1. Alan Pickering Autumn Term 2005
Methods and Techniques in Neuroscience An introduction to neural network models
Alan Pickering Autumn Term 2005

2. Outline: Part 1 Neural learning mechanisms
Learning through connections
Hebbian learning
What is connectionism (some definitions / distinctions) ?
Connectionism
Computational modelling
Neural net modelling
Building a simple model
Terminology & structure
How information passes through a model - exercise 1
How a model learns (supervised & unsupervised learning) - exercise 2

3. Neural learning
Originally, it was thought that new associations/memories were formed by the growth of new nerve cells in the brain
Santiago Ramon y Cajal ( )
Proposed that learning might occur through the strengthening of existing connections between nerve cells
Donald O. Hebb ( )
Formulated Cajal’s ideas into a hypothetical biological mechanism dubbed ‘Hebbian learning’

4. Hebbian Learning Hebbian learning:
When two joining cells fire simultaneously, the connection between them strengthens (Hebb, 1949)
Discovered at a biomolecular level by Lomo (1966) (Long-term potentiation). UR US CS
Learned assocations through the strengthening of connections….

5. What is connectionism? Starting definition:
“Connectionism is the study of how learning can occur through the strengthening and/or weakening of connections between representations of pieces of information and/or behavioural responses”
We can relate this definition straight back to classical and operant conditioning (connections strengthened between stimulus and response, or between CS and CR)
Connectionist modelling is usually concerned with more complex associations and larger numbers of connections. Computers are used to store and process all of this information
A connectionist model is computer simulation of learning

6. What is connectionism? Biological plausibility:
Some (but not all) connectionists appeal to the physical similarity of connectionist models to networks of neurons in the brain (neural net modelling)
Neurons: Nodes
Synapses: Connections (weights)

7. Structure and terminology of connectionist models
Output layer
Output nodes (units)
Hidden nodes (units)
Input layer
Input nodes (units)

8. How a connectionist model works
w = weights
a = activation
o = output j3 j2 j1 u
Activation (au)?
What input arrives at the output node (node u)?
From j1: 1*0.8 = 0.8
From j2: 1*-0.5 = -0.5
From j3: 0*0.2 = 0.0
Sum of inputs = 0.3
Iu = ∑j outj * wju
+0.8
-0.5
+0.2
Weights
(wju) 1
Outputs
(outj)
Activation (aj) .8 .7 .1

9. Exercise 1 What input arrives at the output node (node u)?
w = weights
a = activation
o = output j3 j2 j1 u
Activation (au)?
What input arrives at the output node (node u)?
Iu = ∑j outj * wju
From j1: 1*0.8 = ???
From j2: 1*-0.5 = ???
From j3: 1*0.2 = ???
Sum of inputs = ???
+0.8
-0.7
+0.4
Weights
(wju) 1
Outputs
(outj)
Activation (aj) .8 .7 .6

10. Activations and Outputs 1
Activation = membrane potential of cell
Activation = 0= resting state (-70mV)
+ve activation = cell being depolarised
-ve activation =cell being hyperpolarised (inhibited)
Cells fire (send an action potential) when sufficiently depolarised
Output = mean firing rate of cell
Output of node j1 is a function of its activation, outj = f(aj) j3 j2 j1 u
Activation (aj) .8 .7 .1

11. Activations and Outputs 2
How to convert activations into outputs?
Threshold
Gain (degree of nonlinearity) 1
Outputs
(outj)
Inhu .1
Activation (aj) .8 .7 .6 j3 j2 j1 u
+0.2
+0.8
+0.5
Weights
(wji)
-0.7 k1
Excu

12. An example output function
Hi gain
mid gain
threshold
lo gain

13. Activations and Outputs 3
Creating an activation equation
dau(t)/dt =
dau(t)/dt = ce * Excu(t)
dau(t)/dt = ce * Excu(t) * (Max – au(t))
+ ci * Inhu(t) * (au(t) - Min)
- cd * au(t) 1
Outputs
(outj)
Inhu .1
Activation (aj) .8 .7 .6 j3 j2 j1 u
+0.2
+0.8
+0.5
Weights
(wji)
-0.7 au k1
Excu

