1. Nature requires Nurture Initial wiring is genetically controlled  Sperry Experiment But environmental input critical in early development  Occular dominance columns Hubel and Wiesel experiment

3. CI 1 CI 7 CI 5 CI 6 CI 3 CI 4 CI 2 Cat Striate Cortex Layer IV Monkey Striate Cortex Area 17 (V1) Layer IV CLOSED EYE OPEN EYE

4. Critical Periods in Development There are critical periods in development (pre and post-natal) where stimulation is essential for fine tuning of brain connections. Other examples of columns  Orientation columns

5. Pre-Natal Tuning: Internally generated tuning signals But in the womb, what provides the feedback to establish which neural circuits are the right ones to strengthen?  Not a problem for motor circuits - the infant moves its limbs to refine the feedback and control networks.  But there is no vision in the womb. --Systematic moving patterns of activity are spontaneously generated pre- natally in the retina. A predictable pattern, changing over time, provides excellent training data for tuning the connections between visual maps. The pre-natal development of the auditory system  Research indicates that infants, immediately after birth, preferentially recognize the sounds of their native language over others. The assumption is that similar activity-dependent tuning mechanisms work with speech signals perceived in the womb.

6. Post-natal environmental tuning The pre-natal tuning of neural connections using simulated activity can work quite well –  a newborn colt or calf is essentially functional at birth. This is necessary because the herd is always on the move. For many animals, including people, experience is absolutely necessary for normal development (as in the kitten experiment). For a similar reason, if a human child has one weak eye, the doctor will sometimes place a patch over the stronger one, forcing the weaker eye to gain experience.

7. Adult Plasticity and Regeneration The brain has an amazing ability to reorganize itself through new pathways and connections rapidly. Through Practice: London cab drivers, motor regions for the skilled After damage or injury Undamaged neurons make new connections and take over functionality or establish new functions But requires stimulation Stimulation standard technique for stroke victim rehabilitation

8. When nerve stimulation changes, as with amputation, the brain reorganizes. In one theory, signals from a finger and thumb of an uninjured person travel independantly to separate regions in the brain's thalamus (left). After amputation, however, neurons that formerly responded to signals from the finger respond to signals from the thumb (right).

9. Possible explanation for the recovery mechanism The initial pruning of connections leaves some redundant connections that are inhibited by the more active neural tissue. When there is damage to an area, the lateral inhibition is removed and the redundant connections become active The then can undergo activity based tuning based on stimulation. Great area for research.

10. Summary Both genetic factors and activity dependent factors play a role in developing the brain architecture and circuitry.  There are critical developmental periods where nurture is essential, but there is also a great ability for the adult brain to regenerate. Next: What computational models satisfy some of the biological constraints. Question: What is the relevance of development and learning in language and thought?

11. Connectionist Models: Basics Srini Narayanan CS182/CogSci110/Ling109 Spring 2008

13. (Spike After Potential) Excitatory PSP Inhibitory PSP

14. Neural networks abstract from the details of real neurons Conductivity delays are neglected An output signal is either discrete (e.g., 0 or 1) or it is a real-valued number (e.g., between 0 and 1) Net input is calculated as the weighted spatial sum of the input signals Net input is transformed into an output signal via a simple function (e.g., a threshold function)

15. The McCullough-Pitts Neuron y j : output from unit j W ij : weight on connection from j to i x i : weighted sum of input to unit i xixi f yjyj w ij yiyi x i = ∑ j w ij y j y i = f(x i –  i) t i : target Threshold

16. Neural nets: Mapping from neuron Nervous SystemComputational Abstraction NeuronNode DendritesInput link and propagation Cell BodyCombination function, threshold, activation function AxonOutput link Spike rateOutput Synaptic strengthConnection strength/weight

17. Simple Threshold Linear Unit

18. Simple Neuron Model 1

19. A Simple Example a = x 1 w 1 +x 2 w 2 +x 3 w 3... +x n w n a= 1*x1 + 0.5*x2 +0.1*x3 x1 =0, x2 = 1, x3 =0 Net(input) = f = 0.5 Threshold bias = 1 Net(input) – threshold bias< 0 Output = 0.

