Download Brain(annotated)

Brains…
Ted Brookings
10/18/05
Outline
 Review of Neurons
 Typical Structure
 Interaction
 Information
 Understanding Cognition
 Primitive Neural Nets
 Hawkins’ Ideas
 What the @$&# I’ve been doing
(Hopefully Less Primitive Neural Nets)
A Typical Neuron
Dendrites: numerous small,
branching processes that
conduct signals
Axon: a single, relatively large
process for conducting signals
Synapses: a signal interface
between cells
Myelin Sheath: a separate cell
that wraps around the axon,
speeding up transmission speed.
Stereotypical Interaction
Stereotypically, a neuron receives signals from its dendrites. It
sends signals down its axon to the synapses, where it is transmitted
to the dendrites of a connected neuron (or some enervated tissue).
In the cortex, a typical
neuron will send signals
to ~10,000 postsynaptic
neurons.
Synapses don’t transmit the spike with
perfect efficiency. It will typically take
tens of spikes in a short time to excite the
postsynaptic neuron. The efficiency
varies from connection to connection, it
can even be negative (inhibiting spikes
rather than exciting them).
Neuronal Code: Where is the
Information?
PULSE SHAPE:
 Neurons act as integrators
 Spikes are short (1-2 ms)
 Ion channels have active
control
Neurons send information via spikes, but what
aspects of the spikes encode the information?
It takes many incoming spikes (e.g. 10-50) to
initiate a spike in a neuron. Incoming spikes
are temporally very short, and the neuron
essentially integrates until a threshold is
reached. There are nonlinearities in this
process, but to a large extent, pulse formation
is independent of incoming pulse shape. Also,
if an action potential IS triggered, the neurons
ion channels actively work to produce a
uniform shape, regardless of incoming shape.
=>No (or very little) information in pulse-shape
Neuronal Code: Where is the
Information?
TIMING:
 Spikes are stochastic
 Coding via average firing
rate?
 Short response times to
visual stimuli:
 fly (30-40 ms, 1-2 spikes)
 Human (few hundred ms)
30 neurons over 4 sec.
Comments on next page…
By saying spikes are stochastic, I mean that their arrival times are not regular or (easily)
predictable. Exact timing may depend on thermal fluctuations, or it may be due to the
complexity of many neurons being wired together, or both.
An early hypothesis was that information was encoded in the average firing rate of a neuron.
Presumably the brain averages the number of received spikes over some time window.
However, there are problems with this theory. Visual response times in the fly, humans, and
other animals are far too quick to permit much averaging.
A more likely view is that the information is encoded in exact spike times (and also the
strength of synaptic connections). Thus neurons are communicating by sending numbers
(times) to each other, and interpreting that information via synaptic strengths.
Understanding Cognition
Traditional Neural Nets:
Typically Three layers
Feed-forward
Spikes last infinitely long (i.e.
neurons are excited
permanently or not at all)
Training is an algorithm to update
weights in order to achieve
the correct “answer”
Comments on next page…
In traditional neural networks, the first layer (the “input layer”) is stimulated directly. For instance, if
a bitmap is being analyzed, a neuron may be sensitive to a particular pixel of the image. The input
layer in turn stimulates the second layer (“hidden layer”). The hidden layer stimulates the “output
layer” which corresponds to results. For example, if the net is supposed to analyze images, one
particular neuron in the output layer may have its activity correspond to seeing a circle.
There are no connections between neurons of the same layer, and no connections leading backwards.
If a neuron is stimulated, it is stimulated for all time. Thus a pattern of input leads to a constant
pattern of neuron stimulation ---there are no brief spikes, and no dynamics.
In order to learn, the net is subjected to a training set (a set of inputs) with known correct answers.
An input from the training set will cause the net to display some pattern of activity in the output layer.
The correct answer is known, and an algorithm is used to update the weights in the connections
between the three layers in order to force the net to obtain the correct answer. By exposing the net to
many training examples it is hoped that it has somehow abstracted commonalities between them, and
can accurately respond to future inputs.
Obviously these properties have no basis in biology. Feedback and dynamics are essential properties
of cognition, so biologically realistic neural nets must work differently. It should be noted that while
many neural nets have the form described above, many have attempted more realistic design.
