1. Creating a Computational Model of Place
Cells using a Continuous Attractor
Neural Network
Jacob Elliot Senior: 12001071
Physics and Smart Systems BSc
CSC-30014
25th April 2016.
School of Computing and Mathematics
Keele University
Keele
Staffordshire
ST5 5BG
Word Count: Approx 8,700
2. “We live in a society exquisitely dependent on science and technology, in
which, hardly anyone knows anything about science and technology...”
Carl Edward Sagan
ii
3. Abstract
Presented in this paper is a computational model and simulation of Place Cells,
a type of cell found in mammals that aid the animal with navigation. A
Continuous Attractor Neural Network was implemented to represent the Place
Cells and a Virtual Robot was created along with 4 different Environments.
Numerous studies have been performed by biologists, looking at the activity of
these cells in Rats (O’Keefe and Conway 1978, Knierim and Rao 2003). The
results of the studies were produced by measuring the responses of the cells when
different conditions were applied to the environment. These conditions were
applied to the simulation, and the Activation Pattern of the output of the
CANN was recorded.
The different conditions applied in the simulation produced changes in the
Activation Patterns of the CANN. These were recorded and then compared to
the responses of Place Cells, recorded in the studies on rats mentioned above.
Alone the model discussed and implemented in this paper does not provide a
complete method of Robot Navigation; however, with further development,
combining it with other cells and behaviours such as, Head Directions Cells, Grid
Cells and Path Integration, which also aids the animal during its navigation, we
begin to see a potentially viable model for an alternative method of Robot
Navigation.
Some simplifications and omissions were made in the model mostly due to time
constraints, and these issues would clearly need to be addressed when
considering further development of this model.
iii
6. Acknowledgement
Before we begin, I would like to express my greatest thanks to Dr. Theocharis
Kyricaou for his guidance, encouragement and useful critiques of this work. Thanks
are also due to James Borg for running the module and for the freedom of choice
for final year projects.
Figures were taken directly from the simulation or created in Inkscape.
vi
7. Chapter 1
Introduction
The Hippocampus has become one of the most studied areas of the brain.
This is due to the discovery of its importance in memory, particularly long term
memory, as well as spatial memory and navigation (OKeefe and Conway, 1978).
This has led to research into the underlying mechanisms of this area of the brain,
as it could not only help to provide a better model of brain theory, but also has
relevance in the Computational Intelligence field. The activity and interactions of
different cells in the Hippocampus, could lead to more sophisticated methods to
implement robot navigation that are computationally cheaper and more flexible
than current popular methods (Kyriacou, 2011).
1.1 Place Cells
1.1.1 Background
Place Cells are found in the Hippocampus region of the brain in most mam-
mals (O’Keefe and Conway, 1978; O’Keefe, 1984; Samsonovich and McNaughton
1997). They are thought to assist in building and providing a cognitive or mental
map of an animal’s environment, to aid the animal in navigation (McNaughton et
al. 1998). The Place Cells that fire, and how strongly they fire given certain cues
from a pattern of activity known as the Place Field.
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8. Introduction
Studies on Place Cells have generally been performed using electrodes im-
planted into the brains of rats, providing a set of environments to navigate by
allowing them to explore different shaped mazes, monitoring the activity in the
cells (OKeefe and Conwy, 1978; Muller et al. 1994; OKeefe and Burgess, 1996).
Studies have also been performed, looking at the effect and changes to landmarks
in the environment in animals (Knierim, 2002; Scalpen et al. 2014) and landmark
and vision driven based models (Cruse, 2003; Lew, 2011; Deshmukh and Knierim,
2013).
Research performed over the last 40 years has suggested a mixture of de-
pendencies for the Place Fields, with some authors suggest that they are highly
dependant on the landmarks visible to the animal (OKeefe and Conway, 1978;
Jeffery, 2007). Minor movement in the locations of the landmarks will cause the
place field to also vary slightly; however, a larger change or removal of a landmark
would be perceived as a different environment entirely, producing a different Place
Field (Scalpen et al 2014) .
It has been proposed and observed that each time the animal returns to an
environment and they return to the same location within that environment, the
same Place Cells will fire to produce the same Place Field, thus providing a simple
form of location based memory.
There have been attempts at creating a computational model of Place Cells,
using visual landmarks as cues to Place Fields to fire (McNaughton et al. 1991;
Redish et al. 1996; Stringer and Rolls 2005;), which generally make use of a type
of Attractor Neural Network as the representation of the network of cells.
1.1.2 Computational Comparisons
Generally, the most popular current methods of implementing Robot Naviga-
tion involve either providing the robot with a pre-defined map of it’s environment,
or a programming technique to perform an operation known as Simultaneous Lo-
calisation and Mapping (SLAM) (Kyriacou 2011). The main disadvantages with
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9. Introduction
these methods are, with a pre-defined map, the robot’s environment will always
be limited to the size of the map given to it and the fidelity of the map. SLAM
was created to provide a solution for the problem of building a spatial map of an
unknown environment while maintaining the localization of the robot within the
environment (Thrun and Leonard, 2008).
The most prominent issue is that it often requires multiple, highly accurate
sensors, which can be costly in terms of both money and computational power
requirements (Newman et al. 2001). This is because for every update for the
localization of the robot, each sensor needs to take new readings and compare them
to the previous readings, and perform calculations that determine information such
as the distance travelled, angle rotated, speed etc. Having multiple sensors helps
reduce the total error within the system. This is essential to keep as minimal as
possible as a small error in every update would translate into a large total error
over long distances, due to the large number of updates. It also provides the
robot with back up systems so if a sensor breaks, the robot would still be able to
continue, albeit slightly less accurately. The main draw back is the more sensors
you introduce, the more computational power is required.
