1. Neural Computation 0368-4149-01 Prof. Nathan Intrator
TA: Yehudit Hasson
Tuesday 16:00-19:00 Dan David 111
Office hours: Wed 4-5

2. Neural Computation Neuroscience
The objective is to understand the human brain
Biologically azrealistic models of neurons
Biologically realistic connection topologies
Neural computation
The objective is to develop learning, representation and computation methods
Novel architectures for data representation and processing
Twee hoofdstromen
Vak bij BMT zal op den duur meer kant 1 opgaan
Bij AI komt meer kijken: kennis representatie
reasoning
learning

3. The goals of neural computation
To understand how the brain actually works
Its big and very complicated and made of yukky stuff that dies when you poke it around
To understand a new style of computation
Inspired by neurons and their adaptive connections
Very different style from sequential computation
should be good for things that brains are good at (e.g. vision)
Should be bad for things that brains are bad at (e.g. 23 x 71)
To solve practical problems by using novel learning algorithms
Learning algorithms can be very useful even if they have nothing to do with how the brain works

4. The Brain The brain - that's my second most favorite organ!
- Woody Allen

5. The Brain: Fundamental Questions
What kind of information is extracted from the environment?
How is information represented, e.g. visual?
How is information stored?
How is information altered (learning & memory)?
How is information processed and manipulated?

7. The Brain: Simpler Questions
How is 3D information stored
How is relational information stored:
The child is on the floor
The book is in the bag
How are verbs associated with adjectives
How is information bound together:
Collections of items which are on the table
Collection of edges which form an object

8. Physiological experiments help us learn how a new scene is analyzed, in particular the eye movement is used to learn about the analysis strategy
In this unseen set of images, it takes very long time to detect the changes between the bear and microscope. How do we observe changes in familiar scenes very fast?

9. Man versus Machine (hardware)
Numbers
Human brain
Von Neumann
computer
# elements
neurons
transistors
# connections / element 10
switching frequency
103 Hz
109 Hz
energy / operation
10-16 Joule
10-6 Joule
power consumption
10 Watt
Watt
reliability of elements
low
reasonable
reliability of system
high
Getallen voor de van Neumann computer veranderen met voortschrijden technologie
(Moore en Shannon)

10. Man versus Machine (information processing)
Featuresa
Human Brain
Von Neumann
computer
Data representation
analog
digital
Memory localization
distributed
localized
Control
Processing
parallel
sequential
Skill acqazuisition
learning
programming
Inzicht in hoe information processing in de hersenen verloopt staat nog in de kinderschoenen
In ieder geval is er sprake van een gelaagde structuur
No memory management,
No hardware/software/data distinction

11. Brain Performance

12. Flies have a better stabilizing mechanism than a Boeing 747 Their gyroscope is being studied in a wind tunnel

13. The bat’s external ears pick up both the emitted sounds and the returning echoes to serve as the receiving antennas. Echo delay estimation 20 nanoSec!!

14. Movies: Navigation DARPA Robot Race

15. Dolphin’s sonar properties
Send up to 200 clicks per second!
Frequency range 15 kHz – 120 kHz
Excellent sensor array (whole face)
Discriminate between alloys of aluminum
‘See’ a tennis ball from 75 meters
Distinguish between a penny and dime from 3 meters
Detect fish buried .5 meter underground
Excellent shape discrimination (same material)
Add here a picture of the dolphin head sensor array
W. W. L. Au (1993) The sonar of dolphins. (Springer).

16. Brief Outline Unsupervised Learning Short bio motivation
Unsupervised Neuronal Model
Connection with Projection Pursuit and advanced feature extraction
Supervised Learning Schemes
Perceptron and Multi Layer Perceptron
RBF, SVM, Trees
Training and optimization
Model Selection and Validation (advanced training methods)
Cross Validation, Regularization, Noise injection
Ensembles
Brain Machine Interface
EEG, fMRI modalities
Brain state interpretation based on machine learning model
Recent Research in BMI

17. Introduction to the Brain
By: Geoffrey Hinton

18. A typical cortical neuron
Gross physical structure:
There is one axon that branches
There is a dendritic tree that collects input from other neurons
Axons typically contact dendritic trees at synapses
A spike of activity in the axon causes charge to be injected into the post-synaptic neuron
Spike generation:
There is an axon hillock that generates outgoing spikes whenever enough charge has flowed in at synapses to depolarize the cell membrane
axon
body
dendritic
tree

19. A Neuron

20. The synaptic junction
Synapses, Ca influx, release of neurotransmitter, opening of post-synaptic channels

21. Some relevant terms Axon, dendrite Ion channels
Membrane rest potential
Action potential, refractory period
inputs per neuron,
Na, K, Cl and Ca channels
Action potentials enable cell to cell communication, unlike sub threshold membrane potentials that attenuate over small distances.

22. The Biological Neuron 10 billion neurons in human brain
Summation of input stimuli
Spatial (signals)
Temporal (pulses)
Threshold over composed inputs
Constant firing strength
The soma is the cell body
billion synapses in human brain
Chemical transmission and modulation of signals
Inhibitory synapses
Excitatory synapses

23. Biological Neural Networks
10,000 synapses per neuron
Computational power = connectivity
Plasticity
new connections (?)
strength of connections modified

24. Neural Dynamics Action potential ≈ 100mV
Activation threshold ≈ 20-30mV
Rest potential ≈ -65mV
Spike time ≈ 1-2ms
Refractory time ≈ 10-20ms
Refractory time

25. The Artificial Neuron Neuron i Stimulus Response x1(t) wi1 x2(t) wi2
yi(t)
wi4
Response
x4(t)
wi5
x5(t)
Neuron i
urest = resting potential
xj(t) = output of neuron j at time t
wij = connection strength between neuron i and neuron j
u(t) = total stimulus at time t

26. Artificial Neural Models
McCulloch Pitt-type Neurons (static)
Digital neurons: activation state interpretation (snapshot of the system each time a unit fires)
Analog neurons: firing rate interpretation (activation of units equal to firing rate)
Activation of neurons encodes information
Spiking Neurons (dynamic)
Firing pattern interpretation (spike trains of units)
Timing of spike trains encodes information (time to first spike, phase of signal, correlation and synchronicity

27. Binary Neurons ex: Perceptrons, Hopfield NNs, Boltzmann Machines
Stimulus
Response on
“Hard” threshold
off
= threshold
ex: Perceptrons, Hopfield NNs, Boltzmann Machines
Main drawbacks: can only map binary functions, biologically implausible.

