916 IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, VOL. 23, NO. 6, JUNE 2012 Neural Assembly Computing João Ranhel, Member, IEEE Abstract— Spiking neurons can realize several computational operations when firing cooperatively. This is a prevalent notion, although the mechanisms are not yet understood. A way by which neural assemblies compute is proposed in this paper. It is shown how neural coalitions represent things (and world states), memorize them, and control their hierarchical relations in order to perform algorithms. It is described how neural groups perform statistic logic functions as they form assemblies. Neural coalitions can reverberate, becoming bistable loops. Such bistable neural assemblies become short- or long-term memories that represent the event that triggers them. In addition, assemblies can branch and dismantle other neural groups generating new events that trigger other coalitions. Hence, such capabilities and the interaction among assemblies allow neural networks to create and control hierarchical cascades of causal activities, giving rise to parallel algorithms. Computing and algorithms are used here as in a nonstandard computation approach. In this sense, neural assembly computing (NAC) can be seen as a new class of spiking neural network machines. NAC can explain the following points: 1) how neuron groups represent things and states; 2) how they retain binary states in memories that do not require any plasticity mechanism; and 3) how branching, disbanding, and interaction among assemblies may result in algorithms and behavioral responses. Simulations were carried out and the results are in agreement with the hypothesis presented. A MATLAB code is available as a supplementary material. Index Terms— Bistable neural assemblies, branching, disman- tling, neural assembly computing, neural coalition, polychronous groups, spiking neural networks. I. I NTRODUCTION T HE notion that neural assembly (NA) might represent, memorize, and compute is not new. For instance, at the beginning of the last century, Sherrington pointed out the importance of neural populations in sensorimotor information processing [1], and suggested that motor neurons serving a particular muscle form a pool of potentially active cells [2]. In 1949, D. Hebb proposed that coactivation of cell assemblies could be responsible for representing concepts [3]. However, the idea was not taken further, mainly due to the lack of technology for recording activity in large amount of neurons. Only recently, research in this subject has been boosted [1], [4], (reviews in [5] and [6] for the optical approach). In neuroscience literature, NA phenomena are described by different terms or ideas, for instance, by attractor networks [7], persistent activity and working memory [8]–[11], transient neural synchronization [12]–[15], neural cell assemblies [1], Manuscript received June 4, 2011; accepted March 3, 2012. Date of publication April 18, 2012; date of current version May 10, 2012. The author is with the Polytechnic School, University of São Paulo, São Paulo 05508-970, Brazil (e-mail: jranhel@ieee.org). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TNNLS.2012.2190421 [5], [16]–[19], temporally correlated activity [20], oscillating networks [4], [21], [22], reverberating loops [23], spatiotem- poral firing patterns [24], among others. Texts describing such phenomena depict dynamical neural groups temporarily firing together. NAs must be differentiated from specialized neuron groups, such as central pattern generator (CPG) (for CPG, see [25]–[28] and references therein). According to [17], NAs provide a conceptual framework for dealing with the integration of distributed neural activity, capable of explaining how neural networks select, coordinate, and orchestrate distributed brain activities. NAs may be seen “as distributed local networks of neurons transiently linked by reciprocal dynamic connections” [17]. In the artificial neural networks (ANNs) area, the first two ANN generations were not centered on transient assembly. We focus here on spiking neural networks (SNNs), which are considered the third generation of ANNs [29]. SNNs are remarkably bio-inspired, with neuron models deriving from recent advances in neurosciences [30], [31]. As a result of their operational features, spiking neurons tend to gather in functional groups firing together during strict time intervals, forming coalitions or assemblies [1], [5], [32], also referred here as events. As pointed out in [5], “a widely discussed hypothesis in neuroscience is that transiently active ensembles of neurons, known as ‘cell assemblies,’ underlie numerous operations of the brain, from encoding memories to reasoning. However, the mechanisms responsible for the formation and disbanding of cell assemblies and temporal evolution of cell assembly sequences are not well understood.” In [31] we find: “the current consensus agrees that cognitive processes are most likely based on the activation of transient assemblies of neurons {...}, although the underlying mechanisms are not yet understood well.” Another excerpt, from [21]: “information in the brain has been hypothesized to be processed, transferred, and stored by flexible cell assemblies {...}. The mechanisms by which such ephemeral neural coalitions are brought about are not known.” In summary, there is a strong intuition that NA can compute, but the mechanisms underlying such operations are not yet understood. In this paper, a way by which NA represent, memorize, and control operations by means of branching and disband- ing gathered neurons is presented. In this proposal, neural coalitions become persistent phenomena as assemblies interact with each other. This is a functional approach which describes neural assemblies performing causal and hierarchical opera- tions, capable of carrying out complex algorithms. In Section II, previous approaches in NA investigation, as well as the polychronization concept, are described. In Section III, the bistable assembly formation and how it 2162–237X/$31.00 © 2012 IEEE