20. Simple Neuron Model 1 1 1 1

21. 1 1 1 1 1

22. 1 0 1 1

23. 1 0 1 1 0

24. Abstract Neuron w2w2 wnwn w1w1 w0w0 I 0 = 1 o u t p u t y i2i2 inin i1i1... i n p u t i 1 if net > 0 0 otherwise {

25. Computing with Abstract Neurons McCollough-Pitts Neurons were initially used to model  pattern classification size = small AND shape = round AND color = green AND location = on_tree => unripe  linking classified patterns to behavior size = large OR motion = approaching => move_away size = small AND direction = above => move_above McCollough-Pitts Neurons can compute logical functions.  AND, NOT, OR

26. Computing logical functions: the OR function Assume a binary threshold activation function. What should you set w 01, w 02 and w 0b to be so that you can get the right answers for y 0 ? i1i1 i2i2 y0y0 000 011 101 111 x0x0 f i1i1 w 01 y0y0 i2i2 b=1 w 02 w 0b

27. Many answers would work y = f (w 01 i 1 + w 02 i 2 + w 0b b) recall the threshold function the separation happens when w 01 i 1 + w 02 i 2 + w 0b b = 0 move things around and you get i 2 = - (w 01/ w 02 )i 1 - (w 0b b/w 02 ) i2i2 i1i1

28. Decision Hyperplane The two classes are therefore separated by the `decision' line which is defined by putting the activation equal to the threshold. It turns out that it is possible to generalise this result to TLUs with n inputs. In 3-D the two classes are separated by a decision-plane. In n-D this becomes a decision-hyperplane.

29. Linearly separable patterns Linearly Separable Patterns PERCEPTRON is an architecture which can solve this type of decision boundary problem. An "on" response in the output node represents one class, and an "off" response represents the other.

30. The XOR function i1i1 i2i2 y 000 011 101 110

31. The Input Pattern Space

32. The Decision planes

33. Multiple Layers I1I1 I2I2 1.50.5 1 11 1 1 y

34. Multiple Layers I1I1 I2I2 1.50.5 1 11 1 1 01 y

35. Multiple Layers I1I1 I2I2 1.50.5 1 11 1 1 11 y

36. Types of abstract neuron parameters The form of the combination function - e.g. linear, sigma-pi, cubic. The activation-output relation - linear, hard-limiter, or sigmoidal. The nature of the signals used to communicate between nodes - analogue or boolean. The dynamics of the node - deterministic or stochastic. Spatio temporal information encoding: Pulse coding and Spiking Neurons

37. Different Activation Functions Threshold Activation Function (step) Piecewise Linear Activation Function Sigmoid Activation Funtion Gaussian Activation Function  Radial Basis Function BIAS UNIT With X0 = 1

38. Types of Activation functions

39. The Sigmoid Function x=neti y=a

40. Nice Property of Sigmoids

41. The Sigmoid Function x=neti y=a Output=0 Output=1

42. The Sigmoid Function x=neti y=a Output=0 Output=1 Sensitivity to input

43. Changing the exponent k(neti) K >1 K < 1

44. Nice Property of Sigmoids

45. Radial Basis Function

46. Stochastic units Replace the binary threshold units by binary stochastic units that make biased random decisions.  The “temperature” controls the amount of noise temperature

47. Spiking Neurons and Pulse coding Rate coding (ex. Sigmoid units)  Spatial summation of input  Output is the average number of spikes in some time window (normalized between 0 and 1). Pulse coding (More realistic)  Look at each individual spike (the time it is generated)  Can take into account refractory period EXAMPLE: Integrate and fire neurons EXAMPLE: Time to first spike (Thorpe 1996).  Adds power to the basic neuron by adding temporal information

49. Triangle Nodes: Encoding relational information with abstract neurons The triangle node (aka 2/3 node) is a useful function that activates its outputs (3) if any (2) of its 3 inputs are active Such a node will be useful for lots of representations.

50. Triangle nodes and McCullough-Pitts Neurons? ObjectValue Relation ABC

51. Representing concepts using triangle nodes triangle nodes: when two of the neurons fire, the third also fires

52. Networks of Triangle nodes: example sentence “They all rose” triangle nodes: when two of the abstract neurons fire, the third also fires model of spreading activation

53. Link to Vision: The Necker Cube

54. Basic Ideas behind connectionist models Parallel activation streams. Top down and bottom up activation combine to determine the best matching structure. Triangle nodes bind features of objects to values Mutual inhibition and competition between structures Mental connections are active neural connections

55. 5 levels of Neural Theory of Language Cognition and Language Computation Structured Connectionism Computational Neurobiology Biology MidtermQuiz Finals Neural Development Triangle Nodes Neural Net Spatial Relation Motor Control Metaphor SHRUTI Grammar abstraction Pyscholinguistic experiments