Symbolic AI versus Connectionism in Music Research

In cognitive science and research on artificial intelligence, there are two central paradigms: the symbolic and the analogical. Within the analogical paradigm, interest in artificial neural networks, or connectionism, has experienced a resurgence during the last decade; this change has also been reflected in the field of musical modeling. This article provides a general survey of the relationship between symbolic AI and connectionism, both on a general level and from the point of view of music research. This is followed by a short introduction to artificial neural networks, which includes a description the main principles of their structure and function as well as a presentation examples of their use in the field of music. Introduction During the last few decades, attempts to model human musical activity have mostly been based on traditional AI techniques, which rely on logical manipulation of symbols. While a great deal of impressive results have been obtained within this paradigm (see, e.g., Balaban, Ebcioglu & Laske, 1992), these studies have failed to shed light on certain important areas of music cognition, such as those related to perception, motor action, and performance interpretation. Depending critically upon verbalization and introspection, they have proven ineffective for the investigation of the inarticulate aspects of musical activity. Since the 80s, connectionism, or modeling with artificial neural networks, have gained popularity among music researchers as a tool for exploring such tacit musical knowledge. Artificial neural networks (ANNs), also referred to as connectionist or parallel distributed processing (PDP) systems, can be characterized as strongly idealized models of networks formed by biological neurons: although the basic principles of their mechanisms and structures have been adopted from biological neural networks, they are generally not intended to model the physiological processes in the neural tissue. Technically, they are nonlinear dynamical systems consisting of a multitude of simple, interconnected processing units. They have three important properties. First, they are parallel, i.e., the processing units interact simultaneously and independent of each other. Second, they are distributed, i.e., their knowledge resides in the strengths of interneuronal connections; and the data manipulated by them are represented as patterns of neuronal activation. Third, they are adaptive, i.e., when exposed to data from the environment, they are capable of learning by adjusting the strengths of their interneuronal connections. Development of mathematical models of ANNs began four decades ago with the work of, e.g., McCulloch and Pitts (1943), Hebb (1949), and Rosenblatt (1959). More recent work by Hopfield (1984), Rumelhart and McClelland (1986), Grossberg Toiviainen: Symbolic AI vs. Connectionism 2 (1986), Kohonen (1989), and others has led to a resurgence of interest in the field. This paper is organized as follows: in the first part, the paradigms of symbolic AI and connectionism are compared in detail. This includes comparing the premises and discussing the strengths and weaknesses of the two approaches. The consequences of the latter to music research is discussed, i.e., in which sectors of music research connectionism may be a better choice than symbolic AI. The next section will provide a short introduction to ANNs. This is followed by a review of connectionist research on music, with pointers to some important references. Finally, the work of the present author on timbre recognition with Kohonen self-organizing maps is briefly described. Relationships Between Symbolic AI and Connectionism Premises The premises of symbolic AI and ANNs are fundamentally different. The paradigm of symbolic AI is based on the standard von Neumann-style serial processing under the control of a single powerful central processing unit, whereas ANNs employ brain-style computation, i.e., simultaneous interaction of a large number of simple processing units. Moreover, symbolic AI systems function by applying inference chains to logical variables — for instance, "X mother of Y" & "Y parent of Z" ⇒ "X grandmother of Z" — while ANNs apply evolutive rules to numerical variables. To put it in an other way, symbolic AI relies on logic, while ANNs rely on (nonlinear) dynamics. AI systems work under a centralized control, i.e. a collection of so-called meta-rules used to determine which rules of inference (or production rules) to apply in a given computational stage. An ANN lacks such a centralized control: all its units are simultaneously interacting. With respect to the representation of data, these two paradigms differ significantly from each other. Symbolic AI systems tend to operate on a high conceptual level, using dedicated symbols to represent each concept. They thus adopt a local representation. It is possible to use such a representation in ANN models also. According to a general view, however, a distributed (or subsymbolic) representation seems to better exploit the strengths of ANNs than a local one. A distributed representation can be defined from several points of view. For instance, it may imply representing the data as a vector, each component of which stands for a specific microfeature of the represented domain. Or, it may denote representing many items at once over the same set of processing units or connection weights. It must be noted that there is no clear distinction between local and distributed representation, but rather there exists a continuum between these two extremes. If an item is represented as a collection of microfeatures, each of these features can again be represented either in a local or a distributed manner. For example, the most local way of representing chords in an ANN is to designate one neuron for representing each chord. A more distributed representation is obtained by representing each chord as the tones it is composed of. The degree of distribution can be further increased by representing each of those tones as a harmonic or subharmonic series of frequencies. Knowledge, like data, is represented differently in the two approaches. Schematically, symbolic AI utilizes explicit knowledge represented in a local way, while ANNs employ distributedly represented implicit knowledge. Symbolic AI systems rely on sets of predefined inference rules provided by an external programmer. In ANNs, on the other hand, knowledge resides in a distributed form in the strengths of interneuronal connections. While these connection strengths can also be hard-wired by an external programmer, a more usual way of establishing them is using suitable learning algorithms together with a set of training data. ANNs, thus, build their knowledge by means of automated learning. Toiviainen: Symbolic AI vs. Connectionism 3 Strengths and weaknesses Due to their fundamentally different premises, symbolic AI systems and ANNs display rather unlike qualities. It can be stated that ANNs have proven effective in tasks were symbolic AI systems have problems, and vice versa. The main strengths of ANNs can be summarized as follows (McClelland, Rumelhart & Hinton, 1986; Rumelhart & McClelland, 1986; Gutknecht, 1992): • Learning capability. ANNs are usually not programmed but trained by presenting them with examples. On the basis of those examples, they adapt to their environment by means of specific learning algorithms. The use of automated learning reduces the need for "knowledge engineering". The latter means the process of defining the representation formalisms, data structures and correct rules to be used, and is a crucial task in developing a symbolic AI application. Knowledge engineering is often difficult, unnatural, and error prone, because it requires making explicit of the knowledge which is often implicit. It is also time-consuming and thus expensive. It must be noted that within symbolic AI, research in automated learning is an area of great interest. The learning techniques developed so far in this field, however, require a very accurate choice of examples and often do not tolerate contradictory examples. When used, for instance, for composing music, ANNs can free the composer from the often tedious enterprise of defining the rules which describe a given style of music. • Generalization capability. ANNs are capable of extracting significant features from the training set and using them to process a novel input pattern. For instance, an ANN trained to recognize the timbre of a musical instrument is probably capable of recognizing it even if it is played with a slightly different articulation. • Tolerance towards noise and contradictions. ANNs are robust with respect to the presence of noisy or contradictory data. In the field of music this is a valuable feature, since musical phenomena very often do not follow any consistent set of rules. • Tolerance towards overloading of information. ANNs do not have a fixed storage capacity: when a network is overloaded with input data, similar components of information tend to blend together, resulting in generalization of features. Some of the main problems of the connectionist approach are listed below (Serra & Zanarini 1990; Gutknecht, 1992); • Limitation to "toy-size" problems. At least in the domain of music, ANNs have so far been applied only to small, strongly stylized problems. The application to real size problems is only in its initial phases, one notable example being the work of Leman & Carreras (1996). • Difficulties with long inference chains. Symbolic AI systems are built specifically for dealing with this type of reasoning, and it is not realistic to expect ANNs to be as efficient in this sector. • Limited explanation capabilities. Attempts have been made to explain the behavior of connectionist networks by, for instance, analyzing the structure of the connection strength matrix learned. These explanations are, however, at the level of primitive features of