On Intelligence (Jeff Hawkins)
Intelligence is internal, not behavioral (Chinese room)
Intelligence is (mostly) due to the cortex
Understanding the structure/behavior of the cortex is the key to
understanding intelligence
Traditional neural networks have little in common with the
cortex
Comments on next page…
My Chinese room rant:
The Chinese room is a room filled with a non-Chinese speaker. Chinese writing is shoved into the room,
and the person in the room follows instructions written in a book. The book tells this person to
manipulate the symbols, and eventually to shove the results out of the room. The presumption is that
if the instructions in the book are sufficiently complicated then it could convince a human that it is
intelligent. However, since neither the hum
I believe that Hawkins (and some others) overstated their case with the Chinese room. Consider instead a
series of Chinese rooms. The first is as above. The second has many operators with many books, all
working together and passing each other messages. The final has done away with operators and
books: instead they are replaced by cells, the cells send each other messages and follow rules
according to “rule books” that are encoded into their construction. This third room is the same as a
brain! I think that even the first room would be capable of genuine intelligence, simply by allowing
the operator to write on and erase sections of the book. In MY opinion, there are two real problems
with the setup of the original Chinese room:
1)
There is no (explicit) memory. If the writer can’t alter the book, it can’t learn. Suppose you ask the
Chinese room a question and get an answer. You find the answer is wrong and tell the it. Then if
you ask it the same question, you will still get the same answer ---clearly not intelligent behavior
2)
The setup imagines careless questioning falling prey to some trick. Anyone testing the Chinese room
to see if it exhibits genuine learning will quickly realize that something is wrong, even if its
conversation Chinese is very good.
I believe that behavior IS a valid way of testing for the presence of intelligence, however the tests must be
chosen carefully. I will return to this later. Hawkins believes that intelligence has an internal reality,
apart from any behavior, and emphasizes this. I agree with that.
Cortical Layers
The cortex is a sheet,
approximately
2mm thick and
“the size of a
dinner napkin”
It is scrunched up in
order to fit inside
the skull
Notice that the layers are visible (when
dyed appropriately) ---they are real
structures. However, they are also fuzzy.
Also remember that the physical location
of neurons is not terribly important: it’s
the wiring that really matters.
Cortical layers
Cortical Columns
The cortex also possesses distinct
columns running
perpendicular to the layers.
Cortical columns
Mountcastle’s Theory
Layers and columns are small and ubiquitous
There are few large-scale features in the cortex
However, there are many functions
Therefore, every region of the cortex is (essentially) the same,
and carrying out the same cortical algorithm. Only the data being
processed varies.
Hawkins scheme
The cortex has a few main functions
Hierarchically summarizes/abstracts data
Supplies predictions/feedback
Recognizes missed predictions and passes back error
Creates and recognizes “invariant representations”
These are (my abstraction of) the basic
principles of Hawkins theory of how the
cortex works. Each of these points will
be touched on in detail.
Hierarchy
The cortex is divided into regions by function and hierarchy. Example:
the visual system.
Visual information flows from the retina, into a region of the cortex
known as V1, which feeds into a different region known as V2, which
feeds into V4, followed by IT.
Lower-level regions (such as V1) process simple information (e.g.
responding to vertical lines)
Higher-level regions process complex information based on the
abstracted results in lower-level regions (e.g. responding to a face)
Feedback
There are at least as many connections running from high regions to
low as from low to high.
So if a higher region expects to see a face, it passes back the expected
lines, etc. to lower regions.
In order to pass back expectations, the higher-level regions must have an internal model of the
world. This model sends the sense experience that it expects the lower region to receive.
Errors and Feed-Forward
Data expected by higher-level cortical regions is compared with
information flowing up from lower regions
Data agreements are passed downward
Data disagreements (e.g. an object moved) are passed upward to
refine predictions
Data agreements mean that the internal model (predictions from higher regions) continues to
be accurate. Disagreements occur when the model is incorrect (something unexpected
happens). In that case, the novel sense information is passed upwards to adjust the model.
Thus we “see” what we expect to see, and only notice things that clash with our expectations
---the basic principle of magicians’ work.
Invariant Representations
It should be pointed out that Hawkins believes these representations are localized to specific neurons
(i.e. they don’t “float” from one cortical region to another).
Patterns of activity represent ideas/objects/sense-data
Activity must be invariant to position/timing, etc.
(a face is a face, even if it is upside-down)
Activity must be robust against incomplete information
Patterns must be learned (we are not born with a finite
supply of conceivable ideas/objects)
These invariant representations form the basis of
communication between cortex regions
Hebbian Learning
“Neurons that fire together, wire together.”
Experiment: stimulate a presynaptic
neuron and a postsynaptic neuron, observe
changes in the synaptic strength
Promotes recognition of coincidences (i.e.
patterns)
Cells that fire together with a certain
stimulus form an invariant representation
Comments on next page…
The diagram shows a Hebbian learning experiment. Neuron j sends signals to neuron i. If j fires
first, then i afterwards the connection between them is strengthened. If i fires first the connection is
weakened. The magnitude of this effect decreases exponentially as the time between events
increases.
This type of learning will promote the learning of coincidence: if two invariant representations are
activated simultaneously on a regular basis, they will eventually stimulate each other. The presence
of one will cause the brain to infer the other.
Hawkins Summary
Hebbian learning creates “invariant representations”
Mental model in higher cortical regions predicts input from
senses and lower regions
Input from lower cortical regions updates the model (when
conflicts are observed)
We “see” the model, not direct data from our senses
Of course, other senses work the same way, and are
integrated in even higher regions of the cortex.
