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

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

2. 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)

3. 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)

4. 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”

5. 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)

6. 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

7. 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”)

8. Categorical perception • Categorization • Discrimination

9. 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

10. 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

11. 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…

12. Sensitivity to distributions • Percetual Magnet effects (Kuhl, 91): tokens near prototypes are harder to discriminate • Perhaps a fancier term is “perceptual space warping”

13. 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

14. Categorical perception v.s. perceptual magnets • PM is based on a notion of perceptual space • Higher dimensions • Non-category boundaries

15. 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

16. 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

17. 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

18. 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

19. Self-organizing map in Guenther and Gjaja mj : activation Connection weights

20. Self-organizing map: learning stage mj : activation Connection weights:initialized to be random Learning rate Learning rule: mismatch update activation

21. 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

22. 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)

23. The distributin of Fvote after learning Distribution of Fvote Trainining stimuli Recall: activation

24. Results shown in the paper Kuhl Their model

25. Results shown in the paper With some choice of parameters to fit the “percent generalization”

26. 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 …

27. 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

28. 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

29. Guenther et al, 99 • Result of distribution learning depends on what people do with it control training

30. 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?

31. 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)

32. 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

33. Randomness in the outcome • This is perhaps the nicest • Some other runs

34. 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

35. 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)

36. 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.

37. 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?

38. Commercial:CogSci colloquium this year • Many big names in connectionism this semester

39. 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)

40. Perceptron • Input: x1, …, xn • Output: {0, 1} • Weights: w1,…,wn • Bias: a • How it works:

41. What can perceptrons do? • A linear machine: finding a plane that separates the 0 examples from 1 examples

42. 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

43. 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)

44. 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

45. Networks get complicated: more layers • 3 layer perceptron can solve the XOR problem

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

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

48. 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

49. 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

50. 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