14. Simulated Activations and Outputs

15. How does a connectionist model learn?
Following Cajal and Hebb, connectionist models learn through changes in the strength of connections:
Weight changes
There are two types of learning:
Unsupervised learning
In unsupervised learning the weight changes are made automatically and in relation to the degrees of association between incoming activations (E.g. Classical conditioning -- associations strengthen through temporal contiguity)
Supervised learning
In supervised learning the weight changes are made in proportion to the error at the output. In order to calculate the error at the output a teaching pattern is required for comparison =>hence “supervised” (E.g. Learning to talk or spell)

16. Unsupervised learning: 1
The most commonly used unsupervised learning rule is the “Hebb rule” (c.f. Hebbian learning):
∆w = k au aj
∆w = weight change
k = a constant (e.g. 0.6)
au = post-synaptic activation
aj = pre-synaptic activation

17. Unsupervised learning: 2
Example: Classical conditioning
∆w = weight change
k = a constant (e.g. 0.6)
au = post-synaptic activation
aj = pre-synaptic activation
∆w = k au aj
Before conditioning
food
tone 1
1.0
0.0
During conditioning 1
food
tone
1.0
After conditioning
1.0
food
tone 1 .6
0.6
food
tone 1
0.0
1.0
0.6

18. Supervised learning: 1 ∆wju = k up aj
In supervised learning the weight changes are made in proportion to the error at the output
In order to calculate the error at the output a teaching pattern is required for comparison (hence supervised) (E.g. Learning to read or spell)
The most commonly used supervised learning rule is the “delta rule” (Rosenblatt, 1966; Rumelhart & McClelland, 1986):
∆wju = k up aj
∆wju = weight change
k = a constant
up = error at output for input pattern p
aj = pre-synaptic activation

19. Example: Learning to read
In order to read we need to learn relation how orthography (how a word looks) maps onto phonology (how it sounds)
Imagine a network is learning how to pronounce ‘hit’. Say that hit has the orthography; and the phonology; ………

20. Supervised learning: 2 Example: Learning to read ‘Hit’ has:
Orthography
Phonology
∆wju = k up aj
∆wju = weight change
k = a constant
ip = error at output for input pattern p
aj = pre-synaptic activation 1
Teaching pattern 1
First - the error is calculated at each output
Second the blame is apportioned (to active units contributing to the error) 1

21. Exercise 2 Example: Learning to read ‘Cat’ has: Orthography 0 1 0
∆wju = k up aj
∆w = weight change
k = a constant
up = error at output
aj = pre-synaptic activation
‘Cat’ has:
Orthography 0 1 0
Phonology 1
Teaching pattern
Which connection/s will be altered?
Remember:
1st find the error
2nd apportion blame
3rd alter weights coming from blamed input node/s to errorful output node/s 1 u1 u2 u3 1 j1 j2 j3

22. Neural network models: Part 1 summary
Recap on neural learning mechanisms
Learning through connections: Cajal & Hebb both suggested that learning in the human brain may occur through changes in the strength of connections between neurons
Hebbian learning; Hebb formulated a mechanism by which this associative learning might occur; synchronous pre- and post-synaptic firing increases the strength of the connection
What is connectionism (some definitions / distinctions) ?
Connectionism deals with the ways in which statistical structure in the environment can be learned by the strengthening and/or weakening of connections between representations of items of information
Connectionism involves computer simulations of learning
Neural net modelling: Connectionist models gains credibility because they resemble networks of neurons in the brain

23. Neural network models: Part 1 Summary
Building a connectionist model
Structure
They are a network of ‘nodes’ and ‘weighted connections’. Information passes through the from node to node through the ‘weighted connections, usually in one direction.
Terminology
Nodes can be thought of as neurons, and weighted connections as synapses between neurons
The flow of information through the model
The weighted connections control whether or not information passes from one layer of nodes to the next (∑j outj * wju)
Unsupervised learning
As in Hebbian learning, unsupervised models use correlations of pre and post-synaptic firing to change strengths of connections (∆wju = k au aj)
Supervised learning
Supervised learning relies on the error at the output (provided by a teaching patter) to determine the changes in connection strength (∆wju= k up aj)

24. Outline: Part 2
Why connectionism? (the case for parallel distributed processing)
Parallel processing
Distributed processing (representations)
An example of how connectionist models can help us understand learning:
Learning of inflectional morphology in early childhood
Pinker & Prince (1988)
Rumelhart & McClelland (1986)

