Implications of Polychronous Neuronal Groups for the Nature of Mental Representations

Implications of Polychronous Neuronal Groups for the Nature of Mental Representations William Benjamin St. Clair (wst.clair@ucmerced.edu) David C. Noelle (dnoelle@ucmerced.edu) Cognitive and Information Sciences University of California, Merced 5200 North Lake Road; Merced, CA 95343 USA Abstract eventually making causal contact with the world through sen- sory and motor processes. When using the vector space ap- proach, these cognitive processes are well described in neu- rocomputational terms, with nearby points in a vector space tending to produce similar results when presented to mod- els of downstream neural circuits. While the vector space approach has been criticized as lacking support for compo- sitional and structured conceptual representations (Fodor & Pylyshyn, 1988), and there continues to be extensive work on addressing this critique (Gayler & Levy, 2011), highly promising approaches to compositionality have been pro- posed, making use of vector space operations of superposi- tion, convolution, and sparse coding (Smolensky, 1990; Plate, 2003; OReilly, Bhattacharyya, Howard, & Ketz, 2011). In general, the vector space approach to conceptual representa- tion has been very productive. How are concepts represented in the human mind? Vector space representations based on the instantaneous firing rates of neurons have been used with great success. However, there is growing evidence, both empirical and computational, that relevant information is encoded in spatiotemporal patterns of spikes called polychronous neuronal groups (PNGs). In this paper, we consider the philosophical implications of PNG rep- resentations with regard to their temporal extension, ground- ing, compositionality, and similarity. We suggest that the tem- porally extended nature of PNGs implies that conceptual-level dynamics may only be coherent at coarse time scales. We introduce the notion of PNG trigger sets as a way to ground the meaning of PNG representations, and we discuss potential approachs to compositionality. Finally, we identify the open problem of how to define an appropriate similarity metric for PNG-based mental representations. Keywords: Philosophy of Cognitive Science; Neuroscience; Representation; Dynamical Systems. Introduction How are concepts represented in the human mind? One highly productive approach to this question has involved the application of a continuous dynamical systems perspec- tive to the problem (Spivey, 2008). From this perspective, the currently active concepts of a cognitive system (or sub- system) are jointly encoded as a point in a high dimen- sional vector space (Churchland, 1989). Nearby points in this space, according to some distance metric, are seen as representing similar conceptual states, allowing regions and manifolds within this space to capture more general con- cepts or categories (G¨ardenfors, 2000). The evolution of mental states over time becomes a trajectory in this vector space (Yoshimi, 2012), driven by mechanistic cognitive pro- cesses (Churchland, 1996). This vector space approach to conceptual representation has many strengths. It supports accounts of the biological ba- sis of cognition by viewing the dimensions of the vector space as the activity of neural units, such as their firing rates, offer- ing a framework for mapping from the physical state space of the brain to the conceptual state space of the mind (Spivey, 2008). The approach provides a straightforward way to dis- cuss the cognitive state of a system at any instant in time, as well as how those states change over time. Issues sur- rounding the grounding of representations are well addressed from the perspective of conceptual role semantics (Greenberg & Harman, 2006), with the “meaning” of a representation being a function of the inputs that activate it and the other representations that it produces through causal relationships, Past challenges to the vector space approach have come from above: from more abstract and symbolic characteriza- tions of cognitive content and cognitive processing. More recently, a challenge has arisen from below: from in- sights into the neural coding of information (Rieke, Warland, Steveninck, & Bialek, 1999). There is increasing empirical evidence that, in at least some neural systems, relevant infor- mation is encoded in the spatiotemporal pattern of discrete ac- tion potentials, or spikes, produced by neurons in a given nu- cleus (Rolston, Wagenaar, & Potter, 2007; Madhavan, Chao, & Potter, 2007; Pasquale et al., 2008). While information, in some cases, may be carried by synchronous or coherent firing of neurons (Fries et al., 2005), computational considerations have suggested that content may frequently be encoded in complex asynchronous patterns of spikes (Izhikevich, 2006). These complex spike patterns have been called polychronous neuronal groups (PNGs). The PNG approach to represen- tation differs substantially from the vector space approach. A PNG is a temporally extended pattern of discrete spiking events over a collection of neurons, and it is not clear how such a pattern could be mapped to a point in a continuous vector space so as to preserve relevant aspects of similar- ity between representations. In the vector space approach, temporally extended trajectories capture dynamic changes in cognitive content, while the PNG account encodes individ- ual conceptual states in such trajectories. A PNG need not be oscillatory, so it does not make sense to extract features like frequency or phase to map a PNG into a vector space. In some important ways, the PNG approach is fundamentally