Some Issues
Birds (which have no cortex)
have displayed some intelligent
behavior
Some areas of the visual
cortex are suspiciously both
highly-specialized and
common to all people (e.g.
recognition of faces, objects,
and motion)
The layers and columns in the
cortex may be due to ontogony
Comments on next page…
In addition to tool-making (which is an intelligent, learned behavior, not extinctive), birds have
displayed many other intelligent behaviors. Some parrots have learned to use (very simple)
language, that is to say, they use words in context and in simple phrases (not mere mimicry). Birds
lack a cortex, although they have other brain structures that serve a similar function. Thus the
exact structure of the cortex is not necessary for intelligence. Investigating the cortex structure is
still a valid tactic however, as the cortex is one way of producing intelligence.
There are parts of the brain (discovered via brain-damaged people) that have very specialized tasks.
1)
Seeing faces. When a part of the brain is damaged, the person can no longer recognize faces, not
even their own.
2)
Seeing objects. People with a specific area damaged will no longer be able to recognize objects.
They may be able to figure out what they are (“It’s big and green…. Is it a tree?”) but can’t
recognize them the way we can
3)
Seeing motion. People rely on a part of the brain to detect motion. When it is damaged, moving
objects are confusing and disturbing, their behavior difficult to predict.
One could argue that such regions develop automatically early in development and can’t be relearned
later in life. However, I saw a documentary once were a sighted person was blindfolded for a week
and taught Braille. When she read, the visual cortex was stimulated (even though she was using
her touch sense). This suggests to me that there is some flexibility in the cortex, but some things
that are specific to a certain task. I don’t believe that the cortex is completely uniform, but rather
that the wiring structure has adapted to solve certain categories of problem, while the physical
layout is (mostly) uniform.
Ontogony refers to the development of an embryo.
Structure Formation
Early embryo is shaped like a disk
CNS originates in ectoderm
Embryo and disk fold into tubes
(in opposite directions)
Neural tube sinks into body tube
 The CNS is topologically a hollow tube
 The formation of the brain is simply a
thickening of one end of the tube
 Many structures in the brain can be traced
back to original locations on the neural plate
---this is called a fate-map
 However, there is migration of neurons
between locations, and extensive wiring
between regions
I argue that all this means that the mere presence of layers and columns doesn’t necessarily argue that
they are critical for cognition. They could be entirely due to ontology, or even have a mix of ontology
and function…
Structure vs. Systems
Structures in the brain have purpose, just as structures in
the body have purpose. However, structures in the brain
have many neural systems within them, just as structures
in the body have many systems.
Example: the neck.
Attaches head to body, allows pivoting
Contains part of circulatory system, respiratory system,
and various nervous systems
…and even in the case where a structure IS the result of function, it doesn’t stand to reason that there is
only one function.
Toward a More Realistic Neural
Network
Simplify properties not essential for the basic functioning of
the network:
Spike shape is (largely) irrelevant, so model spikes as
Dirac-deltas Actually just store a list of spike times and amplitudes.
Simplify response of neurons ---model as perfect
Add up incoming spike amplitudes (with some temporal decay).
integrators
amplitude exceeds a threshold, a spike is produced in the neuron.
Keep essential properties:
Feedback
Hebbian learning
MANY connections per neuron
If the
What About Structure?
Cognition depends on network structure (wiring, not location)
Cortical structure is complicated, unnecessary, and the wiring
is largely unknown
That is to say, it seems fruitless to attempt to recreate the human brain if something simpler
can work as well (or better) for my purposes.
Return to the Chinese room, but choose tasks carefully
Use an evolutionary algorithm to incrementally improve
performance
Choose tasks that require learning. One can monitor this learning by testing the networks with novel
tasks, and monitoring progress. If actual learning is taking place, one would expect performance to
increase over time.
More on next page…
The Chinese room can be used to test if intelligence exists, but in order to actually create the structure
necessary for intelligence, an evolutionary algorithm will be used. A carefully chosen problem will be
presented to each generation, and a population of neural nets will be tested against several examples of
this problem. Those that score well will reproduce (with mutation) and go on to the next generation.
Each succeeding generation must have the tests changed sufficiently that the previous tests would not
prepare them to succeed with the new test (i.e. they are not genetically programmed to pass the tests,
they are genetically programmed to learn to pass).
Practical Problems
Speed:
The presence of feedback loops necessitates
updating neuron and synapse states frequently
The kind of computation that must be done is
more taxing than is frequently estimated
Memory usage:
e.g. Hebbian learning requires computation, and is
usually not included in estimates of brain power
Many neurons and realistic numbers of
synapses per neuron results in a huge number
of synapses
Each of those synapses must record the
spikes that pass through it for one time-step
“Progress” So Far…
Code is completed!
Program Results:
Segmentation Faults
Bus Errors
Infinite Loops