25. Parallel distributed processing (PDP)
Rumelhart & McClelland (1986) made a very strong case for the use of connectionist models, highlighting the qualities of parallel and distributed processing
Parallel Processing
Parallel processing can be contrasted with serial processing
Processing several different pieces of information at the same time, rather than one after the other:
Example: face processing
Distributed Processing
Distributed processing can be contrasted with localist processing
Representations of information are distribute across the whole neural network, rather than occupying specific locations
Example: Karl Lashley and the ‘Engram’ (location of memory)

26. Parallel processing Example: Face processing
When looking at this face we recognise it not by looking at individual features one at a time (the eyes, the nose, the smile, the grimace), but by processing these features and their spatial configuration in parallel

27. Parallel processing Example: Face processing Margaret Thatcher
Tony Blair
Nose nodes
Grimace node
Smile nodes
Eye nodes

28. Distributed processing
Example: Lashley and the search for the ‘Engram’
Karl Spencer Lashley ( )
Pioneering researcher in the biological foundations of memory in the rat
Lashley and colleages lesioned the brains of rats in order to test whether or not they had removed the part responsible for memory. They found no single locus (engram) which appeared to be solely responsible for memory
Lashley concluded that memory was distributed throughout the cortex, rather than localised in one specific place

29. A connectionist model of the acquisition of inflectional morphology
The way in which we change words to convey:
Plurality
Past tense
Examples:
Cat + -s --> Cats (Plural)
Play + -ed --> Played (Past tense) - *we focus on this*
In English:
90% of verbs have a regular morphology
10% an irregular morphology

30. Acquisition of inflectional morphology
Past tense morphology
Regular Morphology (90% verbs)
talk => talked
ram => rammed
pit => pitted
Irregular Morphology (10% verbs)
hit => hit ‘no change’
come => came ‘vowel change’
sleep => slept ‘vowel change’
go => went ‘arbitrary’
How do children learn which words require a regular ending and which are irregular?

31. Acquisition of inflectional morphology
U-shaped Development
Initially, children’s early inflections are correct
Later they start making errors:
Hitted
Sleeped
Goed
Over-regularisation errors
Later still children recover from these errors
Phase 1: Rote learning -> initial error free performance
Phase 2: Rule extraction -> over-regularisation errors
Phase 3: Rule + rote -> recovery from errors

32. Acquisition of inflectional morphology
Dual-route model (Pinker & Prince, 1988)?
‘Rule’ route deals with regular verbs
Exceptions route deals with irregulars
Exceptions
Rule
Input Stem
Output Inflection
Errors in the middle of development occur due to overuse of the ‘rule system
But do we really need two routes to explain this pattern of learning?

33. Acquisition of inflectional morphology
Connectionist model (McClelland & Rumelhart, 1986)?
Wickelfeature Representation of Stem
Wickelfeature Representation of Past Tense
One single network learns to produce past tense for all the verbs it is taught
A single route connectionist model for learning the past tense
No rule route for producing the regular ending
The network ‘learned’ to associate regular & irregular English verb stems with their past tense forms.

34. Acquisition of inflectional morphology
Connectionist model (McClelland & Rumelhart, 1986)?
Like the children the network:
Made over-regularisation errors
Demonstrated u-shaped development in its performance on irregular verbs

35. Acquisition of inflectional morphology
Connectionist model of the acquisition of inflectional morphology (McClelland & Rumelhart, 1986)
This model demonstrates that behaviour which looks as if it is driven by a knowledge of rules can in fact be driven by a distributed representation of statistical structure of the input (in this case a distributed representation of language)
This explanation of how it is possible that ‘rule-like behaviour’ can occur in the absence of any actual representation of the rule is an important contribution of connectionist models

36. Neural network models: Part 2 Summary
Why connectionism? (the case for parallel distributed processing)
Parallel processing
Connectionist models process information in parallel, rather than serially; this has intuitive appeal when we consider how we take information in
Distributed processing (representations)
Connectionist models represent learned information in the distributed connections across the network, rather than in single locations or ‘rules’; this helps explain why it is diffiicult to find a single location for memory in the brain
An example of how connectionist models can help us understand learning:
Rumelhart & McClelland’s (1986) model
This models the acquisition of inflectional morphology and demonstrates how networks can show ‘rule-like’ behaviour, in the absence of any representation of a rule.

