Chris Eliasmith

This chapter shows how epistemic coherence can be understood in terms of maximization of constraint satisfaction, in keeping with computational models that have had a substantial impact in cognitive science. It is shown how explanatory coherence subsumes Haack's recent “foundherentist” theory of knowledge. An account of deductive coherence is provided, showing how the selection of mathematical axioms can be understood as a constraint satisfaction problem. Visual interpretation can also be understood in terms of satisfaction of multiple constraints. After a brief account of how conceptual coherence can also be understood in terms of constraint satisfaction, the chapter concludes with a discussion of how the “multicoherence” theory of knowledge avoids many criticisms traditionally made of coherentism.

Cognitive theories have expressed their components using an artificial symbolic language, such as first-order predicate logic, and the atoms in such representations are non-decomposable letter strings. A neural theory merely demonstrates how to implement a classical symbol system using neurons: this is actually an argument against the importance of the neural description. The fact that symbol systems are physically instantiated in neurons becomes a mere implementational detail, since there is a direct way to translate from the symbolic description to the more neurally plausible one. It might then be argued that, while the neural aspects of the theory identify how behavior arises, they are not fundamentally important for understanding that behavior. Classical symbol systems would continue to be seen as the right kinds of description for psychological processes.

To have a fully integrated understanding of neurobiological systems, we must address two fundamental questions: 1. What do brains do (what is their function)? and 2. How do brains do whatever it is that they do (how is that function implemented)? I begin by arguing that these questions are necessarily inter-related. Thus, addressing one without consideration of an answer to the other, as is often done, is a mistake. I then describe what I take to be the best available approach to addressing both questions. Specifically, to address 2, I adopt the Neural Engineering Framework (NEF) of Eliasmith & Anderson [Neural engineering: Computation representation and dynamics in neurobiological systems. Cambridge, MA: MIT Press, 2003] which identifies implementational principles for neural models. To address 1, I suggest that adopting statistical modeling methods for perception and action will be functionally sufficient for capturing biological behavior. I show how these two answers will be mutually constraining, since the process of model selection for the statistical method in this approach can be informed by known anatomical and physiological properties of the brain, captured by the NEF. Similarly, the application of the NEF must be informed by functional hypotheses, captured by the statistical modeling approach.

The ability to improve in speed and accuracy as a result of repeating some task is an important hallmark of intelligent biological systems. Although gradual behavioral improvements from practice have been modeled in spiking neural networks, few such models have attempted to explain cognitive development of a task as complex as addition. In this work, we model the progression from a counting-based strategy for addition to a recall-based strategy. The model consists of two networks working in parallel: a slower basal ganglia loop and a faster cortical network. The slow network methodically computes the count from one digit given another, corresponding to the addition of two digits, whereas the fast network gradually “memorizes” the output from the slow network. The faster network eventually learns how to add the same digits that initially drove the behavior of the slower network. Performance of this model is demonstrated by simulating a fully spiking neural network that includes basal ganglia, thalamus, and various cortical areas. Consequently, the model incorporates various neuroanatomical data, in terms of brain areas used for calculation and makes psychologically testable predictions related to frequency of rehearsal. Furthermore, the model replicates developmental progression through addition strategies in terms of reaction times and accuracy, and naturally explains observed symptoms of dyscalculia.

Neural networks have long been used to study linguistic phenomena spanning the domains of phonology, morphology, syntax, and semantics. Of these domains, semantics is somewhat unique in that there is little clarity concerning what a model needs to be able to do in order to provide an account of how the meanings of complex linguistic expressions, such as sentences, are understood. We argue that one thing such models need to be able to do is generate predictions about which further sentences are likely to follow from a given sentence; these define the sentence's “inferential role.” We then show that it is possible to train a tree-structured neural network model to generate very simple examples of such inferential roles using the recently released Stanford Natural Language Inference (SNLI) dataset. On an empirical front, we evaluate the performance of this model by reporting entailment prediction accuracies on a set of test sentences not present in the training data. We also report the results of a simple study that compares human plausibility ratings for both human-generated and model-generated entailments for a random selection of sentences in this test set. On a more theoretical front, we argue in favor of a revision to some common assumptions about semantics: understanding a linguistic expression is not only a matter of mapping it onto a representation that somehow constitutes its meaning; rather, understanding a linguistic expression is mainly a matter of being able to draw certain inferences. Inference should accordingly be at the core of any model of semantic cognition.

Inductive reasoning is a fundamental and complex aspect of human intelligence. In particular, how do subjects, given a set of particular examples, generate general descriptions of the rules governing that set? We present a biologically plausible method for accomplishing this task and implement it in a spiking neuron model. We demonstrate the success of this model by applying it to the problem domain of Raven's Progressive Matrices, a widely used tool in the field of intelligence testing. The model is able to generate the rules necessary to correctly solve Raven's items, as well as recreate many of the experimental effects observed in human subjects

There has been a long-standing debate between symbolicists and connectionists concerning the nature of representation used by human cognizers. In general, symbolicist commitments have allowed them to provide superior models of high-level cognitive function. In contrast, connectionist distributed representations are preferred for providing a description of low-level cognition. The development of Holographic Reduced Representations (HRRs) has opened the possibility of one representational medium unifying both low-level and high-level descriptions of cognition. This paper describes the relative strengths and weaknesses of symbolic and distributed representations. HRRs are shown to capture the important strengths of both types of representation. These properties of HRRs allow a rebuttal of Fodor and McLaughlin's (1990) criticism that distributed representations are not adequately structure sensitive to provide a full account of human cognition.

