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

Sperry’s experiment Each location in space is seen by a different location on the retina of the frog Each different location on the retina is connected by the optic nerve to a different location in the brain Each of these different locations in the brain causes a different movement direction. In a normal animal, a retinal region which sees in a particular direction is connected to a tectal region which causes a movement in that direction

Innervation of the Optic tectum Ganglion Cells in the frog retina (maps particular regions in space) map systematically to cells in the optic tectum (movement in specific directions).  The retinal cells “see” in a direction and map to tectal cells which cause the frog to move in that direction The image of the external stimulus is inverted in the retina and the mapping from the retina to the optic tectum reverts to the original image. The Nasal ganglion cells of the retina map to the posterior region of the Optic tectum and the temporal ganglion cells map to the anterior region of the tectum

Sperry’s experiment Sperry took advantage of the fact that in amphibians, the optic nerve will regrow after it has been interrupted Sperry cut the optic nerve and simultaneously rotated the eye 180 degrees in the eye socket. In 'learning’ movements to catch prey, the part of the retina now looking forward (backward) should connect to the part of the brain which causes forward (backward) movement.

Sperry’s findings After regeneration, his animals responded to prey items in front by turning around and to prey items behind by moving forward. and kept doing this even though they never succeeded in reaching the prey.

Conclusion from experiment The conclusion from this (and some supporting experiments) is that the pattern of connections between retina and tectum, and the movement information represented is not based on experience. It is innate based on the initial distribution of chemical markers in the brain.

Lecture Overview Summary Overview Development from embryo Initial wiring Activity dependent fine tuning

The role of the environment The development of ocular dominance columns  Cat and later monkey (Hubel and Wiesel) Retinal input connects to the LGN (Thalamus)  LGN is composed of layers. Each layer receives input (axons) from a single eye LGN connects to layer IV of the visual cortex  The visual cortex develops ocular dominance columns  Cells that are connected to similar layers in the LGN get stacked together in columns forming stripes. /

VISUAL CORTEX LGN

Monocular deprivation critical period Hubel and Wiesel deprived one of the eyes of the cat (later macaque monkey) at various times 1 week – 12 weeks (in the monkey case) 4 weeks – 4 months (for the cat). The found that the ocular dominance cell formation was most severely degraded if deprivation occurred at 1 – 9 weeks after birth. Deprivation after the plastic period had no long- term effect.

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

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

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.

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.

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 (phantom limb sensations) Stimulation standard technique for stroke victim rehabilitation

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).

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.

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?

Connectionist Models: Basics Srini Narayanan CS182/CogSci110/Ling109 Spring 2006

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 sum of the input signals Net input is transformed into an output signal via a simple function (e.g., a threshold function)

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

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

Simple Threshold Linear Unit

Simple Neuron Model 1

A Simple Example a = x 1 w 1 +x 2 w 2 +x 3 w x n w n a= 1*x *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.

Simple Neuron Model

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

Types of Activation functions

The Sigmoid Function x=neti y=a

Nice Property of Sigmoids

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

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

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

Nice Property of Sigmoids

Radial Basis Function

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

Types of Neuron parameters The form of the 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.

Computing other functions McCollough-Pitts Neurons can compute logical functions.  AND, NOT, OR

Computing other 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 y0y x0x0 f i1i1 w 01 y0y0 i2i2 b=1 w 02 w 0b

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

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.

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.

The XOR Function X1/X2X2 = 0X2 = 1 X1= 001 X1 = 110

The Input Pattern Space

The Decision planes

Computing other relations The 2/3 node is a useful function that activates its outputs (3) if any (2) of its 3 inputs are active Such a node is also called a triangle node and will be useful for lots of representations.

Triangle nodes and McCullough-Pitts Neurons? BC A ABC

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

“They all rose” triangle nodes: when two of the neurons fire, the third also fires model of spreading activation

Link to Vision: The Necker Cube

Basic Ideas behind the model 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

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

Can we formalize/model these intuitions What is a neurally plausible computational model of spreading activation that captures these features. What does semantics mean in neurally embodied terms  What are the neural substrates of concepts that underlie verbs, nouns, spatial predicates?