Visual Motion Perception using Critical Branching Neural Computation

Visual Motion Perception using Critical Branching Neural Computation Janelle K. Szary (jszary@ucmerced.edu) Christopher T. Kello (ckello@ucmerced.edu) Cognitive and Information Science, 5200 North Lake Rd., Merced, CA 95343 USA Abstract Motion processing in visual systems is supported by various subcortical and cortical microcircuits. However, all motion processing requires a basic capacity to integrate and combine information over time, as may be true for all microcircuits that support perceptual and cognitive functions. In the present study, a generic microcircuit model is presented that self- tunes its recurrent spiking dynamics to its critical branching point. The model is shown to have generic memory capacity that can be tapped for the purpose of visual motion processing. These results suggest that critical branching neural networks may provide general bases for spiking models of motion processing and other perceptual and cognitive functions. Keywords: Critical branching; reservoir computing; leaky integrate-and-fire neural networks; motion perception. Introduction Communication in neural networks largely occurs via thresholded spiking signals between neurons, which are connected by characteristically recurrent loops varying in spatial and temporal scale (Buzsaki, 2006). This connectivity structure produces patterns of network activity that are continually in flux, and in this sense network dynamics cannot be characterized by simple point or limit cycle attractors. This limits the extent to which attractor- based neural network models, common in cognitive science (e.g. connectionist recurrent networks), can relate the brain’s spiking dynamics with cognitive functions. In order to investigate how computational functions might be based in non-attractor network dynamics, Maass et al. (2002b) and Jaeger (2001) developed the concept of reservoir computing. The basic idea is that recurrent networks can produce dynamics with a generic capacity for computation, and so-called “read-out” networks can learn to interpret reservoir dynamics for task-specific purposes. The present work is focused on Maass et al.’s (2002b) liquid state machine (LSM) framework, which consists of a pool of leaky integrate-and-fire (LIF) units with random recurrent connectivity that is roughly constrained to be local and sparse. Time-varying input signals are fed to the network to drive and alter the “liquid” spiking dynamics. Due to recurrence, thresholding, and other non-linearities, the resulting spatial and temporal spike patterns are complex, unknown, and unlearned functions of their inputs. Nonetheless, these spike patterns will contain information about past inputs to the extent that their dynamics are not overly convergent or overly divergent (i.e. with Lyapunov exponents near one; Bertschinger & Natschlager, 2004). Maass et al. (2002b) found that even when the input patterns are non-linearly separable (e.g. XOR and parity), simple linear classification can be used to categorize inputs based on the liquid spike patterns they produce. Thus, simple learning algorithms can be used to interpret complex spiking dynamics for non-trivial functions and tasks. Moreover, the authors showed that functions of past inputs can be learned from current spike patterns because memory is an inherent property of recurrent dynamics that are not overly convergent or divergent. The efficacy and simplicity of reservoir computing makes it an attractive generic mechanism for computational perception tasks. In fact, Verstraeten et al. (2005) used LSMs to classify spoken words, and Maass et al. (2002a) used them to classify the shapes and velocities of visual objects in motion. Burgsteiner et al. (2006) used real-time video footage from the RoboCup Soccer challenge to show that an LSM could be used to predict the future location of a soccer ball in motion. Visual Motion Perception Biological motion perception starts with motion detectors in the retina, where ganglion cells just two or three synapses away from rods and cones detect motion in preferred directions (Vaney et al., 2000). Behaviorally, sensitivity to the direction of motion is demonstrated in motion coherence studies (reviewed in Braddick, 1997), where even minute asymmetries in the percentage of motion in one or another direction can be detected. Information about the direction of motion is used for navigation, such as when coherent motion across the visual field constitutes optic flow, and for the detection of objects in motion, such as when local motion differs from global motion (Srinivasan, 2000). Tracking objects is another important function of motion perception, i.e. the ability to predict future locations of objects in motion. This kind of prediction is hypothesized to be necessary for accurate smooth-pursuit eye movements (Carpenter, 1988), and it enables organisms to either avoid collisions with moving objects, or coincide with them as in catching or hitting a baseball. For instance, McBeath (1990) showed that the motor action of aiming and swinging a bat must be implemented when the ball is just over halfway to the plate, using a prediction of where the ball will be. Similarly, studies of cricket batters’ eye movements show predictive eye fixations on where the ball will be when it crosses the mound, rather than where it currently is (Land & McLeod, 2000). The present work focuses on both of these functions of motion processing: direction classification and future location prediction. Reservoir computing techniques are particularly well-suited for motion perception tasks, as both