We describe some Artificial Life simulations in which a situated model agent controlled by a feed-forward neural network has to solve a simple categorization task involving size constancy abilities in an online fashion. The results show that even a simple neural controller without internal recurrent dynamics is capable of solving a non-trivial size categorization task by exploiting the dynamical interaction of the agent with its environment. Even if at an early stage, this work suggests two possible implications for the study of size constancy and perceptual constancy in general. First, approaching the problem from a functional point of view may open new perspectives on the possible underlying mechanisms. Second, the adoption of an embodied and situated approach may help to explain why perceptual constancy is so efficient in biological cognitive systems.
Perceptual constancy can be either defined as a perceptual
mechanism or as a behavior. In the first case we define it as
the ability to perceive the stable properties of the
surrounding environment despite the continuous change of
the raw information reaching our sense organs. The second
type of definition can be expressed saying that perceptual
constancy allows us to behave in accordance with the stable
properties of the surrounding environment. One definition
puts emphasis on the mechanism (perception) and the other
one on the behavior, but, as claimed by
The behavioral aspects of perceptual constancy, instead,
are hugely neglected except for certain animal research
studies where constancy also reveals its great ecological
relevance. Size-dependent food selection, evaluation of
predator size and distance, foraging in different daylight
conditions are some example of behaviors that have been
studied showing some constancy abilities (but also failures)
even in lower vertebrates. Size constancy has been studied
in frogs and toads for example by
The approach proposed here is based on the methodology
of Artificial Life
The experimental setup proposed here is a computer simulation that represents a simplified model of a brainbody-environment system with the following characteristics: 1) A simulated agent with a sensory-motor system acts in a virtual environment
2) Sensory input and its variations are coherent with the environment structure and its laws
3) Variation of the input is partly determined by the motor system
4) The neural controller of the agent evolves through a Genetic Algorithm, with no prior hypothesis about its functioning
5) The fitness function used to evolve the neural controller is based on the agent performance in a task that requires some degree of perceptual constancy
The main goal of this experimental setup is to provide an embodied and situated context in which a simulated agent can evolve a size constancy behavior.
The simulation environment is described in figure 1. A simulated agent moves in a 2D square arena with sides of length 60 populated with circles randomly placed in a grid of 5x5 cells positions (figure 1 top part). The diameters of the circles can be small (0.5) or big (1.0). There are 10 small and 10 big circles for a total amount of 20 objects. visual receptors by which it is able to “see” objects in front of it with a field of view of 60°. The activation of the receptors is calculated with a perspective projection of the objects in the field of view of the agent so that a near small circle and a distant one can have the same retinal projection (as depicted in figure 1). Distance cues are provided through a sort of “fog effect” (not shown in figure 1) that makes the circles appear lighter and lighter as the viewing distance increases. The fog effect and the grid configuration of objects make the agent input clean and avoid cluttered input patterns. The fog effect in particular avoids that too many objects are visualized at the same time on the retina. This would require the agent to develop some kind of attentional mechanism that would deserve a dedicated work.
The controller of the agent is a three layer feed-forward neural network. The input layer is the above mentioned linear retina with 30 receptors whose activations range from 0.0 to 1.0. The hidden layer has 10 units and the motor layer consists of 4 output units. Both hidden and motor layer neurons use a sigmoid activation function. Each layer is fully connected with the next one. So there are 300 inputhidden weights (30x10) and 40 hidden-output weights (10x4). Figure 2 shows the structure of the neural network.
The agent (see figure 1 bottom part), represented by a small circle of size 0.5, is provided with a linear array of
The agent can move forward or backward with a certain velocity and can rotate around its center to change direction. The four motor units control the movement of the agents with two couples of opposing real units. The linear movement of the robot is determined by the results of two opposing units that determines the forward and backward linear velocities. The agent moves forward if the output of the forward velocity unit is higher than the backward one, and vice versa. The agent direction is determined by two opposing units controlling the right and left angular velocity.
The goal of the agent is to hit as much small circles as possible and to avoid the big ones during its lifetime that lasts 10,000 simulation steps. Circles that are hit by the agent are removed from the environment.
Evaluating circle size is not a trivial task because during environment exploration the sensory input varies continuously and produces ambiguous configurations. The same retinal projection, for example, can be that of a near small circle or the one of a big distant one. So the retinal subtense in itself is not correlated with object size. The same occurs for the object “lightness” that varies with distance. The organism faces a size constancy problem.
