Nengo and the Neural Engineering Framework: Connecting Cognitive Theory to Neuroscience

Nengo and the Neural Engineering Framework: Connecting Cognitive Theory to Neuroscience Chris Eliasmith (celiasmith@uwaterloo.ca) Terrence C. Stewart (tcstewar@uwaterloo.ca) Center for Theoretical Neuroscience, University of Waterloo 200 University Ave West, Waterloo, ON, N2L 3G1, Canada Keywords: cognitive modeling; neural engineering; representation; decision making; working memory with these tutorials (Windows, OS X, and Linux are all supported, and software is provided). In particular, the tutorial covers using the NEF to represent scalars and vectors, perform linear and nonlinear transformations on these values, and store information over time. These are the basic mechanisms required for a wide range of algorithms, and form the basis for our models of sensorimotor systems, working memory, and cognitive control. This provides participants with basic building blocks for constructing novel neural implementations of a wide variety of cognitive models. To supplement this, we more closely examine how the theory of Vector Symbolic Architectures can be implemented using the NEF. This involves using high- dimensional fixed-length vectors to represent symbols and symbol trees. The nonlinear operation of circular convolution is used to manipulate these symbol trees. This can be seen as a non-classical symbol system, capable of performing the operations required for symbolic cognition. The result is a scalable and efficient neural cognitive architecture, constructed from the basic approaches described in the first half of the tutorial. Finally, a variety of other uses of the NEF are provided. This includes learning rules for modifying synaptic connection weights (with examples for implementing an associative memory and reinforcement learning), a model of the Wason card task (symbol manipulation and generalization), and a model of the basal ganglia-thalamus- cortex loop which implements a basic production system. Together, these hands-on examples will introduce participants to many of the major components needed to address a wide variety of cognitive behaviour. A previous version of this tutorial was presented at ICCM 2009 and CogSci 2010. Slides and step-by-step instructions are available at . As a result of feedback from these tutorials, we have continued to improve Nengo's user interface, making common actions easier and developing new displays for observing and the ongoing neural activity and adjusting its inputs as the simulation runs (see Figure 1). Tutorial Objectives As we learn more about the neural activity underlying cognitive function, there is an increasing demand to explicitly and quantitatively connect cognitive theories to neurological details. Bridging these levels provides benefits in both directions; aspects of the cognitive theory can predict and be constrained by neurological details, and the neurological details can identify important modifications to the overall cognitive theory. This tutorial introduces the Neural Engineering Framework (NEF; Eliasmith and Anderson, 2003) and the associated open-source toolkit Nengo ( ), which offer a general method for implementing high-level cognitive theories using biologically realistic spiking neurons. The NEF allows researchers to 1) provide a high- level description of a cognitive theory (in terms of information being represented and transformed) and 2) identify relevant neural constraints (anatomical, neurophysiological, and so on). It then produces a detailed model of neural activity, including predicted spike patterns, firing rates, connectivity, and overall behaviour. These methods have been made more accessible by the construction of a software package (Nengo), which provides a graphical interface suitable for network construction. This tutorial introduces the NEF theory explaining how high- level function can be systematically related to single cell activity, and provides extensive hands-on experience building these neural models using Nengo. Our central objective is to allow participants to leave the tutorial with a method for constructing cognitive models with spiking neurons, and experience using that method in an intuitive software environment. Tutorial Structure The tutorial is structured so as to combine the theoretical bases of the Neural Engineering Framework with hands-on examples of practically applying these concepts. To do this, we make use of Nengo , an open-source Java- based neural simulator that supports the NEF. For example, the presentation of the theory for how a scalar value can be represented by the spiking pattern in a group of neurons is paired with a tutorial on using Nengo to generate such a neural group and simulate its behavior over time. Participants are encouraged to bring a laptop to follow along Tutorial Justification The Neural Engineering Framework provides a method to bridge the gap between cognitive and neural theories. Its earlier applications have been to sensory and motor systems, including the barn owl auditory system, rodent navigation, escape and swimming control in zebrafish, and the translational vestibular ocular reflex in monkeys. However,

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