Place Cells are an interesting topic of research from a computational perspec-
tive. Creating computational models of different areas of the brain have helped
attain a better understanding of the underlying mechanisms of neurons, which in
turn led to more sophisticated models of brain theory and more advanced imple-
mentations and uses for robotics and artificial intelligence systems. As Place Cells
are thought to build a cognitive map for animals, they could potentially provide
a computationally cheaper environmental mapping method than SLAM, but also
a more flexible option to supplying the robot with a predefined map.
All animals have evolved their methods of navigation to best suit the environ-
ment they need to navigate, even the smallest animals have efficient and effective
methods of navigation, so perhaps to further develop robot navigation, inspiration
can be taken from the basic underlying mechanisms of animal navigation rather
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10. Introduction
than just trying to replicate the overall behaviours (Kyriacou 2011).
Of course, another key aspect of research is if it has any real world applica-
tions. When combined with computational models of other cells in the hippocam-
pus, such as Head Direction Cells and behaviours that aid navigation like Path
Integration, a different method to assist in, or possibly a full implementation of
robot navigation could be created.
1.2 The Simulation
1.2.1 Development Considerations
Java was chosen as the programming language primarily due to time con-
straints as it was the most familiar language, but it also has a number of ad-
vantages such as Platform Independence, and has an efficient garbage collection
system among others.
The Integrated Development Environment (IDE) used was Netbeans. This
is a complete environment for writing code, with features such as code comple-
tion, reference look up, debugging processes and an integrated GUI builder. The
other IDE available was BlueJ, which was not suitable for a large project as it is
considered to be an IDE to assist in learning how to code.
Although the software developed is for a specific purpose, and it was not too
complex, it was still necessary for Design Heuristics to be taken into consideration.
Jakob Nielsens heuristics are among the most popular used today, so were the
chosen set to be considered for the Simulation.
As this is fairly simple software, only a few of the heuristics were relevant.
Error prevention and User recovery from errors are two important heuristics for
any piece of software, as well as providing good and regular feedback with reason-
able timing as this increases the usability of the software. Some of the heuristics
such as ’Providing Shortcuts’ for experienced users and Recognition rather than
Recall are not relevant due to the lack of overall interactions between the User
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11. Introduction
and the Software.
1.2.2 Aims and Objectives
With all this taken into consideration, a set of aims and objectives can be
made for the project:
1. Create a model of Place Cells using a Continuous Attractor Neural Network
(CANN).
2. Implement the model into a simulation of a Virtual Robot.
3. Apply different conditions to the simulation and record the Activation Pat-
tern produced by the CANN.
4. Compare these to responses from studies performed by Biologists.
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12. Chapter 2
Methodology
Discussed in this section is how each component of the simulation was created
and implemented. For each part of the model and simulation, the most basic
element of the component was constructed first. This was then used to build the
next part of the component. For example, a CANN is a network of fully connected
nodes, so it was constructed by building a single node first, then creating multiple
of them. The connections between the nodes were initialised, the network was
trained, and finally the network was made to respond to an applied stimuli.
The CANN and Virtual Robot simulation were created separately and then
combined when a User Interface (UI) was created. Four different environments and
positions for the Virtual Robot were created, and three different test conditions
were applied to the simulation to see if the CANN behaved similarly to the Place
Cells of rats when exposed to the same conditions. The different tests applied to
the simulation were inspired by studies performed on rodents by Muller (1994),
Lew (2011) and Scalpen et al. (2014).
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13. Methodology
2.1 The Continuous Attractor Neural Network
2.1.1 Description
The type of neural network currently believed to best represent this type of
biological neural network is the CANN (Stringer et al. 2002, Kyriacou. 2011).
To better understand this system, the following analogy can be made. Imagine a
grid of 100 light bulbs, an amount of electricity is randomly applied to the grid,
enough to light up a single bulb maximally. A bulb is randomly chosen to light
up each time the current is applied. To spread the electricity throughout the grid
each bulb is then connected to every other bulb in the circuit. This time, when
the electricity is applied to a single bulb, multiple bulbs light up. However, as
there is only enough electricity to light up one bulb, only the light bulbs closest
to the one supplied with electricity manage to get enough power to light up.
Figure 2.1: A diagram of a 5x5 CANN, showing connections of the central node.
This is similar to an Artificial Neural Network. In this network, instead of
a grid of light bulbs, there is a grid of nodes, which are computational versions of
biological neurons. The nodes in this project have a variety of properties such as
its location in the grid, firing rate and activation. Each node is connected to every
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14. Methodology
other node, including itself, like the light bulbs in the analogy above. The strength
of the excitatory and inhibitory connections, and the initialisation of these prop-
erties are discussed in the Section 2.1.2. As in biology, the nodes have weighted
connections between them which are trained and adjusted during the network’s
learning phase. Returning to the light bulb analogy, the learning phase is akin
to changing the lengths of the connections between the light bulbs depending on
certain information or cues. This would result in a different dispersal of electricity
throughout the grid, which would make a different pattern of illuminated light
bulbs when the current is applied.
Attractor Neural Networks are recurrently connected network whose dynam-
ics allow it to settle into a subset of states. Different types of attractors have dif-
ferent useful implementations, Line Attractors are good for motor control, Point
Attractors are useful in long term memory and content addressable memory.
Continuous Attractors are one of the most apt artificial networks for Place
Cells. To explain why, another example is needed. Imagine a person is sitting
in his kitchen, a certain Place Field would be produced by his Place Cells for
that location. If his visual sense was removed and he had no other source of
information, the same Place Field would be produced by his Place Cells, as he
would have received no other information to suggest otherwise. If he was then
moved from his kitchen into his lounge (still with no visual sense and with no other
source of information), the Place Field would stay the same until the blindfold was
removed, and the Place Cells received the information they needed to update. This
is a property that Continuous Attractor Neural Networks possess, as they have
one or more quasi-continuous sets of attractors, allowing the activation pattern to
remain even if inputs are removed.
