Synchronous vs. Conjunctive Binding: A False Dichotomy?

Synchronous vs. Conjunctive Binding: A False Dichotomy? Robert F. Hadley (hadley@sfu.ca) School of Computing Science, Simon Fraser University Burnaby, B.C. V5A 1S6, Canada Abstract It is argued that claims about the superiority of synchronous binding methods are premature. A hypothetical explanation for synchronous firing is offered, which portrays such firing as a symptom of a deeper binding process that employs con- junctive nodes. It is shown that only a feasibly small number of conjunctive binding nodes would be required in the deeper process. In contrast with conjunctive coding, synchronous firing, considered as a binding method, has in recent years attracted considerable notice, both because of its biological basis (cf. Singer, 1999, 2003) and because it (purportedly) avoids the proliferation of nodes attributed to conjunctive coding. Evi- dence for the role of synchronously firing neurons in sensory feature binding is substantial (Singer, 1999), and synchronous firing has been used as a basis for variable binding in some models of inference, including SHRUTI (Shastri and Ajjana- gadde, 1993) and LISA (Hummel and Holyoak, 1997). Despite the considerable positive acclaim that synchrony has attracted as a solution to the binding problem, its touted advantages over conjunctive coding might, for all we actu- ally know, be illusory. I say this because synchronous neu- ral firing cannot be regarded as a fundamental, unanalysable phenomenon. It is well known that the firing of an individual neuron is caused by underlying processes, both chemical and electrical. For this reason, among others, it would be scientif- ically incoherent to regard the systematic firing of neurons in synchrony as a fundamental, inexplicable phenomenon. We cannot both claim that the firing of an individual neuron has deeper causes and that the synchronous firing of a set of neurons must be regarded as absolutely basic and inexplica- ble. Yet, the causes of synchronous firing in non-perceptual realms (which include language comprehension, reasoning, and other forms of higher cognition) are not presently known. The few causal indications that do exist are compatible with the following supposition: apart from spurious coincidences, neurons fire in synchrony only when they are each connected to explicit conjunctive binding nodes (dub them CBN) whose cyclical firing engenders synchrony in the firing cycles of neurons that the CBNs are immediately connected to. The simplest form of this supposition would require one conjunc- tive binding node for each pair of synchronously firing nodes. I have no wish to defend the simple form of this supposi- tion, but, as will soon emerge, I will propose a variant con- jecture which requires only a feasibly small number of con- junctive nodes. Regardless of that, we should bear in mind that until the causes of synchronous firing are understood, we are not in a position to judge the number of neurons involved in the genesis of synchrony firing. In consequence, we are not entitled to flaunt the putative greater efficiency of syn- chronous binding schemes. In section 2, the genesis problem for synchronous firing is examined. There, I present a hypothetical model which might, in principle, explain how the relevant kind of syn- chronous firing is ever engendered. This model posits the mediation of a feasibly small number of conjunctive coding nodes which lie at the core of a network which ultimately links with neurons that are caused to fire synchronously. Al- though this proposed model is unlikely to be accurate in its details, it is hopefully indicative of the direction in which a true explanation of the causes of synchronous firing is to Introduction A long standing issue in connectionist research has concerned the manner in which the human brain contrives to bind values to variables, fillers to roles, and (sensory) features to features. Closely related to this issue is the quest for an elegant and efficient solution to “variable binding” in artificial connec- tionist networks. In the present paper, I shall be concerned ultimately with biological neural networks, and for this rea- son the discussion will focus upon the two binding methods whose biological bases have been most directly confirmed. In brief, these two methods are: (a) conjunctive coding, where the binding of two elements is signaled by the cyclical fir- ing of a particular node (realized by one or more neurons) that receives input from other nodes that represent the ele- ments which are to be bound together (or “conjoined”). (b) synchronous firing, where distinct nodes (or distinct sets of neurons) are represented as being bound together when the distinct nodes fire in approximately synchronous cycles. 1 The concepts of conjunctive coding and binding via syn- chronous firing will be elaborated in following sections, but for the present some observations may be helpful. The use of conjunctive coding as a method for binding values to vari- ables and fillers to roles can be observed in several early con- nectionist models (cf. Rumelhart, McClelland, et al, 1986) and has been especially valuable in network models of lan- guage parsing and/or acquisition (see Cottrell, 1985, Steven- son, 1994, Hadley and Cardei, 1999, Hadley and Hayward, 1997). Moreover, the binding of sensory features via explicit, conjunctive binding neurons has been empirically verified in studies of the visual cortex of mammals and other cortical re- gions (Singer, 2003). Such binding of elements (whether they be features, concepts, variables, or roles) is known to be both reliable and fast. However, binding via conjunctive coding has often been criticized as being combinatorially explosive in the number of nodes (or neurons) required to effect all the bindings possible in a given domain. Unfortunately, this crit- icism has at times been made in a sweeping form, without regard to the fact that the number of conjunctive nodes re- quired may merely be the simple product of the number of fillers and roles involved (the latter being feasibly sparse in non-perceptual domains). 1 Other proposed solutions to the binding problem include Lange and Dyer (1989); and CONSYDERR, by Sun (1992). Each of these solutions possesses merit and features of interest.