Transcript Structures and Learning Simulations

Computational Intelligence
Structures and
Learning
Simulations
Based on a course taught by
Prof. Randall O'Reilly
University of Colorado and
Prof. Włodzisława Ducha
Uniwersytet Mikołaja Kopernika
Janusz A. Starzyk
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Neurons and rules
Individual neurons allow to detect single features.
How can we use a neuron’s model?
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W  A  Wi Ai  2
Classical logic:
i 1
If A1 and A2 and A3 then Conclusion
e.g. If Headache and Muscle ache and Runny nose then Flu
Neural threshold logic:
If M of N conditions are fulfilled then Conclusion
Conditions can have various weights; classical logic can be easily
realized with the help of neurons.
There’s a continuum between rules and similarity: for a few variables,
rules are useful; for many others, similarity.
|W-A|2 = |W|2 + |A|2 - 2W.A = 2(1 - W.A), for normalized X, A,
so a strong excitation = a short distance (large similarity ).
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Pandemonium in action
Demon (gr. daimon - one who divides or distributes),
Demons observing features:
| vertical line
D1
-- horizontal line
D2
/ forward slash
D3
\ backslash
D4
V
T
A
K
demons 3, 4
=>
D5
demons 1, 2
=>
D6
demons 2, 3, 4
=>
D7
demons 1, 3, 4
=>
D8
demons 6,7,8
=>
D9
The better it fits the louder they shout.
Demon making decisions: D9 doesn’t distinguish TAK from KAT ...
for this we need sequence recognition
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Each demon makes a simple decision but the entirety is quite complex.
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Simulations
What traits should we observe to understand speech? language?
images? faces? Act creatively?
http://psych.colorado.edu/~oreilly/cecn_download.html
Simulations: write equations describing how good is the fit, how loud
the demons should shout.
How to reduce biology to equations?
Synaptic efficiency: how strong
Activity of a presynaptic neuron: how
many vesicles, how much
neurotransmitter per vesicle, how much is
absorbed by the postsynaptic
Postsynaptic: how many receptors,
geometry, distance from the spine etc.
Extreme simplification: one number
characterizing efficiency.
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Neurons and networks
1.
2.
What properties does a neural network have?
How can we influence a neural network to do something
interesting?
Biology: networks are in the cortex (neocortex) and subcortical structures.
Excitatory neurons (85%) and inhibitory neurons (15%).
Generally excitations can be:
 mainly in one direction
 signal transformation;
 in both directions
 supplementing missing information
 agreeing upon hypotheses and strengthening weak signals.
 most excitatory neurons are bi-directional.
Inhibition: controls mutual excitations, necessary to avoid extra feedback
(epilepsy).
The entirety makes possible the interpretation of oncoming information in
the light of knowledge of its meaning, encoded in the network structure.
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General network structure
Does the cortex have some general properties or does its structure
depend on the function: perceptive, motor, associative?
There is a functional specialization of the cortex, observable differences
in various areas, from this comes the division into Brodmann’s fields.
The general scheme is retained:
•A excitatory neurons
• main NT is glutamic acid,
• AMPA receptor opens Na+ channels, excites long axons,
communication within and between neural groups
• NMDA receptor opens Ca++ channels, leads to learning
• around 85%, mainly pyramidal cells, spiny stellate cells + ...
•B
inhibitory neurons
• main NT is GABA (gamma-aminobutyric acid), opens Cl- channels,
interneurons, local projections, regulation of the excitation level;
• GABA-A short-term effect BAGA – B long-term effect
• around 15%: basket cells and chandelier cells + ...
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Pyramidal, spiny stellate, basket,
chandelier, spindle cells
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Excitatory and inhibitory neurons
Pyramidal and
spiny stellate
Glutamic acid
opens Na+
channels,
(excitatory),
GABA works on Clchannels inhibiting
excitation.
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Basket
chandelier
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Laminar structure
The cortex has a thickness of 2-4 mm
and consists of 6 layers, with different
thicknesses in different parts of the brain.
A
B
C
D
A - the visual cortex has a thicker
input layer 4a-c;
B - the parietal cortex has thicker
hidden layers 2 and 3;
C - the motor cortex has thicker
output layers 5-6;
D – the prefrontal cortex doesn’t
have markedly thicker
layers.
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Layer connections
Functional division of layers:
input layer 4, receives information from the thalamus, senses;
 output layers 5/6, subcortical centers, motor commands;
 hidden layers 2/3, transform local information and information from
distant neuron groups, coming through axons on layer 1.

In each layer we have local bidirectional connections.
