A Self-Organizing Map Architecture for Arm Reaching Based on Limit Cycle Attractors

Abstract

Creating and studying neurocognitive architectures is an active and increasing focus of research efforts. Based on our recent research that uses neural activity limit cycles in selforganizing maps (SOMs) to represent external stimuli, this study explores the use of such limit cycle attractors in a neurocognitive architecture for an open-loop arm reaching task. The goal is to learn to produce a static motor command for arm joints that moves the manipulator to a target spatial location, while the internal neural activity remains oscillatory. Unlike with static SOMs, stabilizing output based on changing neural activity becomes an important issue. Our architecture is also characterized by simple and forgiving timing requirements, meaning that the time of gating among neural components can be set relatively arbitrarily due to the repetitiveness of limit cycle activity. The results indicate that our architecture generalizes to unseen data, and that the overall performance is insensitive to exact gate timing.

A limit-cycle self-organizing map architecture for stable arm control

“…Our choices of enabled α values are determined empirically so that each source of inputs has approximately equal contribution to the net input. While our preliminary results indicated that a wide range of α values led to similar limit cycle properties, the values used here are kept consistent with our past studies [20,21]. At each time step, afferent weights w are updated based on a typical unsupervised SOM learning rule, and recurrent weights u are updated based on temporally asymmetric Hebbian learning [44]:…”

“…Parameter t out represents a fixed time step at which the output is taken. Although here the output is taken at a specific time step, we have shown in a recent study that continuous outputs with an open system alone yield stable joint angles with very small oscillations (e.g., around 5 × 10 −5 in a normalized Cartesian space) [20]. This means that t out can be chosen quite arbitrarily, but it must be late enough such…”

“…are obtained using certain values for the timing parameters t assoc , t filter , and t out ( of "open-loop-only" in this context is only intended to be a convenient label, to be consistent with the terminology of our earlier paper [20] and to signify the fact that the manipulator's position X is never fed back, which is more relevant in inverse kinematics problems. position and the spatial target are the same as those used in Fig.…”

“…pected since the open-loop subsystem here does not have a perfect internal representation, and thus the movement is likely to be erroneous without being regulated by error feedback along the trajectory [20,26]. On the other hand, Fig.…”

“…To address these issues, we have recently begun to explore the possibility of designing neural architectures using SOMs based on a limit cycle representation [19][20][21]. With these limit cycle SOMs, each input pattern is encoded by a short periodic sequence of multi-winner activity patterns that collectively form a limit cycle attractor.…”