The task is similar to the one proposed by Scheier, Pfeifer,
Kunyioshi (1998) and
A genetic algorithm is used to evolve the weights of the neural network to solve the simple size discrimination task described above. As mentioned before, the goal of the agent is to hit as much small objects as possible and to avoid the big ones. Objects that are hit by the agent are removed from the environment. The fitness function is calculated with the following formula:
F = Cs – Cb where Cs and Cb are the number of small and big circles hit at the end of the agent life. Since there are a total of 10 small circles and 10 big ones, the highest fitness score is 10 and the lowest is -10. The evolutionary experiment consists in evolving the weights of the neural controllers in a populations of 100 agents for 100 generations with a selection criterion based on the fitness function described before.
The weights of the neural networks in the first generation are initialized in the range (-1/sqrt(d), +1/sqrt(d)) where d is the number of input to each neuron. When all the individuals of one generation have been tested they are sorted based on their fitness scores and the 20% of the best individuals are selected to produce the next generation of agents. The genetic operator consists of a mutation mechanism that changes 10% of the weights of the neural network adding a random number between -0.5 and +0.5. The genetic algorithm uses elitist selection allowing the best individual of one generation to carry over to the next generation with unaltered connection weights.
The genetic algorithm described above was used to run 10 seeds of the same simulation some of which gave interesting results. Figure 3 shows the best and mean fitness along each generation of the best simulation obtained. The best fitness of the best individual in the last generation is 9, which is nearly the maximum score possible for the fitness. This result indicates that the evolution process produced some kind of behavior capable of avoiding big circles and approaching and hitting the small ones.
Considering that, as explained before, the size of the
circle cannot be evaluated relying on a single retinal
projection at a given moment, or the intensity of retinal
receptors, we can expect the evolved neural system to
develop a form of size constancy behavior based on the
dynamical interaction of the agents with its environment to
exploit the information contained in the optic flow as
theorized by
It could sound strange that a simple neural controller like the one used in this experiment is capable of such complex behaviors. Actually a feed-forward neural network is a simple type of controller with no internal states, where information flows in only one direction, with each input producing always the same output. In this respect it is comparable with a simple associative mechanism. What makes this experiment interesting is that the neural network is inside an embodied and situated agent whose sensor and motor systems allow it to interact with its environment (Figure 4). Each input, at a given time, produces an output that is used to move the agent. The agent movement, in turn, changes the next input, which produces a new output and so on. This mechanism gives rise to interesting “organismenvironment” dynamics that allow the agent exhibit a functional size discrimination behavior.
Some preliminary behavior analysis have been performed on the best organism of the last simulation and gave some interesting results. First of all, to accomplish their task, most of the successful organism develop a sort of exploratory behavior consisting in turning around their centers and moving slowly until some object fall in their receptive field. Once an object shows up in the receptive field the agent gets close to the object and then start to oscillate back and forth for a few times. of the behavior has a time course and therefore is more complex than a one shot discrete response. This should be enough to convey the idea that designing by hand a system capable of acting in a dynamical environment is not a trivial task. At this point the behavior is different depending on whether the object is a small circle or a big one. In the case of small circles the agent goes forward and hit it (see figure 5). In the case of big circles the oscillating behavior ends with the agent getting away from the object (see figure 6) towards a location favorable for the complete exploration of the environment. The oscillating behavior could be interpreted as a discrimination phase and always takes place at approximately the same distance (about 2.0) from the target object.
At a first glance it could be thought that a simple “hand – made” linear function using the number and intensity of receptors should be enough to discriminate between the large and small circles. But looking at the results and considering the dynamical context in which the agent lives it is clear that a far more complex behavior is required to solve the task. Indeed, the behavior obtained with the genetic algorithm is quite articulated and comprises at least five sub components: explore, approach, discriminate, hit object, avoid object. Moreover, each of this sub components Further analysis are required to better understand what happens inside the neural controller and to explain the agent behavior in more detial. The most tempting hypothesis, at the moment, is that the agent performs some kind of expansion gradient assessment during the discrimination phase as suggested by the fact that the oscillating behavior occurs more or less at the same distance from the object, and rather close to it. Indeed, the expansion gradient of two objects must be evaluated at the same distance, and the nearer an object is to the observer the wider and more informative its expansion gradient is. Some “laboratory” manipulation are needed to clarify this and many other aspects. For example we don’t know how robust this behavior is in different environmental conditions, what happens if the agent starting position is changed or if the objects are not placed in a grid pattern.
We described an Artificial Life simulation in which a simulated agent controlled by an evolved neural network shows some size constancy abilities in solving a simple categorization task. Even if a more detailed analysis is required, the preliminary results described here seem to confirm that a simple feed-forward sensory-motor system can solve a rather complex size constancy problem exploiting its dynamical interaction with the surrounding environment. These results strongly support an embodiedsituated approach to perceptual constancy, and also suggest that the ability of a cognitive system can be better understood in a framework that fully considers the importance of the brain-body-environment dynamics.
In the future work we are planning to explore different experimental conditions varying the size constancy task, the agent sensory-motor apparatus and its neural controller.