To find the Firing Rate, change in Synaptic Weights and Activation of the
Nodes, the equations below had to be implemented and used. These three variables
were combined to produce the Activation Patterns of the CANN, which was the
Place Fields produced in the simulation.
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15. Methodology
2.1.2 Equations implemented
The following equations were sourced from (Stringer et al. 2002, 2004). The
firing rate is initially set using equation 2.1 where α is the Sigmoid function, β is
the slope and hP
i (t) is the activation of place cell i.
rP
i (t) =
1
1 + exp[−2β(hP
i (t) − α)]
(2.1)
The synaptic weights between each node were initially set to a Gaussian function,
which produced excitatory and inhibitory connections described above, with a
location of peak activation. The firing rate and synaptic weights are then modified
during a learning phase.
There is a common phrase ”Practice makes Perfect”, this is, of course, re-
ferring to one of the most effective ways to improve a skill, through practise.
When someone attempts to perform a new task, a certain combination of neurons
in their brain activate. This activity pattern corresponds to the required bodily
operations to do the task. The more frequently the person performs this task,
the more effective those neurons will become at firing. The higher the efficiency
of firing, the better the person becomes at that task. This ability to grow and
strengthen synaptic connections is the fundamental basis of how humans learn to
perform new tasks. Drawing back to the light bulb analogy once more, it would
be akin to replacing the cables between the active bulbs to more efficient or more
conductive materials. This would result in more electricity reaching the bulbs, so
more light is produced.
The computational version of this process is known as the learning phase.
Each epoch of a Learning cycle, the firing rates and synaptic weights were updated.
This was then repeated for each node and every position of the Virtual Robot, in
an environment. The learning phase was comprised of learning cycles in different
environments, as explained below.
Each time the ’Learn Environment’ button in the UI was pressed, the neural
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16. Methodology
network was trained for 19 epochs. Tests were performed, using 5, 10, 20, 50, 75,
and 100 epochs of training. Any training cycles over 20 epochs quickly led to an
over-trained network; below 10 epochs per training cycle, the speed of the learning
was much slower than cycles in the 10-20 epoch range. After further testing, the
optimum training was found to be the following: The Virtual robot visited each
environment sequentially, with one repeat. Each time the Virtual Robot visited
an environment it underwent a 19 epoch training cycle, and was then moved to
the next environment.
For each epoch, the firing rates and synaptic weights were updated according
to Equations 2.2 and 2.4 respectively.
rP
i = exp
−(sP
i )
2
2(σP )2
(2.2)
Equation 2.2 is the learning firing rate for Place cell i, rP
i is the firing rate, sP
i
corresponds to the distance between the Virtual Robot and the location which
Place Cell i fires maximally and σP
is the standard deviation.
sP
i was be found by using the following equation:
sP
i = (xi − x)2 + (yi − y)2 (2.3)
Where xi, yi are the location of the Virtual Robot that causes Place Cell i to fire
maximally, and x, y are the location of the Virtual Robot.
Using Equation (2.4), the synaptic weight between Place Cell i and j is
updated, where δwRC
is the change in synaptic weight, k is the learning rate
constant, rP
i and rP
j are equal to the firing rate of cell i and j respectively.
δwRC
= krP
i rP
j (2.4)
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17. Methodology
2.1.3 Place Cell Activation Equation
When the learning phase was complete, the output of the CANN changed
from a Gaussian peak of node activation into patterns where all the nodes of
the CANN had varying strengths of activation. The equation used to derive the
activation for each node of a CANN in this field is documented in (Stringer et al.
2002, 2004) and is the following differential equation:
τ
dhP
i (t)
dt
= −hP
i (t) +
φ0
CP
j
(ωRC
ij − ωINH
)rP
j (t) + IV
i (2.5)
Where τ is the time constant, φ0 is a constant as well as ωINH
. CP
is the number
of synaptic connections for each Place Cell. IV
i represents the visual input to
Place Cell i. The equation implemented from this was found by setting t=0 and
re-arranging:
τhP
i (t) =
φ0
CP
j
(ωRC
ij − ωINH
)rP
j (t) + IV
i (2.6)
As a differential equation simply describes how a certain quantity changes over
time, a timer was used to update the activation of each Place Cell. When each
timestep occurred, the activation of each node was updated using Equation 2.6.
Information that was previously used to calculate where each place cell fired max-
imally, along with the Virtual Robot’s x and y coordinates, was used to determine
how strongly each Place Cell should fire.
Finally, to produce the Activation Pattern of the CANN, the network was
represented as a 2D grid of squares. Each square then changes colour, based on
the activation of the node for that particular position, in that environment.
The activations of the nodes are highest at Red decrease as the colour moves
through orange, yellow, green and blue, displayed in Figure 2.2.
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18. Methodology
Figure 2.2: Example of CANN Activation pattern
2.2 Robot, Environment and UI Implementation
2.2.1 Virtual Robot and Environments
With the CANN implemented and producing the expected responses, at-
tention turned to the creation of its host, a Virtual Robot and environments for
it to learn, navigate and eventually remember. To begin, a basic 400x400 pixel
environment was created and within it the Virtual Robot and the landmarks were
created to fill the environments.
Four different environments were created for the Virtual Robot to learn and
move in. Three environments had the landmarks set up with no clear symmetry,
and one with complete symmetry in which each landmark resides in a corner.