Hidden layers: they extract certain
attributes of the signal, strengthen some
and weaken others; this enables the
realisation of complex signal
transformations.
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This kind of organization is also
required by episodic memory.
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Connections in more detail
these blocks may
be connected
sequentially
1) Input layer 4, initial processing of outside information.
2) Hidden layers 2/3, further processing, associations, a little I/O.
3) Output layers 5/6, subcortical centers, motor commands.11
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Simple transformations
Unidirectional connections are rare, but this model can be generalized
to a situation with feedback.
Bottom-up processing: collectively, neural detectors perform
transformations, categorize chosen signals, differentiating similar from
dissimilar ones.
Detectors create a representation
of information coming in to the
hidden layer.
Simplest case:
binary images of digits in a 5x7
grid on input, all images similar to
the given digit should activate the
same unit hidden in the 5x2 grid.
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Digit detector - simulation
We activate the PDP++ simulator, leabra++.exe
(Menu Start, or PDP++/bin/CYGWIN)
In the PDP++ window we select .projects, open in root
we exit the catalog ../ twice, we enter sims/
we select chapter_3, then transform.proj.gz
The window ...Network_0
shows the network structure, two
layers, input and output.
Looking at the weights connected
with the selected hidden unit:
we click on r.wt, and then on the
given unit: the weights are
matched precisely to the digits.
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Digit detector - network
Input weights for
the selected digit
r.wt shows
weights for
hidden units, here
all 0 or 1.
s.wt shows
individual
connections, eg.
the left upper
input corner =1
for 5 and 7.
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Digit detector - operation
Instead of r.wt we select
act (in ...network_0).
In the control window
xform_ctrl we select
step, activating one
step, the presentation of
successive digits.
The degree of activation of the hidden
units for the selected digit is large
(yellow or red color), for the others it
is zero (gray color).
Those easily distinguished, eg. 4,
have a higher activation than those
which are less distinct, eg. 3.
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GridLog
What is the activity of individual
detectors in response to a single
input image?
In the control window xform_ctrl
we select view, GridLog.
For
each image all units activate
to a certain degree;
we can see here the large role
of the thresholds, which allow us
to select the correct unit;
in the ctrl window we can turn
off the thresholds (biases off)
and see that some digits are not,
recognized.
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Events window
From the window xform_ctrl we select Events: we see all images,
here we can change them, remove or add new ones.
Adding bit 1 to the
image: click on
square;
removing a bit:
shift+click.
The selection in
the lower left
corner will show a
larger window with
this image.
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Similarity of images
From the window xform_ctrl we select Cluster and Cluster digits.
Clustering with the help of a dendrogram illustrates the reciprocal
similarity of vectors, the length of line d(A,B) = |A-B|.
Hierarchical
clustering of vectors
representing input
images: highly
probable are the
digits 8 and 3:
13 identical bits, as
well as 4 and 0, only
4 common bits.
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Likelihood of distorted images
From the window xform_ctrl we select Noisy_digits, Apply and Step
observing in window Network_0, we watch act, awakening of hidden
neurons.
We have image + 2
distorted,
likelihood of
distorted digits is
shown by the
dendrograms.
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Leakage channels (potassium)
A change in the conductivity of the leakage channels affects the selectivity
of neurons, for smaller values of ĝl the answers become gradual.
In the window xform_ctrl we will decrease ĝl =6, to 5 i 4.
More associations  less precision.
ĝl =6
ĝl = 5
ĝl = 4
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Letters
We will apply the network for digits to letters... only S resembles 8, the
other hidden units don’t recognize anything.
Detectors are specialized for specific tasks!
We won’t recognize Chinese characters if we only know Korean.
Dendrograms for the representation of letters before and after the
transformation.
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What
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Local and distributed representations
Local representations : one hidden neuron represents one image
these neurons are referred to as grandmother cells.
Distributed representations : many neurons respond to one image, each
neuron takes part in reactions to many images.
Observation of the neural
response in the visual
cortex of a monkey to
different stimuli confirms
the existence of distributed
representations
http://www.brain.riken.go.jp/labs/cbms/tanaka.html - nice demo.
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Distributed representations
Images can be represented in a distributed manner by
an array of their traits (feature-based coding).
Traits are present "to a certain degree."
Hidden neurons can be interpreted as the degree of
detection of a given feature – that's what you do in fuzzy
logic.
Advantages of distributed representation (DR):
 Savings: images can be represented by combining the activation of
many units; n local units = 2n combinations.
 Similarity: similar images have comparable DR, partly overlapping.
 Generalization: new images activate various DR usually giving an
approximation to sensory response, between A and B.