To have a fully integrated understanding of neurobiological systems, we must address two fundamental questions: 1. What do brains do (what is their function)? and 2. How do brains do whatever it is that they do (how is that function implemented)? I begin by arguing that these questions are necessarily inter-related. Thus, addressing one without consideration of an answer to the other, as is often done, is a mistake. I then describe what I take to be the best available approach to addressing both questions. Specifically, to address 2, I adopt the Neural Engineering Framework (NEF) of Eliasmith & Anderson [Neural engineering: Computation representation and dynamics in neurobiological systems. Cambridge, MA: MIT Press, 2003] which identifies implementational principles for neural models. To address 1, I suggest that adopting statistical modeling methods for perception and action will be functionally sufficient for capturing biological behavior. I show how these two answers will be mutually constraining, since the process of model selection for the statistical method in this approach can be informed by known anatomical and physiological properties of the brain, captured by the NEF. Similarly, the application of the NEF must be informed by functional hypotheses, captured by the statistical modeling approach

In a recent series of publications, dynamicist researchers have proposed a new conception of cognitive functioning. This conception is intended to replace the currently dominant theories of connectionism and symbolicism. The dynamicist approach to cognitive modeling employs concepts developed in the mathematical field of dynamical systems theory. They claim that cognitive models should be embedded, low-dimensional, complex, described by coupled differential equations, and non-representational. In this paper I begin with a short description of the dynamicist project and its role as a cognitive theory. Subsequently, I determine the theoretical commitments of dynamicists, critically examine those commitments and discuss current examples of dynamicist models. In conclusion, I determine dynamicism's relation to symbolicism and connectionism and find that the dynamicist goal to establish a new paradigm has yet to be realized

Several approaches to implementing symbol-like representations in neurally plausible models have been proposed. These approaches include binding through synchrony, “mesh” binding, and conjunctive binding. Recent theoretical work has suggested that most of these methods will not scale well, that is, that they cannot encode structured representations using any of the tens of thousands of terms in the adult lexicon without making implausible resource assumptions. Here, we empirically demonstrate that the biologically plausible structured representations employed in the Semantic Pointer Architecture approach to modeling cognition do scale appropriately. Specifically, we construct a spiking neural network of about 2.5 million neurons that employs semantic pointers to successfully encode and decode the main lexical relations in WordNet, which has over 100,000 terms. In addition, we show that the same representations can be employed to construct recursively structured sentences consisting of arbitrary WordNet concepts, while preserving the original lexical structure. We argue that these results suggest that semantic pointers are uniquely well-suited to providing a biologically plausible account of the structured representations that underwrite human cognition.

I argue that of the four kinds of quantitative description relevant for understanding brain function, a control theoretic approach is most appealing. This argument proceeds by comparing computational, dynamical, statistical and control theoretic approaches, and identifying criteria for a good description of brain function. These criteria include providing useful decompositions, simple state mappings, and the ability to account for variability. The criteria are justified by their importance in providing unified accounts of multi-level mechanisms that support intervention. Evaluation of the four kinds of description with respect to these criteria supports the claim that control theoretic characterizations of brain function are the kind of quantitative description we ought to provide.Keywords: Neural computation; Control theory; Neural representation; Cognitive architecture; Cognitive models; Theoretical neuroscience

  Van Gelder (1995) has recently spearheaded a movement to challenge the dominance of connectionist and classicist models in cognitive science. The dynamical conception of cognition is van Gelder's replacement for the computation bound paradigms provided by connectionism and classicism. He relies on the Watt governor to fulfill the role of a dynamicist Turing machine and claims that the Motivational Oscillatory Theory (MOT) provides a sound empirical basis for dynamicism. In other words, the Watt governor is to be the theoretical exemplar of the class of systems necessary for cognition and MOT is an empirical instantiation of that class. However, I shall argue that neither the Watt governor nor MOT successfully fulfill these prescribed roles. This failure, along with van Gelder's peculiar use of the concept of computation and his struggle with representationalism, prevent him from providing a convincing alternative to current cognitive theories

Many contemporary philosophers favor coherence theories of knowledge (Bender 1989, BonJour 1985, Davidson 1986, Harman 1986, Lehrer 1990). But the nature of coherence is usually left vague, with no method provided for determining whether a belief should be accepted or rejected on the basis of its coherence or incoherence with other beliefs. Haack's (1993) explication of coherence relies largely on an analogy between epistemic justification and crossword puzzles. We show in this paper how epistemic coherence can be understood in terms of maximization of constraint satisfaction, in keeping with computational models that have had a substantial impact in cognitive science. A coherence problem can be defined in terms of a set of elements and sets of positive and negative constraints between pairs of those elements. Algorithms are available for computing coherence by determining how to accept and reject elements in a way that satisfies the most constraints. Knowledge involves at least five different kinds of coherence - explanatory, analogical, deductive, perceptual, and conceptual - each requiring different sorts of elements and constraints.