Convergence of a spreading activation neural network with application of simulating aphasic naming errors in Finnish language

Abstract

Aphasia is a language disorder caused by brain damage. Difficulties in word processing called anomia constitute the most common type of errors in aphasia. Naming errors are characteristic of aphasia and can be used to investigate the disorder. In this context, naming refers to a psycholinguistic test where the subject is asked to utter the names of target objects presented to him or her in the form of simple pictures. In the case of aphasia the subject may name objects presented or concepts incorrectly by word blends (e.g. semantic error to say “right” for “left”) or even forming nonwords (words without sensible meaning). Previously [5], [6], [8], [10], [11], we have constructed a simulation technique with a spreading activation algorithm to model the mental word processing of an aphasic by employing a succession of four neural networks with semantic, phonological, syllabic and phonemic processing functions, respectively. Treating words and their component parts as textual units, naming errors are generated in the system by spreading activation in the networks. In this paper we study the convergence properties of the algorithms which are used for spreading activation in these networks. Convergence shows which component parts dominate other parts in the networks employed. It can be reasonable also in the psycholinguistic sense, at least concerning the so-called perseveration in which some word or sound is repeated being unable to form a correct word. To enable to predict and control the behaviour of the model the convergence property is useful to understand.

Introduction

In aphasic speech, as in normal slips of tongue, there can be various naming errors. Aphasic naming errors constitute an important basis in the pursuit of developing computer simulation for aphasic word processing. We have previously developed a simulation model based on activation spreading in neural networks [5], studied its properties [10], [11], and compared the simulation results to real aphasic naming errors [6], [8]. The aim of such a simulation is to generate naming errors which are similar to the errors typically found in the speech of aphasic patients. In this paper we investigate the mathematical convergence properties of the networks employed; in other words, whether the simulation process approaches some asymptotic stable state as the number of iterative steps tends to infinity.

There is plenty of evidence to suggest that word retrieval is a multistage mental process [1], [3]. We have constructed our simulation model to consist of four neural networks in series of stages with lexical–semantic, lexical–phonological, syllabic and phonemic functions, respectively [5], [10], [11]. This model is able rather well to describe some typical aphasic naming errors, e.g. semantic and phonological [5], [6], [8], [10], [11]. A semantic error corresponds to the utterance of a wrong word that is semantically associated with the target word as for instance “cat” for “dog”. Saying “cap” instead of “cat” represents a phonological error.

In each network of the model the nodes (or “artificial neurons”) are associated with words or their component parts, syllables or phonemes, depending on the processing function of the network. Furthermore, for the purpose of spreading activation in the network, each node is connected to some other related nodes, the strength of the connections being given by weights determined as will later be discussed. The simulation process is started by assigning in the lexical–semantic network a positive activation value to the node corresponding to the target word and setting the activation values of all other nodes equal to zero. The lexical–semantic network comprises the 10 target words of the chosen test set together with 17 of their semantic associates [5], [8], [11]. The function of this first network is to generate naming errors of the semantic type, e.g. naming “kuppi” (cup) incorrectly as “kahvi” (coffee), since the meanings of these words are commonly conceived in the same context. After having applied the activation spreading algorithm a number of times, the word with the greatest activation value is input into the lexical–phonological network, which includes all the 27 words of the lexical–semantic network and another 11 words which are phonologically associated with them. In this network activation spreading generates naming errors of the phonological type, like naming “kuppi” (cup) as “nuppi” (knob). Unlike the lexical–semantic network the lexical–phonological network is not connected but is composed of a few separate connected subnetworks [10], [11] one of which is shown in Fig. 1. The syllables of the word of maximum activation value from the phonological network are passed on to the syllabic network which consists of all the 58 distinct syllables which make up the 38 words of the lexical–phonological network. This network simulates naming errors with syllabic changes, e.g. naming “kup-pi” (cup) as “kup-ka” (nonword). Lastly, the phonemes of the output word of the syllabic network are input into the phonemic network consisting of the 15 consonants and 8 vowels, separated into two connected subnetworks, which appear in our word set. We have already encountered a naming error of phonemic type: naming ‘kuppi” as “nuppi” is a phonemic error as well as being a phonological one. The final outcome of the simulation process, corresponding to the subject's utterance, is then obtained as the output string of the phonemic network.

Although we consider word production and speech, in executing our simulation words and their component parts are treated as textual strings that can easily be input, processed and output using computer programs. Textual treatment of phonemes presents no difficulties in Finnish, for there is an almost one-to-one correspondence between the letters of the Finnish alphabet and the sounds of the spoken language. With some modifications our simulation system could also be applied to model naming errors of speakers of other languages, because the basic concepts of the simulation technique and spreading activation algorithm are independent of word-level of the language.

The 38 words used in our model have been chosen from a standard set of approximately 100 words employed in psycholinguistic tests designed to study aphasic naming errors. Even though the number of words in our system may seem inadequately small compared to the tens of thousands of words in the actual mental lexicon of an average person, it has been found to be sufficient for examining the dynamics of the word processing by simulation. The weights between the nodes of the networks have been determined in tests with healthy subjects, but since such connection strengths cannot be measured exactly we have restricted the number of the possible values to just four: 0.4 (strong), 0.2 (moderate), 0.15 (weak) and 0.0 (no connection). These values were estimated between 0.0 and 1.0 when the former weight means that no error occurred between two certain words in the tests, i.e. nobody of the test subjects uttered one word when aiming at saying the other. The latter value of 1.0 corresponds to “the entirely correct naming” in those tests, i.e. the word itself or the connection of the node back to the same node (not drawn in Fig. 1) in a network. Frequencies of all objects named by the test subjects were calculated and classified according to their types (e.g. semantic). For all networks of the model such frequencies were sorted into three commonest sets whose means were about 0.15, 0.2 and 0.4 after having scaled them between 0.0 and 1.0. Ultimately, weights were given the nodes on the basis to which set a connection between the two nodes belonged.