Download Modelling Language Evolution Lecture 1: Introduction to

Modelling Language Evolution
Lecture 1: Introduction to Learning
Simon Kirby
University of Edinburgh
Language Evolution & Computation Research Unit
Course Overview
 Learning
 Introduction to neural nets
 Learning syntax
 Evolution
 Syntax
 Learning bias and structure
 Culture
 Iterated learning
 The Talking Heads (practical)
Computers for modelling
 Computers in linguistics
 Engineering (speech and language technologies)
 Research tools (waveform analysis, psycholinguistic
stimuli etc.)
 Recently: modelling building
 Why build models?
 Why use computers?
 What is a model anyway?
What is a model?
 One view:
MODEL
THEORY
PREDICTION
OBSERVATION
 We use models when we can’t be sure what our
theories predict
 Especially useful when dealing with complex
systems
A simple example
 Vowels exist in a “space”
 Only some patterns arise cross-linguistically
 E.g. vowel space seems to be symmetrically filled
 Why?
Theory to Model
 We need a theory to explain vowel-space universal
 Possible theory:
 Vowels tend to avoid being close to each other to
maintain perceptual distinctiveness.
 Use model to test theory
(Liljencrants & Lindblom 1972)
 In general, computational models
are useful when dealing with
“complex systems”
Is language a complex system?
 Yes – evolution on many different timescales:
Individual
learning
Cultural
evolution
Biological
evolution
 Computational models will help us understand these
interactions…
Learning
 Language learning is crucial to language evolution
 What is learning?
 Learning occurs when an organism changes its internal
state on the basis of experience
 What do we need to model learning?
1. a model of internal states
2. A model of experience
3. An algorithm to change 1 into 2
One approach: Neural nets
 An approach to internal
states based on the
brain
 An artificial neuron is a
computational unit that
sums inputs and uses
them to decide whether
to produce an output
Networks of neurons
 Typically there will be many connected neurons
 Information is stored in weights on the connections
 Weights multiply signals sent between nodes
 Signals into a node can be excitatory or inhibitory
An artificial neuron
neti   wij a j
j
 Add up all the inputs multiplied by their weights
 f(net) is the “activation function” that scales the input
A useful activation function
1
ai 
1  e  neti
 All or nothing for big excitations or inhibitions…
 … but more sensitive in between.
AND: a very simple network
 A network that works out if both inputs are activated:
OUTPUT
-7.5
5
5
BIAS NODE
(always set to 1.0)
INPUT 1
INPUT 2
 Network gives an output over 0.5 only if both inputs are 1.
OR: another very simple network
 A network that works out if either input is activated:
OUTPUT
-7.5
10
10
BIAS NODE
(always set to 1.0)
INPUT 1
INPUT 2
 Network gives an output over 0.5 if either input is 1.
XOR: a difficult challenge
 A network that works out if only one input is activated:
OUTPUT
?
?
?
BIAS NODE
(always set to 1.0)
INPUT 1
INPUT 2
 Solution needs more complex net with three layers. WHY?
XOR network - step 1
 XOR is the same as OR but not AND
 Calculate OR
 Calculate NOT AND
 AND the results
AND
NOT AND
OR
XOR network - step 2
OUTPUT
BIAS NODE
-7.5
-7.5
5
5
AND
7.5
HIDDEN 1
HIDDEN 2
10
10
-5
-5
INPUT 1
INPUT 2
NOT AND
OR
But what about learning?
 We now have:
 a model of internal states (connection weights)
 a model of experience (inputs and outputs)
 Learning:
 set the weights in response to experience
 How?
 Compare network behaviour with “correct” behaviour
 Adjust the weights to reduce network error
Error-driven learning
1. Set weights to random values
2. Present input pattern
3. Feed-forward activation through the network to get
an output
4. Calculate difference between output and desired
output (i.e. error)
5. Adjust weights so that the error is reduced
6. Repeat until network is producing the desired
results.
Gradient descent




Gradient descent is a form of error-driven learning
Start on random point of “error surface”
Move on surface in direction of steepest slope
Potential problems:
 May overshoot the global minimum
 Might get stuck in local minimum
Example: learning past tense of verbs
 Network that takes present tense form of verb…
 …and produces past tense.
 Uses examples to set weights
 Generalises to add /-ed/ to verbs it’s never seen before.
 Has it learnt a linguistic rule?
Is this psychologically plausible?
 We need an error signal
 Where does this error signal come from?
 Possibilities:
 A teacher
 Reinforcement
 The outcome of some prediction:
 e.g. what’s the next word?
 what’s the past tense of this verb?
Summary
 Modelling tests theories
 Computer modelling appropriate for complex
systems
 Language evolution involves several complex
systems
 Neural nets are one approach to modelling learning
 Networks can be made to adapt to data through
error-driven learning
 Next lecture: how to model acquisition of syntax