Ling 696b categorical perception perceptual magnets and neural nets
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LING 696B: Categorical perception, perceptual magnets and neural nets. 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)

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

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Ling 696b categorical perception perceptual magnets and neural nets

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


From last time quick overview of phonological acquisition

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)


A quick overview of phonological acquisition

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)


A quick overview of phonological acquisition1

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”


A quick overview of phonological acquisition2

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)


A quick overview of phonological acquisition3

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


Next few weeks learning phonological categories

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”)


Categorical perception

Categorical perception

  • Categorization

  • Discrimination


Eimas et al 1971

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


Eimas et al 19711

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


Eimas et al 19712

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…


Sensitivity to distributions

Sensitivity to distributions

  • Percetual Magnet effects (Kuhl, 91): tokens near prototypes are harder to discriminate

  • Perhaps a fancier term is “perceptual space warping”


Categorical perception v s perceptual magnets

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


Categorical perception v s perceptual magnets1

Categorical perception v.s. perceptual magnets

  • PM is based on a notion of perceptual space

    • Higher dimensions

    • Non-category boundaries


Kuhl et al 1992

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

Percent

of treating

as the same


Kuhl et al 92 s interpretation

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


Modeling attempt guenther and gjaja 96

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


Self organizing map in guenther and gjaja

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


Self organizing map in guenther and gjaja1

Self-organizing map in Guenther and Gjaja

mj : activation

Connection weights


Self organizing map learning stage

Self-organizing map: learning stage

mj : activation

Connection weights:initialized to be random

Learning rate

Learning rule:

mismatch

update

activation


Self organizing map learning stage1

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


Self organizing map testing stage

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)


The distributin of f vote after learning

The distributin of Fvote after learning

Distribution of Fvote

Trainining stimuli

Recall: activation


Results shown in the paper

Results shown in the paper

Kuhl

Their model


Results shown in the paper1

Results shown in the paper

With some choice of

parameters to fit the

“percent generalization”


Local summary

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 …


Categorization discrimination training guenther et al 99

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


Guenther et al 99

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


Guenther et al 991

Guenther et al, 99

  • Result of distribution learning depends on what people do with it

control

training


Guenther s neural story for this effect

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?


Guenther s neural story for this effect1

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)


The untold story of guenther and gjaja

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


Randomness in the outcome

Randomness in the outcome

  • This is perhaps the nicest

  • Some other runs


A technical view of g g s model

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


A technical view of g g s model1

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)


Other questions for g g

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 withspeech segmentation?

  • More next time.


Homework problems related to perceptual magnets

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?


Commercial cogsci colloquium this year

Commercial:CogSci colloquium this year

  • Many big names in connectionism this semester


A digression to the history of neural nets

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)


Perceptron

Perceptron

  • Input: x1, …, xn

  • Output: {0, 1}

  • Weights: w1,…,wn

  • Bias: a

  • How it works:


What can perceptrons do

What can perceptrons do?

  • A linear machine: finding a plane that separates the 0 examples from 1 examples


Perceptron learning rule

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


Criticism from traditional ai minsky papert 69

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)


Revitalization of neural nets connectionism

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


Networks get complicated more layers

Networks get complicated: more layers

  • 3 layer perceptron can solve the XOR problem


Networks get complicated combining non linearities

Networks get complicated: combining non-linearities

  • Decision surface can be non-linear


Networks get complicated more connections

Networks get complicated: more connections

  • Bi-directional

  • Inhibitory

  • Feedback loops


Key to the revitalization of connectionism

Key to the revitalization of connectionism

  • Back-propagation algorithm that can be used to train a variety of networks

  • Variants developed for other architectures

error


Two kinds of learning with neural nets

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


Statistical insights from the neural nets

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


Big question neural nets and symbolic computing

Big question: neural nets and symbolic computing

  • Grammar: harmony theory (Smolensky, and later Optimality Theory)

  • Representation: Can neural nets discovery phonemes?


Next week

Next week

  • Reading will be posted on the course webpage


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