28. Analog Neurons ex: MLPs, Recurrent NNs, RBF NNs...
Stimulus
Response on
“Soft” threshold
off
ex: MLPs, Recurrent NNs, RBF NNs...
Main drawbacks: difficult to process time patterns, biologically implausible.

29. Spiking Neurons Stimulus Response = spike and afterspike potential
urest = resting potential
e(t,u(t)) = trace at time t of input at time t
= threshold
xj(t) = output of neuron j at time t
wij = efficacy of synapse from neuron i to neuron j
u(t) = input stimulus at time t
Response

30. Spiking Neuron Dynamics
y(t) 
urest+(t-tf)

31. Hebb’s Postulate of Learning
When an axon of cell A is near enough to excite a cell and repeatedly or persistently takes part in firing it, some growth process or metabolic change takes place in one or both cells such that A’s efficiency as one of the cells firing B is increased.
Hebb’s postulate captures plasticity of the synapses
This does not capture inhibitory synapses
Simple form of Hebb’s rule is the product rule F(y, x) = \eta * y * x
The mathematical form does

32. Hebb’s Postulate: revisited
Stent (1973), and Changeux and Danchin (1976)
have expanded Hebb’s rule such that it also models inhibitory synapses:
If two neurons on either side of a synapse are activated simultaneously (synchronously), then the strength of that synapse is selectively increased.
If two neurons on either side of a synapse are activated asynchronously, then that synapse is selectively weakened or eliminated.a
Synchrony and asynchrony have to do with firing frequency

33. Synapses
When a spike travels along an axon and arrives at a synapse it causes vesicles of transmitter chemical to be released
There are several kinds of transmitter
The transmitter molecules diffuse across the synaptic cleft and bind to receptor molecules in the membrane of the post-synaptic neuron thus changing their shape.
This opens up holes that allow specific ions in or out.
The effectiveness of the synapse can be changed
vary the number of vesicles of transmitter
vary the number of receptor molecules.
Synapses are slow, but they have advantages over RAM
Very small
They adapt using locally available signals (but how?)

34. How the brain works Each neuron receives inputs from other neurons
Some neurons also connect to receptors
Cortical neurons use spikes to communicate
The timing of spikes is important
The effect of each input line on the neuron is controlled by a synaptic weight
The weights can be
positive or negative
The synaptic weights adapt so that the whole network learns to perform useful computations
Recognizing objects, understanding language, making plans, controlling the body
You have about neurons each with about 10 weights
A huge number of weights can affect the computation in a very short time. Much better bandwidth than pentium. 11 3

35. Modularity and the brain
Different bits of the cortex do different things.
Local damage to the brain has specific effects
Specific tasks increase the blood flow to specific regions.
But cortex looks pretty much the same all over.
Early brain damage makes functions relocate
Cortex is made of general purpose stuff that has the ability to turn into special purpose hardware in response to experience.
This gives rapid parallel computation plus flexibility
Conventional computers get flexibility by having stored programs, but this requires very fast central processors to perform large computations.

36. Idealized neurons
To model things we have to idealize them (e.g. atoms)
Idealization removes complicated details that are not essential for understanding the main principles
Allows us to apply mathematics and to make analogies to other, familiar systems.
Once we understand the basic principles, its easy to add complexity to make the model more faithful
It is often worth understanding models that are known to be wrong (but we mustn’t forget that they are wrong!)
E.g. neurons that communicate real values rather than discrete spikes of activity.

37. Linear neurons These are simple but computationally limited
If we can make them learn we may get insight into more complicated neurons
bias
i input th y
weight on b
output th i
input
index over
input connections

38. Binary threshold neurons
McCulloch-Pitts (1943): influenced Von Neumann!
First compute a weighted sum of the inputs from other neurons
Then send out a fixed size spike of activity if the weighted sum exceeds a threshold.
Maybe each spike is like the truth value of a proposition and each neuron combines truth values to compute the truth value of another proposition! 1
1 if y
0 otherwise z
threshold

39. Linear threshold neurons
These have a confusing name.
They compute a linear weighted sum of their inputs
The output is a non-linear function of the total input y
0 otherwise z
threshold

40. Sigmoid neurons
These give a real-valued output that is a smooth and bounded function of their total input.
Typically they use the logistic function
They have nice derivatives which make learning easy (see lecture 4).
If we treat as a probability of producing a spike, we get stochastic binary neurons. 1
0.5

41. Types of connectivity output units Feedforward networks
These compute a series of transformations
Typically, the first layer is the input and the last layer is the output.
Recurrent networks
These have directed cycles in their connection graph. They can have complicated dynamics.
More biologically realistic.
hidden units
input units

42. Types of learning task Supervised learning
Learn to predict output when given input vector
Who provides the correct answer?
Reinforcement learning
Learn action to maximize payoff
Not much information in a payoff signal
Payoff is often delayed
Unsupervised learning
Create an internal representation of the input e.g. form clusters; extract features
How do we know if a representation is good?