Chris Eliasmith

It will always remain a remarkable phenomenon in the history of philosophy, that there was a time, when even mathematicians, who at the same time were philosophers, began to doubt, not of the accuracy of their geometrical propositions so far as they concerned space, but of their objective validity and the applicability of this concept itself, and of all its corollaries, to nature. They showed much concern whether a line in nature might not consist of physical points, and consequently that true space in the object might consist of simple [discrete] parts, while the space which the geometer has in his mind [being continuous] cannot be such

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.

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

  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