Time limited the number of testing environments that could be made, and would
be a relatively easy way to further the simulation. The final Environment was
chosen as a special case, to test how the CANN dealt with uncertainty. It was
expected to be an Environment where the Virtual Robots CANN struggled the
most to differentiate between positions within it. This is due to the information
from landmarks being much similar than asymmetric environments, meaning a lot
of the positions looked the same to the Virtual Robot.
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19. Methodology
Figure 2.3:
Position 1,
Environment 1
Figure 2.4:
Position 2,
Environment 2
Figure 2.5:
Position 3,
Environment 3
Figure 2.6:
Position 4,
Environment 4
Two methods of controlling the Virtual Robot were implemented, using the
mouse pointer or the W, A, S and D keys in their traditional mapping. A basic
form of collision detection was included to stop the Virtual Robot from travelling
into landmarks and through the walls. This was achieved by simply checking if
the command the user applied moved the Virtual Robot on top of a landmark or
wall, if so the robot would not move.
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20. Methodology
2.2.2 Geometric Calculations
To calculate the distance to each landmark, Pythagoras’ equation (Equation
2.7) was implemented by using the location of the Virtual Robot and the centre
of the Landmark, treating it as a point, rather than a whole shape.
a2
= b2
+ c2
(2.7)
The differences in the x and y coordinates between the Virtual Robot and each
landmark were calculated, and substituted into Equation 2.7. This produced the
distance along a straight path between the Virtual Robot and the landmark.
θ = tan
Opposite
Adjacent
(2.8)
These differences are then used in Equation 2.8, to give us the angle between the
Virtual Robot and the landmark. These calculations are displayed in Figure 2.7
below.
Figure 2.7: Calculating the angle and distance from Virtual Robot to landmark
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21. Methodology
2.3 Combining Robot and the CANN
2.3.1 Combining
Using the above method, the distance and angle to each of the landmark can
be found. This is then used to determine the location the Virtual Robot needs
to be at for each Place Cell to fire maximally. This was quite difficult to find
in literature as papers (Stringer et al. 2002, 2004) did not go into detail about
how this is determined, despite being one of the more important elements of the
simulation. Eventually, a viable solution was found, and an abstraction of Bota
et al. (2001) was implemented. Using the average distance and angles to each
landmark, normalised between 0-400; the X and Y Coordinates of the Virtual
Robot that causes each place cell to fire were found.
This was the final major obstacle of the simulation, as it was the Virtual
Robot’s sense of vision. Although humans generally do not need to think about
the precise distance and angles to certain objects, the information is almost always
being processed by the brain, and is the one of the primary functions for our visual
sense. The simplest way to emulate this for simulating purposes was to use the
coordinates of the centre of the landmarks and the coordinates of the robot. As
discussed in the Introduction, vision systems rely on maintaining the smallest
possible error or operate effectively, and this was the most accurate and simplest
implementation.
As the development of the CANN, Virtual Robot simulation and UI occurred
separately, all these pieces needed to be unified into the UI, which was achieved
by creating an instance of the Environment class in the CANN class. This also
allowed the transfer from using the mouse pointer to apply stimuli to the CANN,
to using the coordinates of the Virtual Robot.
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22. Methodology
Figure 2.8: The completed simulation program
2.3.2 Testing Methods
Tests need to be applied to simulations to prove that they correctly emulate
the aspect of nature they are re-creating. In this project, the Neural Network
needs to display the expected behaviour of Place Cells. There have been numerous
experiments on this topic, providing different conditions that can be applied to the
simulation and the responses expected to be produced by the CANN. The simplest
test used was to see if the Virtual Robot ’remembered’ positions in environments.
The conditions applied have been inspired by the studies of Muller et al (1994),
Lew (2011), Scalpen et al. (2014) and Muller and Kubie (1987).
As previously described, the learning process in the brain occurs when certain
patterns of activity increase in strength, when a task is repeated. The equivalent
version of memory for this project was displaying the same patterns of activation
when the Virtual Robot returned to the same location, in the same environment,
after training had been completed.
Another test to see if the Virtual Robot ’remembered’ environments was to
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23. Methodology
train the Virtual Robot in each environment individually. This would produce
the activation pattern for each separate environment. If the prominent features
of each pattern appeared in the activation pattern of the CANN trained in all
environments, then it could be inferred that the Virtual Robot would be able to
identify environments by comparing the activation patterns.
The easiest way to check this is to be able to place the Virtual Robot in
exactly the same place, which was accomplished by including four position buttons
in the UI. Four buttons for changing the Environment were included along with
four buttons for applying the different conditions, to simulate different situations
that have been tested in literature. The responses to different conditions were
the main metric for the success of the model. If the CANN replicated the same
behaviours as the Place Cells in Rats when exposed to the same changes, it would
suggest the model is an accurate recreation of Place Cells. The different four
conditions used were as follows:
1. Lights On
2. Lights Off (Loss of Vision, No other sense of input)
3. Landmark’s location changed by a small amount
4. Environment rotates 90 degrees clockwise
The first condition was to have the environments the same as during the
learning phase, and visual input enabled. This was needed for the initial test,
seeing if the Virtual Robot remembered different environments. This also allowed
the simulation to return to its standard state after different conditions had been
applied.
The second condition is effectively removing the light source to simulate loss
of visual input. The Virtual Robot depended on this input to determine which
Place Cells fire and how strongly. The response to this change is expected to be
no change of activation in the CANN; without the visual information and with no
other inputs, the Virtual Robot would think it is still in the same positions that it
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24. Methodology
was in before the lights were turned off. This hypothesis can be extended further
to suggest that if the Virtual Robot’s environment changed while its vision was
disabled, it should maintain the same activation pattern as the position in the
environment that the Virtual Robot last “saw”. When vision is returned to the
Virtual Robot, the CANN would update its activity pattern with respect to its
new position and/or environment.