 Resistance to damage, system redundancy.
 Exactness: DR of continuous features is more realistic than discrete
local activations.
 Learning: becomes easier for continuous small changes in DR.
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Experiment with RR
Project loc_dist_proj.gz from chapter_3.
To represent digits we now use 5 units.
The network reacts to the presence of certain
features, eg. the first hidden neuron reacts to =>
Distributed representations can work even on
randomly selected traits: new DR = projection of
input images to some feature space.
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Gridlog shows the distribution
of net activation and output of
the network, showing the
degree of presence of a given
feature.
The dendrogram looks
completely different than for a
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local network.
Feedback
Networks almost always have feedback between neurons.
Recurrence: secondary, repeated activation; from this come networks
with recurrence (bidirectional).
Bottom-up and vice versa, or recognition and imagination.
Recurrence makes possible the completion of
images, formation of resonances between
associated representations, strengthening of weak
activations and the initiation of recognition.
Example: recognize the second letter in simple words:
CART (faster)
BAZS (slower)
Strange: text recognition proceeds from letters to words;
so how does a word help in the recognition of a letter?
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Recurrence for digits
A network with a hidden layer 2x5, connected bi-directionally with the
inputs.
Symmetrical connections: the same weights Wij=Wji.
The center pixel activates 7 hidden neurons,
each hidden neuron activates all the pixels of a
given digit, but the inputs are here always taken
from the images of the digits.
Combinations of
hidden neuron
activations
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Completion of images
Project pat_complete.proj.gz in Chapter_3.
A network with one 5x7 layer, connected bi-directionally
with itself.
Symmetrical connections: the same weights Wij=Wji.
Units belonging to image 8 are connected to
themselves with a weight of 1, remaining units have a
weight of 0.
Activations of input units here are not fixed by the
images (hard clamping), but only initiated by the
images (soft clamping), so they can change.
Check the dependence of the minimum number of
units sufficient to reconstruct the image from the
conductivity of ion channels.
For a large ĝl start from a partial image requires a
greater and greater number of correctly initialized
pixels, for ĝl = 3 we need >6 pixels, for ĝl = 4 we need
>8 pixels, for ĝl = 5 we need >11 pixels.
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Recurrent amplification
Project amp_top_down.proj.gz in Chapter_3.
From a very weak activation of some image,
amplification processes can lead to full activation of the
image or uncontrolled activation of the whole network.
The network currently has two hidden layers.
A weak excitation leads to a growth
in activation of neuron 2, and
reciprocal activation of neuron 1.
For a large ĝl>3.5 the effect
disappears.
The same effect can be achieved through feedback inside a single layer.
Weak activation of letters suffices for word recognition, but word
recognition can amplify letter activation and accelerate the response.
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Amplifying DR
Project amp_top_down.dist.proj.gz in Chapter_3.
Distributed activation can lead to uncontrolled
activation of the whole network.
Two objects: TV and Synthesizer; 3 features: CRT
monitor, Speaker and Keyboard.
The TV has CRT and Speaker, the Synthesizer has
Speaker and Keyboard – one feature in common.
Feedback leads to activation of layer 1, then 2, then
1 again, repeatedly.
From the ctrl panel we select View/Grid_Log, then RunUniq.
Starting from an arbitrary activation at the input, Speaker activates both
neurons, TV and Synthesizer, and all 3 features in layer 1, in effect all
elements are completely active.
Manipulating the value of ĝl ~ 1.737 shows how unstable these networks
are => we need inhibition!
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Inhibitory interactions
We need a mechanism which reacts dynamically, not a constant leak
current – negative feedback, inhibitory neurons.
Two types of inhibition: thanks to the use of these same input
projections, we can anticipate activations and inhibit directly; this
selective inhibition allows for the selection of neurons best suited to
specific signals.
Inhibition can also be a reaction to excessive activation of a neuron.
Inhibition leads to rare distributed representations.
Feedforward inhibition: depends on
the activation of the lower level
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Feedback inhibition: reacts to
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activation within the layer
Inhibitory parameters
A model with inhibitory neurons is costly: there are additional neurons and
the simulation must be done with small increments in time to avoid
oscillation.
We can use simpler models with competition among neurons, leading to
the selection of a generally small number of active neurons (sparse
distributed representation).
Inhibitory parameters:
 g_bar_i_inhib, self-inhibition of a neuron
 g_bar_i_hidden, inhibition of hidden neurons
 scale_ff, weight of ff connections, input-inhibition
 scale_fb, weights of reciprocal connections
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WTA and SOM approximation
Winner
Takes All, leaves just 1 active neuron
and doesn't lead to distributed representation.
