Feb. 28 (Thursday) Mario Negrello (Cornell University)
Attractor Landscapes and Active Tracking
Abstract:
Neurodynamics:
We study the behavior generated by recurrent neural networks in artificial agents, from the dynamical systems perspective. Following philosophy remounting as far back as Democritus (and also cyberneticists as Ashby and Von Foerster, existentialists and phenomenologists such as Heidegger and Merleau-Ponty), that points to the unescapable fact that organisms’ neural systems are extended in the world. Taken together, our methodology and philosophy lead us to build robotic models of cognitive systems, in which recurrent neural networks couple robots and world. Such coupling is expressed in alterations of the network structures for control, structures that are evolved with evolutionary algorithms, in virtual worlds, and eventually implemented on real robots. The crucial facet of the work is to understand how the neural networks generate behavior, from the dynamical stand point. The formal tools of neurodynamics make it possible to understand the dynamical underpinnings of behavior, and to proffer causal explanations of behavior as a physical phenomenon.
Attractor Landscapes as Behavior Invariants:
More specifically, we note that between networks and function there is a many to one mapping. In other words, for one selected function there may be many equivalent networks to execute it. Is there then something that does not vary among different networks that execute similar function? Our answer is given in our language of neurodynamics. We start by observing that a recurrent neural network parametrized by the input, is in fact a collection of dynamical systems. Moreover, associated with one set of parameters, there exists a single dynamical system. Each of these dynamical systems possesses an attractor structure of varying complexity, where one may find different kinds of attractors, including fixed points, periodic attractors, as well as quasi-periodic and chaotic attractors. The attractor structure is determined by the basins of attraction and the potentially coexisting attractors of one network, which are determined by the network’s structure.
The capacity for behavior of an embodied neural network is then given by the set of attractors accessible through parametrizations, and realizable through motor efferences. Furthermore, the capacity for behavior is constrained by the possible parametrizations to the network; that being the set of possible input stimuli. The possible input stimuli are a function of the structural coupling, resulting from the problem of physical nature; meaning, how is the world regimented in terms of physical laws, and how is the agent built, in terms of its morphology, sensors and actuators. The invariant we find in control, or the capacity for behavior of the network we call the attractor landscape, which can be thought of as the behavioral invariant of the neural network. I will show a couple of examples of different evolved agents, with different networks, and point to what is invariant in their set of attractors, with respect to executed function.