37. Outline: Part 3 A history of neural network models
Single layer networks
Rosenblatt’s perceptron (1958)
Minsky & Papert’s (1969) criticism of perceptrons
Multi layer networks
McClelland & Rumelhart’s (1986) ‘Backpropagation of error’ learning rule

38. Structure and terminology of connectionist models
Output layer
Output nodes (units)
Hidden nodes (units)
Input layer
cover that connectionist model transforms material at the input into something else at the output -this is through the connection weights between input and output nodes…
Input nodes (units)

39. One-layer vs multi-layer networks
One-layer networks were the first connectionist models to emerge in the 1950s
Frank Rosenblatt’s (1958) ‘Perceptron’
In these networks learning occurs through changes in the weights of only one layer
However, networks which only change one layer of weights have some important limitations
These were pointed out by Minsky & Papert (1969)…

40. Minsky & Papert (1969)
Minsky & Papert (1969) made the point that single-layer networks cannot solve ‘non-linearly separable problems’
Maths Example: The XOR problem
If you think about the sums of the inputs then we can see why this isn’t linearly separable:
When the sum of the inputs increases to 2, the desired output goes back down to 0
inputs
output
Task: to learn to solve XOR
input output
1 1 0
1 0 1
0 1 1
0 0 0
sums 2 1
Single layer networks cannot solve this kind of problem

41. Minsky & Papert (1969)
The inability to solve non-linear problems is a problem for any model of human learning because humans can solve non-linear problems..
Psychological Example 1: Learning to eat the right amount
We all have to learn to eat enough to stay fit, but not so much as to make us sick
This is like solving the XOR problem (we can learn to eat some of the food but not all of it)
Psychological Example 2: Connected and unconnected figures a b c d

42. Minsky & Papert (1969)
Psychological Example 2: Connected and unconnected figures a b c d
How might a single layer network try to solve this? (1 = connected, 0 = unconnected)
All figures have three horizontal lines so have to work this out on the basis of the presence of vertical lines (at particular locations)
The net might start by discriminating between two connected and unconnected figures (e.g. c and d) by locating a vertical line (e.g. in the bottom left)
But this also leads the net to discriminate between figures which we want to group together (e.g. c and b)

43. A solution: Multi-layered networks
Rosenblatt & Minsky & Papert agreed that this problem would be solved if you could train networks with more than one layer:
Networks with ‘hidden units’ can redescribe the input into a format that can be separated linearly
“Hidden units allow the network to treat physically similar inputs as different, as the need arises”

44. Multi-layered networks solve XOR
A multilayered network can solve the XOR problem:
inputs
output
Task: to learn to solve XOR
input hidden output +1 -1
You can set up a two layered network like the example on the left (with appropriate weights) to solve the XOR problem
But the real problem envisaged by Minsky & Papert was how to train the weights on a network with two layers……..???

45. Training multi-layered networks
When a network learns through the delta rule, a teaching pattern is there to correct the weights leading into the output by measuring the difference between the teaching pattern and the output:
Teaching pattern 1
BUT!! - there is no teaching pattern for the hidden layer, which can be used to change the weights from the input..!!
The inability to find a learning rule which would change all weights in a network stifled connectionist research until a solution was found in 1986…. 1 1

46. Back-propagation of error
McClelland & Rumelhart (1986) came up with a learning rule to solve this: ‘back-prop’
Teaching pattern 1 1
Backprop learning:
Backprop is an extension of the delta (supervised learning) rule
Error at the output is used to assign blame to particular hidden units
Then this blame is converted to error, and this is then used to calculate weight changes to the weights from input to hidden units

47. Summary: Part 3 Single layer networks Rosenblatt’s perceptron (1958)
The first connectionist models were known as ‘perceptrons’, and learned through changes to a single layer of weights
Minsky & Papert’s (1969) criticism of perceptrons
Single layer networks cannot be set up to solve non-linearly separable problems (e.g. the XOR problem)
This is a problem because humans can solve non-linearly separable problems (e.g. M & P’s connected figures discrimination)

48. Summary: Part 3 A history of connectionist models Multi-layer networks
Multi-layered networks can solve non-linearly separable problems by redescribing the input in a linearly separable way at a set of intermediary nodes called ‘hidden units’
Minsky & Papert (1969) knew that mutilayered networks could provide a solution to non-linearly separable problems, but were not very optimistic about finding a way of training both layers of weights, until…..
McClelland & Rumelhart (1986)
… came up with a learning rule which could change the weights in multiple layers of weights - ‘Back-propagation of error’ (BP)
BP works as an extension of normal ‘delta rule’ supervised learning, but by changing the weights arriving at the hidden units in relation to the blame assigned to these units

49. Outline: Part 4 Some applications Modelling human memory
McClelland’s (1981) Jets and Sharks model
Modelling double dissociations in acquired dyslexia
Plaut & Shallice (1988)

50. Parallel distributed processing in memory
McClelland’s (1981) ‘Jets and sharks’ model of memory
A simulation of how humans might store information about people
Imagine the Jets and Sharks are two rival gangs in your town
You know a lot about the gang members
How old they are (20s, 30s, 40s)
How well educated they are (Junior high, High school, College)
What their marital status is (single, married)
What their job is (pusher, bookie, burglar)
How do you access this information????