In the implementation of Kohonen’s SOM the
winner is chosen along with its neighborhood.
Activation of the neighborhood depends on
distance from the winner.
Other approaches use combinations of
excitatory and inhibitory neurons:
 McClelland and Rumelhart – interactive
activation and competition;
introduced the superiority of the higher
layer over the lower, allowing for the
supplementation of missing features and
making predictions
 Grossberg introduced bi-directional
connections between layers using
minicolumnar structures
separate inhibitory neurons
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Layer 6
- next
layer
interaction
poziome
2/3
feedback
4
5
inhibition
poziome
6
input activation
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kWTA approximation
k Winners Take All, the most common approximation leaving only k active
neurons.
Idea: inhibitory neurons decrease activation so that no more than k
neurons can be active at the same time.
Find the k most active neurons in the layer; calculate what level of
inhibition is necessary so that only these remain above the threshold.
•The
distribution of activation levels in a
larger network should have a Gaussian
character.
•We have to find this level of threshold
activation giQ so that for a value between k
and k+1 it could be balanced by inhibition:
•
Two methods: basic and averaged.
•Weaker
winners are eliminated by the
minimal threshold value
•kWTA model constitutes a simplification
of biological interactions
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Basic kWTA
Equilibrium for potential Q for which currents don't flow is established by
the level of inhibitory conductance.
For confirmation, that only k neurons are above the threshold we take:
Typically constant q=0.25; depending on the distribution of excitation
across the layer, we can have a clear separation (c) or inhibit highly active
neurons (b).
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Averaged kWTA
In this version inhibitory conductance is placed between the average of
the k most active neurons and the n-k remaining neurons.
An intermediate value is computed from:
Depending on the distribution we have in (b) a lower value than before
but in (c) a higher value, which gives somewhat better results.
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Projects with kWTA
Project inhib.proj.gz in Chapter_3.
Input 10x10,
hidden layer 10x10
2x10 inhibitory neurons,
realistic proportions.
A bi-directional network has a second
hidden layer; kWTA stabilizes excitation
leaving few active neurons.
Detailed description: section 3.5.2 i 3.5.4
Project inhib_digits.proj.gz in Chapter_3.
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Constraint satisfaction
Environmental activations, and internal inhibition and activation
compatible with the fixed parameters of the network, form a set of
constraints on possible states; the evolution of activations in the network
should lead to satisfaction of these constraints.



Attractor dynamics
System energy
The role of noise
Changes in time, starting from
the "attractor basin,” or
collection of different starting
stages, approach a fixed state.
Attractor states maximize harmony between internal knowledge
contained in the network parameters and information from the
environment.
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Energy
The most general law of nature: minimize energy!
What does an energy function look like?
where the summation runs through all the neuron pairs.
Harmony = -E is greatest when energy is lowest.
If the weights are symmetrical then the minimum of this energy function
is at a single point (point attractor); if not then attractors can be cyclical,
quasiperiodic or chaotic.
For a network with linear activation the output is =>
The derivative of harmony = yj shows the direction
of growth in harmony.
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The role of noise
Fluctuations on the quantum level as well as the input from many
coincidental processes in the greater neural network create noise.
 Noise changes the moments of impulse transmission,
 helps to prevent local solutions with low harmony,
 supplies energy effecting resonance,
 breaks impasses.
Noise doesn't allow a fall into
routine, enables exploration of new
solutions, is also probably
necessary to creativity.
Noise in the motor cortex.
Demonstration of the role of noise in the visual system.
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Inhibition and constraint satisfaction
Constraint satisfaction is accomplished in the network by a parallel search
through the neuron activation space.
Inhibition allows us to restrict the search space, speeding up the search
process if the solution still exists in an accessible area of the state space.
Without kWTA all states
in the configuration of two
neurons are accessible;
the effect of kWTA
restriction is the
coordination of activation
of both neurons and a
decrease in the search
space.
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Constraint satisfaction: cats and dogs
Project cats_and_dogs.proj.gz in Chapter_3.
The knowledge encoded in the network is in the table.
The exercise described in section 3.6.4 leads to
A simple semantic network which can
Generalize and define unique characteristics
Show the relationship between characteristics
Determine if characterstics are stable
Supplement missing information
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Constraint satisfaction: Necker cube
Project necker_cube.proj.gz in Chapter_3.
Bistability of perception: this cube can be seen with its closest face facing
either left or right.
Bistable processes can be simulated allowing for noise.
The exercise is described in section 3.6.5.
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