vocabulary growth from 50 words to a “burst” Lexical representation?

Toddlers: learning morpho-phonology Example: U-shaped curve

went --> goed --> wented/went

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Next few weeks: learning phonological categories The innovation of phonological structure

requires us to think of the system of vocalizations as combinatorial, in that the concatenation of inherently meaningless phonological units leads to an intrinsically unlimited class of words ... It is a way of systematizing existing vocabulary items and being about to create new ones.

-- Ray Jackendoff (also citing C. Hockett in “Foundations of Language”)

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Categorical perception Categorization

Discrimination

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Eimas et al (1971) Enduring results: tiny (1-4 month)

babies can hear almost anything Stimuli: 3 pairs along the /p/-/b/

synthetic continuum, differing in 20ms

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Eimas et al (1971) Babies get

Very excited hearing a change cross the category boundary

Somewhat excited when the change stay within the boundary

Bored when there is no change

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Eimas et al (1971) Their conclusion: [voice] feature

detection is innate But similar things were shown for

Chichillas (Kuhl and Miller, 78) and monkeys (Ramus et al)

So maybe this is a Mammalian aditory system thing…

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Sensitivity to distributions Percetual Magnet effects (Kuhl,

91): tokens near prototypes are harder to discriminate

Perhaps a fancier term is “perceptual space warping”

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Categorical perception v.s. perceptual magnets Gradient effects: Kuhl (91-95) tried

hard to demonstrate these are not experimental errors, but systematic Refererce 1 2 3 4

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Categorical perception v.s. perceptual magnets PM is based on a notion of

perceptual space Higher dimensions Non-category boundaries

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Kuhl et al (1992) American English has /i/, but no /y/ Swedish has /y/, but no /i/ Test whether infants can detect

differences between prototype and neighbors

Percentof treating

as the same

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Kuhl et al (92)’s interpretation Lingustic experience changes

perception of native and non-native sounds (also see Werker & Tees, 84)

Influence of input starts before any phonemic contrast is learned

Information stored as prototypes

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Modeling attempt: Guenther and Gjaja (96) Claim: CP/PM is a matter of

auditory cortex, and does not have to involve higher-level cognition

Methodology: build a connectionist model inspired by neurons

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Self-organizing map in Guenther and Gjaja Input coding:

So for each (F1,F2) pair, use 4 input nodes This seems to be an artifact of the

mechanism (with regard to scaling), but a standard practice in the field

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Self-organizing map in Guenther and Gjaja

mj : activation

Connection weights

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Self-organizing map: learning stage

mj : activation

Connection weights:initialized to be random

Learning rule: mismatch

activationupdate

Learning rate

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Self-organizing map: learning stage Crucially, only update connections

to the most active N cells The “inhibitory connection”

N goes down to 1 over time Intuition: each cell selectively

encodes certain kind of input. Otherwise the weights are pulled in different directions

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Self-organizing map: testing stage Population vector: take a weighted sum

of individual votes

Inspired by neural firing patterns in monkey reaching

How to compute Fvote? X+, X- must point to the same direction as Z+,

Z-

Algebra exercise: derive a formula to calculate Fvote (homework Problem 1)

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The distributin of Fvote after learning

Trainining stimuli Distribution of Fvote

Recall: activation

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Results shown in the paper

Kuhl

Their model

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Results shown in the paper

With some choice of parameters to fit the“percent generalization”

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Local summary Captures a type of pre-linguistic /

pre-lexical learning from distributions (next time) Distribution learning can

happen in a short time (Maye&Gerken, 00)

G&G: No need to have categories in order to get PM effects Also see Lacerda (95)’s exemplar model

Levels of view: cognition or cortex Maybe Guenther is right …

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Categorization / discrimination training (Guenther et al, 99)

1. Space the stimuli according to JND

2. Test whether they can hear the distinctions in control and training regions

3. TRAIN in some way(45 minutes!)

4. Test again as in 2.

Band-passed white noise

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Guenther et al, 99 Categorization training:

Tell people that sounds from the training region belong to a “prototype”

Present them sounds from training region and band-edges, ask whether it’s prototype

Discrimination training: People say “same” or “different”, and get

feedback Made harder by tighter spacing over time

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Guenther et al, 99 Result of distribution learning

depends on what people do with it

control

training

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Guenther’s neural story for this effect Propose to modify G&G’s

architecture to simulate effects of different training procedure

Did some brain scanto verify the hypothesis(Guenther et al, 04)

New model forthcoming?

