Commentary on Steels, L. & Belpaeme, T., Coordinating Perceptually Grounded Categories through Language. A Case Study for Colour.
Abstract: 28 words
Main Text: 856 words
References: 263 words
Total Text: 1207 words
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The experiments proposed in the paper of Steels and Belpaeme can be considered as a starting point towards a general methodology for the automatic learning of conceptual spaces.
In recent years, several frameworks for cognitive robotics have been proposed that take into account a level which is intermediate between the “subsymbolic” low level, directly linked to the external sensors, and the “linguistic” high level, oriented to symbolic inferences.
A cognitive intermediate level of such kind has been proposed by Gärdenfors (2000). Differently from other proposals, Gärdenfors introduces an intermediate level, based on “conceptual spaces”, with a precise geometric structure. Briefly, a conceptual space is a metric space whose dimensions are related with the quantities processed by the agent sensors. Examples of dimensions could be colour, pitch, volume, spatial co-ordinates. Dimensions do not depend on any specific linguistic description: a generic conceptual space comes before any symbolic-propositional characterization of cognitive phenomena.
A point in a conceptual space is the epistemologically primitive perceptive element at the considered level of analysis. Chella et al. (1997), (2000) describe a robot vision system based on conceptual spaces in which each point corresponds to a geon-like 3D geometric primitive (Biederman 1985) perceived by the robot. Therefore, the perceived objects as the agent itself, other agents, the surrounding obstacles and so on, are all reconstructed by means of geons and they all correspond to suitable sets of points in the agent's conceptual space. A related conceptual space has been proposed by Edelman (1999) which also proposes an implementation based on RBF Neural Networks. Song & Bruza (2003) adopted a conceptual space framework for information retrieval applications, and Aisbett & Gibbon (2001a) propose a suitable conceptual space for clinical diagnosis applications. From a theoretical point of view, Gärdenfors & Williams (2001) discuss the conceptual space approach for generating non monotonic logic inferences and Chella et al. (2004) discuss about conceptual spaces in the framework of the anchoring problem in robotics. Balkenius (1998) proposes a more realistic implementation of a conceptual space from an empiric point of view by a set of RBF units and Aisbett & Gibbon (2001b) discuss a related implementation based on Voltage Maps.
One of the problems of all the previously cited approaches is that the structure of the adopted conceptual spaces are a priori defined by the designer according to the addressed problem, in the sense that the designer has to define how many axes are necessary for a correct representation of the problem at hand, what is the meaning of the axes and the corresponding type and range of values, what are the separable and the integral dimensions and so on. No general methodology has been adopted or proposed to let the machine to inductively learn a conceptual space, with the exception of the multidimensional scaling algorithm (Shepard 1962a, 1962b) proposed by Gärdenfors, which is generally not suitable for real world robotic applications.
Analyzing the paper of Steels and Belpaeme from the point of view of the conceptual space theory, the described agents effectively build a conceptual space in order to represent the perceived colours. A “category”, implemented by a RBF neural network, identifies a subspace of integral dimensions of colours, because each RBF unit defines a colour sub-dimension, while different categories correspond to separable subspaces of colours. Therefore, the colour conceptual space of the agent is generated by the union of all the subspaces of integral dimensions of colours corresponding to all the agent categories. The agent inner representation of a colour is therefore given by the collection of the responses of all the RBF units built by the agent, i.e., by the components of the conceptual space dimensions, in agreement with the conceptual space theory. It should be noted that each colour subspace is implemented by a RBF Neural Network, in the line of the approaches by Edelman and by Balkenius.
The new and important point in the Steels and Belpaeme experiments is that the agent conceptual space is not defined a priori by the system designer but it is learned by the agent itself according to its inner and external constraints, as fully described in the target paper. Therefore, the strategy adopted by Steels and Belpaeme is effectively able to address the previously described problem of how to learn a conceptual space. Interestingly, the conceptual space is generated not only by means of the agent perceptions, but also by the linguistic interactions among agents, i.e., by means of the agent actions.
In this line, it would be interesting to investigate the possibility for an agent to have more powerful representation capabilities that let the agent to infer the conceptual spaces of other agents, through, e.g., a sort of higher order guessing game. In this way, the problem of sharing categories among populations could be correctly addressed, in the sense that an agent belonging to a population Ax may build an inner representation of the conceptual space of another agent belonging to a population Ay in order to acquire all the needed capabilities to “translate” its own colour categories to the colour categories of the other agent.
In conclusion, the Steels and Belpaeme paper is a seminal starting point for the investigation of a general methodology for inferential learning of conceptual spaces from the agent external perceptions, its inner and external constraints and its actions.
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