The third and fourth conditions should have a similar response, in terms of
the change to the environment we see, rather than to each other. Condition three
was a small change in the position of the landmarks (McNaughton et al. 1995;
Knierim and Rao, 2003), which should correlate to a similar, small change in the
activation pattern. If we return to the blindfolded person in his kitchen, this time
when his blindfold is removed, and objects in the room have been moved, he would
still think he was in his kitchen, only some of the visual cues would be slightly
different. This would naturally translate into slight variations of the Place Field
produced by the Place Cells, with the predominate features remaining, so is the
expected response of the simulation’s activation pattern.
Figure 2.9:
Position 1,
Environment 1,
Condition 1.
Figure 2.10:
Position 1,
Environment 1,
Condition 3.
Condition four was a 90 degree, clockwise rotation of the Landmarks, to
which the activation pattern of the Place Cells should rotate by 90 degrees in the
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25. Methodology
same direction. Considering the person in his kitchen one final time, if somehow
when his blindfold was removed and his kitchen had been rotated by 90 degrees,
he would still recognise it as his kitchen, but rotated. A 90 degree rotation of
the Place field has been observed under these conditions in studies performed
by Knierim (2002) and Knierim and Rao (2003), and is therefore expected to be
emulated in our simulation.
Figure 2.11:
Position 1,
Environment 1,
Condition 1.
Figure 2.12:
Position 1,
Environment 1,
Condition 4.
Other possible conditions that could be applied to the simulation could be
to rotate the environments in the opposite direction, expecting to see the opposite
response compared to condition 4, and shifting 1, 2 and 3 landmarks by large
distances to see if there is a limit to the amount of change in landmark position
until the Virtual Robot would consider it to be a different environment.
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26. Chapter 3
Results
This section will be primarily displaying, and briefly discussing, the different
Activation Patterns produced by the CANN. The expected responses from the
CANN under each condition was discussed in the previous section. For example,
if the Virtual Robot’s visual input was disabled, it would be unable to tell if the
environment changed, so the activation pattern should remain unchanged until
the visual inputs are enabled.
3.1 CANN Outputs
The first set of Activation Patterns recorded were the individual patterns
for each position in each environment. This was achieved by running eight, 19
epoch training cycles (as discussed in the methodology) on each environment and
resetting the CANN between each environment (Figures 3.1-3.16).
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27. Results
Figure 3.1:
Position 1,
Environment 1.
Figure 3.2:
Position 2,
Environment 1.
Figure 3.3:
Position 3,
Environment 1.
Figure 3.4:
Position 4,
Environment 1.
Figure 3.5:
Position 1,
Environment 2.
Figure 3.6:
Position 2,
Environment 2.
Figure 3.7:
Position 3,
Environment 2.
Figure 3.8:
Position 4,
Environment 2.
Figure 3.9:
Position 1,
Environment 3.
Figure 3.10:
Position 2,
Environment 3.
Figure 3.11:
Position 3,
Environment 3.
Figure 3.12:
Position 4,
Environment 3.
Figure 3.13:
Position 1,
Environment 4.
Figure 3.14:
Position 2,
Environment 4.
Figure 3.15:
Position 3,
Environment 4.
Figure 3.16:
Position 4,
Environment 4.
The Virtual Robot then completed eight training cycles, without resetting
the CANN when changing environments. The expected response was that promi-
nent features of each environment’s activity pattern, as shown above, should ap-
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28. Results
pear in the activation pattern for the CANN when it revisits each position and en-
vironment after learning each one. When comparing Figures 3.17-3.32, to Figures
3.1-3.16, it can be seen that for the first three positions in first three environments,
there were a number of similarities in the patterns between each position in each
environment, respectively. The biological Place Cell equivalent of this behaviour
would be recognition of an environment from the visual cues; this response implies
that the model has some type of spatial recognition.
The model did struggle identifying the fourth positions, located in the centre
of each environment (Figures 3.20, 24, 28, 32). The fourth environment was also
poorly represented; however, this was implemented precisely because it was a
perfect symmetric environment (Figure 2.5). This environment was the most
likely to ’confuse’ the CANN as the difference between the distance and angles
to all the landmarks was much smaller than in an asymmetric environment. The
difference between the Activation Patterns produced during the learning phase of
the environment was much smaller too.
Figure 3.17:
Position 1,
Environment 1.
Figure 3.18:
Position 2,
Environment 1.
Figure 3.19:
Position 3,
Environment 1.
Figure 3.20:
Position 4,
Environment 1.
Figure 3.21:
Position 1,
Environment 2.
Figure 3.22:
Position 2,
Environment 2.
Figure 3.23:
Position 3,
Environment 2.
Figure 3.24:
Position 4,
Environment 2.
Page 22
29. Results
Figure 3.25:
Position 1,
Environment 3.
Figure 3.26:
Position 2,
Environment 3.
Figure 3.27:
Position 3,
Environment 3.
Figure 3.28:
Position 4,
Environment 3.
Figure 3.29:
Position 1,
Environment 4.
Figure 3.30:
Position 2,
Environment 4.
Figure 3.31:
Position 3,
Environment 4.
Figure 3.32:
Position 4,
Environment 4.
For the second condition, visual inputs were removed from the simulation.
The expected response was actually no change in the Activity Pattern of the
CANN, when the Virtual Robot moved, or its environment was changed. As
discussed earlier, this is because the Virtual Robot has no other inputs, so no
way to tell if it had moved. This behaviour is displayed below; Figures 3.33-35
show the process from vision disabled to re-enabled when the Virtual Robot has
been moved. Figures 3.36-38 are showing the same, but for the change of the
environment without visual inputs.
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30. Results
Figure 3.33: Virtual Robot has vision
disabled.