51. Jets and Sharks
A computer (or conventional database) might store the information indexed to name:
The name links all the information about that person together:
John HS single jet burglar
Terry JH married shark pusher
Fred JH married shark burglar
Name indexing is good for answering questions like. “is Fred a burglar?”
But bad at answering, “who is a burglar?”

52. Jets and Sharks
McClelland set up the following connectionist database:
Links between names and professions /education /marital status etc.. are made by excitatory connections (green)
Within areas of knowledge, categorical items have inhibitory connections (red) - these inhibitory connections help the network give a concrete answer (I.e. jet or shark, but not both)

53. Jets and Sharks Content addressability:
By putting activation into the network at the burglar node, we get information about who is a burglar (al, jim, john, doug, lance, george) - this is known as ‘content addressability’
There is also information about what age the burglars mostly are, whether the burglars are mostly jets or sharks etc…

54. Jets and Sharks Typicality effects:
McClelland’s network also nicely models an aspect of human memory called ‘typicality’:
If we ask the net to tell us the name of a pusher, it is more likely to retrieve some pushers than others (Fred & Nick, but not Ol)
This is because Ol is not a typical pusher (and does not benefit from the excitation coming from the activated typical pusher nodes

55. Parallel processing in memory
McClelland’s (1981) ‘Jets and sharks’ model of memory shows how a database of information can be set from which information about several different attributes (e.g. marital status, name, gang etc..) can be retrieved in parallel
Furthermore, more than one address in memory (e.g. several names) can be accessed at once (in parallel) by activation of an attribute (e.g. jets) - this is an aspect of human memory called ‘content addressability’, and contrasts with a memory system in which items are searched one-by-one (serially)
The memory in the network is distributed across all of the connection weights…(a distributed database)..

56. Connectionist models of double dissociations
Double dissociations are situations in neuropsychology in which you find that one brain damaged patient has a deficit in cognitive function A, but not B, whereas another patient has a deficit in B but not A
This has been traditionally interpreted as indicating that A and B are cognitive functions which are independent (and located in different parts of the brain)
Example: Dissociation between conditioned and expected fear

57. A double dissociation in acquired dyslexia
People can occasionally acquire dyslexia (reading difficulty) after brain injury
Different types of acquired dyslexia have been identified:
Difficulty reading concrete words (e.g. tack) vs. difficulty reading abstract words (e.g. tact)
While most patients show a superiority for concrete words, some demonstrate better performance with abstract words (Warrington, 1981)
This has been described as a double dissociation, and researchers have suggested separable semantic memory stores for concrete and abstract words (at different locations in the brain)
Plaut & Shallice (1993) constructed a connectionist simulation to determine whether we do need to posit two separate stores on the basis of this double dissociation…..

58. A double dissociation in acquired dyslexia
After training, Plaut & Shallice’s (1993) model was able to correctly read concrete and abstract words
The next step was to lesion the model in several different ways (cut some connections), to determine what deficits would occur
Orthography & semantics
phonology
Plaut & Shallice found that if you lesion several models in different locations you can model the double dissociation with a single system

59. A double dissociation in acquired dyslexia
Plaut & Shallice’s (1993) finding is very significant as it shows that double dissociations do not necessarily mean that there are two separate systems involved.
In this case both concrete and abstract words are represented in a distributed fashion across the entire system rather than in separate localised stores

60. Summary: Part 4 What connectionist models can do
Modelling human memory
McClelland’s (1981) Jets and Sharks model is a distributed memory database (rather than a serially accessed database
It neatly models content addressability and typicality - two aspects of human memory which a serially accessed memory store cannot model
Modelling double dissociations in acquired dyslexia
Plaut & Shallice (1993) show that clinical double dissociations of ability to read concrete and abstract words can be modelled in a single route network, in which information about both is processed in parallel, and distribuited across the net