1. Modelling Language Evolution Lecture 1: Introduction to Learning Simon Kirby University of Edinburgh Language Evolution & Computation Research Unit

2. Course Overview Learning Introduction to neural nets Learning syntax Evolution Syntax Learning bias and structure Culture Iterated learning The Talking Heads (practical)

3. 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?

4. What is a model? One view: We use models when we can’t be sure what our theories predict Especially useful when dealing with complex systems THEORY MODEL PREDICTION OBSERVATION

5. A simple example Vowels exist in a “space” Only some patterns arise cross-linguistically E.g. vowel space seems to be symmetrically filled Why?

6. 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”

7. Is language a complex system? Cultural evolution Individual learning Biological evolution Yes – evolution on many different timescales: Computational models will help us understand these interactions…

8. 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

9. 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

10. 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

11. An artificial neuron Add up all the inputs multiplied by their weights f(net) is the “activation function” that scales the input

12. A useful activation function All or nothing for big excitations or inhibitions… … but more sensitive in between.

13. AND: a very simple network A network that works out if both inputs are activated: INPUT 1INPUT 2 BIAS NODE (always set to 1.0) OUTPUT 55 -7.5 Network gives an output over 0.5 only if both inputs are 1.

14. OR: another very simple network A network that works out if either input is activated: INPUT 1INPUT 2 BIAS NODE (always set to 1.0) OUTPUT 10 -7.5 Network gives an output over 0.5 if either input is 1.

15. XOR: a difficult challenge A network that works out if only one input is activated: INPUT 1INPUT 2 BIAS NODE (always set to 1.0) OUTPUT ?? ? Solution needs more complex net with three layers. WHY?

16. XOR network - step 1 XOR is the same as OR but not AND Calculate OR Calculate NOT AND AND the results NOT ANDOR AND

17. XOR network - step 2 OUTPUT BIAS NODE HIDDEN 1HIDDEN 2 INPUT 1INPUT 2 10 -7.5 -5 7.5 5 5 -7.5 NOT ANDOR AND

18. 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

19. 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.

20. 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

21. 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?

22. 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?

23. 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