Figure 3.34: Position changes;
CANN does not.
Figure 3.35: Vision enabled; CANN
changes.
Figure 3.36: Virtual Robot has vision
disabled.
Figure 3.37: Environment changes;
CANN does not.
Figure 3.38: Vision enabled; CANN
changes.
When condition 3 was selected, the landmarks of Environments 1-3 were
shifted slightly. As described in previous sections, there should have been a slight
change in the activity pattern in the CANN, as the changes in the landmark co-
ordinates are relatively small (each landmark x and y location were displaced by
Page 24
31. Results
10 pixels). This condition was applied to rats in Muller and Kubie (1987), and
Knierim (2002), and resulted in the expected response, described above. Environ-
ment 4 was not included in this test as the Activity Patterns recorded displayed
barely any noticeable change. The Activation patterns produced by applying the
third condition to the CANN were:
Figure 3.39:
Position 1,
Environment 1.
Figure 3.40:
Position 2,
Environment 1.
Figure 3.41:
Position 3,
Environment 1.
Figure 3.42:
Position 4,
Environment 1.
Figure 3.43:
Position 1,
Environment 2.
Figure 3.44:
Position 2,
Environment 2.
Figure 3.45:
Position 3,
Environment 2.
Figure 3.46:
Position 4,
Environment 2.
Figure 3.47:
Position 1,
Environment 3.
Figure 3.48:
Position 2,
Environment 3.
Figure 3.49:
Position 3,
Environment 3.
Figure 3.50:
Position 4,
Environment 3.
Finally, condition 4 was a 90 degree clockwise rotation of environments 1-3.
Environment 4 was not rotated as it would still be the same environment due to
Page 25
32. Results
its symmetry. The activity pattern of the first three environments should respond
by a displaying the same pattern but rotated by 90 degrees, as described above.
The activation patterns produced were as follows:
Figure 3.51:
Position 1,
Environment 1.
Figure 3.52:
Position 2,
Environment 1.
Figure 3.53:
Position 3,
Environment 1.
Figure 3.54:
Position 4,
Environment 1.
Figure 3.55:
Position 1,
Environment 2.
Figure 3.56:
Position 2,
Environment 2.
Figure 3.57:
Position 3,
Environment 2.
Figure 3.58:
Position 4,
Environment 2.
Figure 3.59:
Position 1,
Environment 3.
Figure 3.60:
Position 2,
Environment 3.
Figure 3.61:
Position 3,
Environment 3.
Figure 3.62:
Position 4,
Environment 3.
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33. Results
3.2 Findings
3.2.1 Condition 1
Condition one was implemented to represent the ’Control’ state for the sim-
ulation. This nullifies any changes made by selecting other conditions, but also
allowed the conduction of the first tests. Comparing the first two sets of Acti-
vations Patterns when the Virtual Robot was in the same position, in the same
environments, it can be seen that there are clear similarities between each of the
Activation Patterns. This indicates that the Virtual Robot can effectively remem-
ber the environments it has previously visited, which implies the implementation
has worked.
From literature, the Activation Pattern itself was expected to be a single
defined peak, rather than a pattern across the neurons (Samsonsovich and Mc-
Naughton, 1997; Stringer et al. 2002). This sort of response could be explained
by either growing activity, where the inhibitory connections are weak compared to
the excitation, which leads to the whole map becoming active, or the parameters
of the CANN need refining. The fourth position, in the centre of the environ-
ments, appeared to be the position that had the most similar Activation Patterns
between environments. It was for this reason the position was chosen, as it was
the most likely position within the environments to cause some confusion, as the
centre is a unique point in any environment.
3.2.2 Condition 2
When Condition 2, the disabling of visual inputs was applied to the simu-
lation, the expected response from the CANN was displayed. There should have
been no change in the Activation Pattern when the visual information was re-
moved as vision was the only source of information available to the Virtual Robot
about its environment. As there was no information to the update the CANN, the
activity pattern must remain the same. This was demonstrated when the Virtual
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34. Results
Robot was moved in both Position and Environment.
3.2.3 Condition 3
The response expected from a small movement in the position of landmarks
was minor changes in the Activation Pattern of the CANN. This is because the
landmarks are generally in a very similar position so the environments appear
very similar to the Virtual Robot. This results in small changes in the Activation
Patterns, for each position in each environment. Figures 3.39-50 and 3.17-28
show the Activation Patterns for each Position and Environment, displaying minor
differences between the Patterns.
3.2.4 Condition 4
A 90 degree rotation of the landmarks was expected to have a 90 degree
rotation in the output of the CANN. This is because the environment still looks
essentially the same, but rotated. Comparing Figures 3.51-62 to Figures 3.17-28,
it’s visible that this was also the response of the CANN.
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35. Chapter 4
Discussion
The results gathered from comparing the Activation Patterns in various con-
ditions indicate that this visual-landmark driven model of Place Cells, despite
being relatively simple, has worked as expected. This implication can be made
because the model simulated in this project displayed the same behaviours and
responses to changes displayed by the Place Cells of rodents when exposed to
the same changes. The Activation Patterns produced when the Virtual Robot
returned to a location in an environment were similar to the patterns that were
produced when the Virtual Robot visited that location previously; it can therefore
be inferred that the Virtual Robot can remember locations in environments it has
learned when given the same visual cues.
When visual inputs were disabled, the CANN responded correctly by not
changing at all. This is expected because if you were sat in a room and then
blindfolded and moved with no other sensual information, you would still believe
you were in the same position as you received no other information from stimuli
to inform you otherwise. So, as you would believe you were in the same location
and position, the Place Cells firing would also remain the same. Only when visual
inputs were regained would your Place Cells have the information required to
update.
