Function approximation with uncertainty propagation in a VLSI spiking neural network Dane Corneil * , Daniel Sonnleithner * , Emre Neftci * , Elisabetta Chicca † , Matthew Cook * , Giacomo Indiveri * , Rodney Douglas * * Institute of Neuroinformatics University of Zurich and ETH Zurich Email: emre@ini.phys.ethz.ch † Cognitive Interaction Technology - Center of Excellence Bielefeld University, Germany Abstract—The brain combines and integrates multiple cues to take coherent, context-dependent action using distributed, event- based computational primitives. Computational models that use these principles in software simulations of recurrently coupled spiking neural networks have been demonstrated in the past, but their implementation in hybrid analog/digital Very Large Scale Integration (VLSI) spiking neural networks remains challenging. Here, we demonstrate a distributed spiking neural network architecture comprising multiple neuromorphic VLSI chips able to reproduce these types of cue combination and integration operations. This is achieved by encoding cues as population activities of input nodes in a network of recurrently coupled VLSI Integrate-and-Fire (I&F) neurons. The value of the cue is place-encoded, while its uncertainty is represented by the width of the population activity proﬁle. Relationships among different cues are speciﬁed through bidirectional connectivity matrices, shared between the individual input node populations and an intermediate node population. The resulting network dynamics bidirectionally relate not only the values of three variables ac- cording to a speciﬁed relation, but also their uncertainties. When cues on two populations are speciﬁed, the standard deviation of the activity in the unspeciﬁed population varies approximately linearly with the widths of the two input cues, and has less than 6% error in position compared to the value speciﬁed by the inputs. The results suggest a mechanism for recurrently relating cues such that missing information can both be recovered and assigned a level of certainty. I. I NTRODUCTION The combination of sensory input cues and the inference of missing information from noisy, incomplete sensory cues are fundamental computations carried out by the brain [1]. The brain performs these prodigious feats using networks of heterogeneous, spike-communicating neurons, which stand in stark contrast to the technology and algorithms employed by digital processors. Recent theoretical studies have demon- strated with simulations how such computations could be performed in a biologically plausible manner, using arrays of ideal neurons with real-valued outputs [2]–[4]. A class of neural networks using probabilistic population codes are capable of near-optimal manipulation of probabilistic distributions [2], [3], [5]. One attractive feature of this type of network is that the uncertainty of the input cues, typi- cally encoded in the width of a population activity proﬁle, is propagated in the network [2]. The propagation of cue uncertainty in neural populations is relevant for many tasks such as sensorimotor transformations [6], cue integration [2] and decision making [5]. Our contribution here is to develop an electronic VLSI emulation of a spiking neural network that communicates by asynchronous events to infer, in real-time, the value and the variability of a cue based on the other cues available to the system. The neural architecture is based on a recently proposed one [7] consisting of four networks of spiking neurons, three of which provided sensory input while the fourth encoded the relation between these inputs. The three input networks were conﬁgured as 1-D arrays of I&F neurons whose lateral excitatory and global inhibitory couplings implemented a soft Winner-Take-All (sWTA) network [8]. The recurrent pattern of connections in the sWTA is consistent with the observed connectivity of the neocortex [9] and has been proposed as an important neural computational primitive [10] that can be combined easily and stably in large networks [11]. These input sWTA populations provided place-encoded representations of their sensory variables. The relationship between the variables was speciﬁed by the bidirectional connectivity between the individual sWTA networks and the central 2-D WTA network. One shortcoming of this architecture, however, was that it disregarded the uncertainty of the cues. This was due to the hard WTA computations taking place in the intermediate node that caused only a single unit to become active. Here, we extend this architecture by allowing the intermediate node to select multiple winners in a sequential manner. The result is that the network conveys, in addition to the value of a variable, the information related to the widths of the neural activity proﬁles, causing them to be sharpened or broadened according to the widths of the activity proﬁles in all other nodes. As in the previous implementation, the recurrent excitation developed by the input sWTA networks, constrained by the patterns embedded in their interconnections with the central node, provides the gain necessary to recover an unspeciﬁed cue when the two others are speciﬁed (function approximation). Thanks to the bidirectional connections in the network, each node acts simultaneously as an input and an output node. The interaction of populations of neurons with various proﬁles of activation resembles the interaction of statistical U.S. Government work not protected by U.S. copyright WCCI 2012 IEEE World Congress on Computational Intelligence June, 10-15, 2012 - Brisbane, Australia IJCNN 2990