1. Framework For PDP Models Psych 85-419/719 Jan 18, 2001

2. What A Model Is A set of processing units A pattern of connectivity A propagation rule net to generate input a a A transfer function f f.. To generate output o o A learning rule to change the connections A training environment cat dog meows barks.. With weights w w w w

3. Formally... Consider unit j communicating with unit i at time t. net i (t) = g(w j,i,o j (t-1)) (propagation rule) a i (t) = net j (t) (activation function) o i (t)= f(a i (t)) (transfer function)

4. The Propagation Rule net Computes input to unit a i –From outputs of other units o j –And the weights from those units w j,i Ex: weighted sum a i = SUM j (w j,I * o j ) Ex: sigma pi unit a i = PRODUCT j (w j,I * o j )

5. Weighted Sum: Matrix Algebra.1.5 1.0.1.5 1.0 2 1.5 -3.2 -6 2 -6 -3 1.2 5 X = -5.8 5.2 -5.85.2

6. The Transfer Function f: o=f(a) Simple linear: o=k * a

7. Transfer Functions: Clipped Linear o = zero (if a < zero) o = 1 (if a > 1) o = a (otherwise)

8. Transfer Functions: Threshold o = 1 (if a > thresh) o = zero otherwise thresh

9. Transfer Functions: Logistic o = 1/(1+e -a )

10. Transfer Functions: Hyperbolic Tangent o = TANH(a)

11. Transfer Functions With and Without Memory Memoryless: The output is a function of its activation at that moment in time. Stateless. With memory: The output is a function not only of the activation at time t, but its own output at time t-1. Which one is more like real neurons? Can you build a unit with memory out of units without memory? w

12. Time In PDP Networks Feedforward networks –Activity is passed from input to output in one pass Discrete time networks –At each time sample, each unit computes its output based on output of other units at previous time step Continuous time networks –Activation ramps up gradually over time

13. Discrete Time Example 1 0.1 1 1 0.2 0.1 0.2 0.3 0.2

14. Continuous Time Example 1 0.1 1 -0.5

15. Learning in Models “Knowledge is in the weights!” –Grow new connections –Prune existing connections –Modify existing connections Examples? –Developmental biology –Learning skills –Unlearning (brain damage: stroke, Alzheimer’s, etc.)

16. Types of Learning Supervised learning –Input and target outputs are specified –Learning involves teaching network what correct output should be Reinforcement learning –Actual target isn’t specified. Reward is given Unsupervised learning –No teaching signal available –“discover” interesting things about environment

17. Training Data (Environment) Specifies input to network Can specify targets (with supervised), or reward (with reinforcement) Inputs can be sampled by network, or pre- specified Sequential, random, or weighted random

18. An Example: Content Addressable Memory Humans can recall items from memory based on partial information; a subset of that memory –“What was the name of that guy in my math class who always wore the Misfits t-shirt?” Graceful degradation: you don’t lose all information as you forget things

19. The Challenge Standard data structures, as used by computers, don’t tend to have these properties Why would human memory have these properties in the first place? A simple model to demonstrate how a neural system gives rise to these behaviors

20. An Example Model: Interactive Activation The theory: processing units representing features of the world are interconnected Their dynamics are such that for coherent memories, they maintain each other’s state Partial information can bootstrap further memory through the weights between units

21. An Example Model: Interactive Activation (details) Unit output zero if activity below threshold Equal to difference between activity and threshold if above threshold Decay term: units tended to decay, lacking proper excitation See PDP1, pages 71-72 for more details

22. Jets and Sharks

23. The Jets and Sharks Network

24. Nice Properties of this Model Content addressability –“Who is a Shark in their 20’s?” Graceful degradation –“I know Al is a burglar in his 30’s… is he in the Jets or the Sharks?” Default assignment –“What could Lance’s job be?” Spontaneous generalization –“What is a member of the Jets like?”

25. For Next Time Read for class: PDP2, Chapter 14, pages 7- 38 only Also read material handed out today Homework 1 will be handed out. Don’t fall behind on the reading!