The implementation discussed above shows that a CANN can be trained
Page 29
36. Discussion
to operate as a collection of Place Cells, using information from landmarks to
determine which cells fire and the strength of their firing. The fact that the
CANN responses were generally very similar to the responses expected from other
studies(Muller, 1994;, Lew, 2011; Scalpen et al. 2014) means that, despite being
a fairly simple implementation of the overall biological system, it provides a good
basis for further research and development in the area.
This model presented here has some similarities to other models of cells
found in the Hippocampus. Work replicating Head Direction cells and Place Cells
using CANNs have produced similar results. A more thorough investigation into
the optimal parameters for the CANN would perhaps produce a more defined
Activation Pattern, and could be aided by the use of Evolutionary Algorithm
techniques.
Page 30
37. Chapter 5
Conclusion
This paper presents a visually driven model of Place Cells using a Continuous
Attractor Neural Network and a Landmark based Virtual Robot Simulation. The
model worked as predicted, responding to different stimuli and conditions in the
same manner as Place Cells recorded in biological studies. The model on its own,
however, could not be used as a method of robot navigation. The simplifications
made, such as the crude representation of the visual inputs, hold the model back
somewhat. However, it does provide a proof of concept for creating a computa-
tional model of Place Cells, and has potential for a large number of directions for
further work.
5.1 Further Development
5.1.1 Modifications to the Model
The most obvious and unrealistic simplification used in the model was a 360
degree view range as this meant all the distances and angles to each landmark
could be used at the same time. While there are robotic vision systems that do
provide a 360 degree view of their environment (Gaspar et al. 2000), there are no
animals that have this property. Rats, for example, have a fairly wide, 270 degree
viewing angle. Chimps, on the other hand, have a much narrower, 35 degree
Page 31
38. Conclusions
viewing angle, which has led to studies into the how the properties of Place Cells
change with the viewing angle of the animal (Stringer et al 2001). In regards to
this simulation, a change in the viewing angle would mean that all the information
from all the landmarks could not be used all of the time, as they may not all be
visible at the same time. The Virtual Robot would also need to rely more heavily
on its internal bearing, to help with its position and the direction it is facing in
an environment.
There were also simplifications applied to the neurons of the system. Our
assumptions about the neurons were that: nodes could be updated simultaneously,
the distance of the synaptic connections is negligible and time for propagation of
spikes is instantaneous. This is simply not the case we see in nature. Biological
neurons are far more dependent on the number and timing of spikes, and can
be thought to act more as a spike generator, firing according to the firing rate
rather than having a continuous output of activation at a constant value. Spikes
from other neurons are not transmitted instantaneously and have to travel a finite
distance. This would need to be considered, if a truer-to-biology model is desired.
Neurons of the same type can display a wide range of behaviours and are very noisy
in terms of how often and strongly they express their characteristic properties,
which was also not taken into consideration in this model.
Another interesting path that could be explored is to investigate how differ-
ent sized landmarks effect the firing of place cells; for example, a Landmark that
is double the size but twice the distance from the Virtual Robot than another
landmark could have an equal effect on the location of the firing of the Place
Cells. Scalpen et al. (2014) have suggested that there is a connection, that larger
landmarks give a broader sense of location, but smaller landmarks are needed for
the finer details of an animal’s location in an environment. This is relatable in
some sense as the closer to a destination you get, the more precise information is
needed to get to the actual location, e.g city-town-street-house number.
As mentioned briefly in the introduction, a more complete simulation and
Page 32
39. Conclusions
model of Hippocampus functions would begin at including Head Direction cells
and Path Integration. Head Direction Cells act as a biological compass for the
animal, to give it a sense of orientation in an environment. Path integration is
also thought to play a key part in the forming of a cognitive map for an animal, as
it uses information such as distance and direction of travel from a start point to
help estimate its current position (Etienne and Jeffery, 2004). Some attempts have
been made to unify these three aspects of the Hippocampus (O’Keefe et al. 1995,
Bota et al. 2001), showing some promising results and would be an important
step to a more complete model.
A sense of self locomotion could also be implemented, which would help assist
the Virtual Robot when visual inputs are disabled. Rather than the Activation
Pattern remaining the same when the Virtual Robot moves in an environment, the
pattern would change as if the Virtual Robot had visual inputs, but the strength of
the outputs would be reduced. An uncertainty factor would need to be considered
too, as without visual information there will be a loss of precision. With a change
of environments applied to the simulation, the Activation Pattern would have to
remain the same as the pattern for the last seen environment for all positions of
the Virtual Robot.
For simplicity, the calculation of the distance between landmarks does not
take into account whether landmarks are blocked from the view of the Virtual
Robot by other landmarks. Of course, this is not an accurate representation
of how animals use visual information, as if an object is not visible, no visual
information can be processed from the landmark. This aspect of vision becomes
more complex when the size of landmarks are also taken into account, and if the
simulation was converted to 3D, the height of landmarks would also play a large
part in landmark visibility.
Page 33
40. Conclusions
5.1.2 Performance Improvements
The above implementations would yield a more complete model, that could
be used for robot navigation, and this is also truer to the behaviours we find in
nature and literature (Samsonovich and McNaughton, 1997; and Stringer et al.
2002). The remainder of this section discusses changes to improve performance,
and possible implementations of the system.
One of the first areas to consider for further development of the software
would be to change to a more suitable programming language. MatLab and
Python are currently very popular languages for programming Artificial Neural
Networks. The developer of MatLab, MathWorks, includes an entire toolbox for
designing, implementing, and training Artificial Neural Networks. This would as-
sist with speed and efficiency of the CANN. Python is also a very useful scripting
language that can increase the speed and efficiency of complex calculations and
array searches. The actual simulation could be re-written in C++ and use the
ODE physics engine. This would be used to create full 3D environments that
the Virtual Robot is simulated in. Realistic Physics and collision detection are
already robustly implemented in ODE, which could potentially eliminate the need
to update those parts of the program. An extra dimension of information could
be incorporated in the visual inputs, for greater fidelity in the CANNs activation.