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Guenther’s neural story for this effect Propose to modify G&G’s

architecture to simulate effects of different training procedure

Did some brain scanto verify the hypothesis(Guenther et al, 04)

New model forthcoming?(A+ guaranteed if you turn one in)

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The untold story of Guenther and Gjaja Size of model matters a lot

Larger models give more flexibility, but no free lunch: Take longer to learn Must tune the learning rate parameter Must tune the activation neighborhood

100 cells 500 cells 1500 cells

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Randomness in the outcome This is

perhaps the nicest

Some other runs

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A technical view of G&G’s model “Self-organization”: a type of

unsupervised learning Receive input with no information on

which categories they belong Also referred to as “clustering” (next

time) “Emergent behavior”: spatial input

patterns coded connection weights that realize the non-linear mapping

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A technical view of G&G’s model A non-parametric approximation to

the input-percept non-linear mapping Lots of parameters, but individually do

not correspond to categories Will look at a parametric approach to

clustering next time Difficulties: tuning of parameters,

rates of convergence, formal analysis (more later)

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Other questions for G&G If G&G is a model of auditory cortex,

then where do F1 and F2 come from? (see Adam’s presentation)

What if we expose G&G to noisy data? How does it deal with

speech segmentation? More next time.

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Homework problems related to perceptual magnets Problem 2: warping in one dimension

predicted by perceptual magnets

Problem 3: program a simplified G&G type of model or any other SOM to simulate the effect shown above

Before Training data After?

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Commercial:CogSci colloquium this year Many big names in connectionism

this semester

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A digression to the history of neural nets 40’s -- study of neurons (Hebb,

Huxley&Hodgin) 50’s -- self-programming

computers, biological inspirations ADALINE from Stanford (Widrow &

Hoff) Perceptron (Rosenblatt, 60)

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Perceptron

Input: x1, …, xn

Output: {0, 1} Weights: w1,

…,wn

Bias: a How it works:

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What can perceptrons do? A linear machine: finding a plane

that separates the 0 examples from 1 examples

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Perceptron learning rule Start with random weights Take an input, check if the output,

when there is an error weight = weight + a*input*error bias = bias + a*error

Repeat until no more error Recall G&G learning rule See demo

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Criticism from traditional AI(Minsky & Papert, 69) Simple perceptron not capable of

learning simple boolean functions More sophisticated machines hard

to understand Example: XOR (see demo)

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Revitalization of neural nets: connectionism Minsky and Papert’s book stopped

the work on neural nets for 10 years …

But as computer gets faster and cheaper,

CMU parallel distributed processing (PDP) group

UC San Diego institute of cognitive science

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Networks get complicated: more layers 3 layer perceptron can solve the

XOR problem

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Networks get complicated: combining non-linearities Decision surface can be non-linear

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Networks get complicated: more connections Bi-directional Inhibitory Feedback loops

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Key to the revitalization of connectionism Back-propagation algorithm that can be

used to train a variety of networks Variants developed for other

architectureserror

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Two kinds of learning with neural nets Supervised

Classification: patterns --> {1,…,N} Adaptive control: control variables -->

observed measurements Time series prediction: past events -->

future events Unsupervised

Clustering Compression / feature extraction

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Statistical insights from the neural nets Overtraining / early-stopping Local maxima Model complexity -- training error

tradeoff Limits of learning: generalization

bounds Dimension reduction, feature

selection Many of these problems become

standard topics in machine learning

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Big question: neural nets and symbolic computing Grammar: harmony theory

(Smolensky, and later Optimality Theory)

Representation: Can neural nets discovery phonemes?

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Next week Reading will be posted on the

course webpage