These two modifications would bring the model much closer to a full implementa-
tion on a real robot.
Evolutionary Algorithm techniques are useful when trying to determine the
optimum topology, weights, or parameters for a Neural Network. This is as they
provide a very efficient method to searching and comparing different solutions to
a problem. They have been used to determine the parameters for the behaviour
of a Head Direction Cell System (Kyriacou, 2011). Applying this approach to
the Place Cell CANN implemented in this paper could help bring the activation
patterns closer to the expected outputs found in literature. (Muller et al. 1994;
Samsonovich and McNaughton, 1997)
Page 34
41. Conclusions
5.1.3 Further Tests and Implementations
One test that would be more difficult to implement is providing the robot
with an Activation Pattern of a location in an environment, seeing if it could
navigate to the correct place in the environment so the Activation Pattern of the
CANN matches the one provided to it. Another could be to train it in the manner
described in this model and then expose it to a previously unseen environment
and record its activation. These patterns would be compared to the Activation
Pattern of the CANN when it is trained separately in that environment. This
would provide an indication of the performance of the CANN when it is exposed
to new environments, if the patterns have some resemblance then it would be able
to learn new environments relatively easily.
The final development would be to attempt to combine all of this and im-
plement it into an actual robot and then compare it to a robot using a pre-defined
map and/or SLAM navigational techniques, over a series of tests. To be considered
as a potential method of Robot Navigation, the fully integrated system described
above would need to perform as well as or better than the other methods under
the same conditions, as they are the current methods commonly used today, and
therefore the metric new methods should be tested against.
Implementing the model on a real Robot would require a fairly large change
to some of the program. The distance to landmarks would have to be calculated
through actual visual information from cameras rather than knowing the coor-
dinates of the centre. This could also help increase the efficiency of the code
in general as there are nested for loops found in the simulation components for
drawing the robot, collision detection and drawing the landmarks. Without these
complex searches the program will run more efficiently; however, the complexity
of implementing vision system and processing that data will require a fair amount
of computing power instead.
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42. Conclusions
5.2 Shortcomings
The biggest deviation from other similar implementations of CANNs is the
pattern of activation that is displayed. As previously discussed, it was expected
from Samsonovich and McNaughton (1997) and Stringer et al (2002) to be a
single defined peak instead of the whole map becoming active. The solutions
detailed above, describing the fuller implementation of the Activation Equation
and Evolutionary Algorithm Techniques, should produce a pattern more similar
to the output we find in literature.
One common shortcoming when attempting to model biological neural net-
works is that, due to technological constraints, the number of neurons that can
be simulated is a fraction of the number of neurons that these biological systems
contain. More neurons in the model would also not affect the overall behaviours
of the CANN when responding to different stimuli. It would instead increase
the fidelity of the model, which may be necessary for further and more complex
implementations of the system.
The 4th position in the centre of each environment seemed to have the most
similar patterns of activation, also being the patterns most dissimilar to their single
environment trained CANNs counter-parts. The inputs for the controls would also
need refining: especially if it were to be implemented into a 3D model, or in a real
robot. This is as they need a much higher degree of accuracy to properly move in
an environment, as well as responding and correcting for collisions and changes in
slope angle.
This model does not provide a method of robot navigation on its own, the
same way that an animal does not just use Place Cells to navigate environments.
Instead, this simple model should be viewed as a basis to start to build up a
different approach to implementing robot navigation. Rather than just trying to
replicate the overall behaviours of animals, understanding the underlying mecha-
nisms of these behaviours, and how they evolved, could prove to be an interesting
new method for creating computationally cheaper, and more flexible implementa-
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43. Conclusions
tions for robot navigation (Kyriacou 2011).
5.3 Contribution to wider field
This model provides a good basis for modelling and implementing naviga-
tional cells found in the hippocampus to be used in robot navigation. However, a
more rigorous and fuller implementation of hippocampus navigational cells would
be required to be able to utilise this model for robot navigation. It does poten-
tially provide a new avenue to explore different implementations of robot navi-
gation. The mechanisms evolved by nature are fast, efficient, and adaptable. It
could be argued that these three things are among the top priorities for developing
autonomous vehicles and animal-like robots.
As this model is highly dependent on landmarks and fixed environments,
a potential use for the model could be in a warehouse style environment, where
levels of automation are rapidly increasing. A more complete version of this model
could provide robots in this type of environment with a fast, flexible, and efficient
method of navigating warehouses. This would lead to an increase in productivity
and efficiency whilst also reducing the costs of operation and number of accidents.
Household robots, like autonomous vacuum cleaners, could also make use of this
system as they generally operate in a relatively small environments.
During the Introduction, it was proposed that Place Cells could provide a
cheaper alternative to SLAM, and a more flexible option than providing a robot
with a pre-defined map. While the former is still to be proven with further de-
velopment of the model, the ability to learn new environments shown by this
simulation is more flexible than the latter. Therefore, more complex iterations of
this model could be an alternative to using pre-defined maps.
As previously mentioned throughout this paper, although the model pre-
sented operated as expected, it is far too simplistic to act as a navigational system
in its current state, this result is not entirely unexpected as Place Cells are a
Page 37
44. Conclusions
single type of cell within the very complex systems that describe biological envi-
ronmental navigation. How well these biological mechanisms and behaviours can
be abstracted for implementations in robotics could be an important consideration
when building more advanced navigational systems, in the future.
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