A distributed cellular approach of large scale SOM models for hardware implementation

Brain-Inspired Self-Organization with Cellular Neuromorphic Computing for Multimodal Unsupervised Learning

“…An FPGA distributed implementation model for SOMs was proposed in Reference [81], where the local computation and the information exchange among neighboring neurons enable a global self-organization of the entire network. Similarly, we proposed in Reference [21] a cellular formulation of the related neural models which would be able to tackle the full connectivity limitation by iterating the propagation of the information in the network. This particular cellular implementation, named the Iterative Grid (IG), reaches the same behavior as the centralized models but drastically reduces their computing complexity when deployed on hardware.…”

“…This particular cellular implementation, named the Iterative Grid (IG), reaches the same behavior as the centralized models but drastically reduces their computing complexity when deployed on hardware. Indeed, we have shown in Reference [21] that the time complexity of the IG is O( √ n) with respect to the number of neurons n in a squared map, while the time complexity of a centralized implementation is O(n). In addition, the connectivity complexity of the IG is O(n) with respect to the number of of neurons n, while the connectivity complexity of a distributed implementation with all-to-all connectivity [49] is O(n 2 ).…”

“…For the SOM afferent weights learning, the data to be propagated is the maximum activity for the BMU election, plus its distance with respect to every neuron in the map. The maximum activity is transmitted through the wave of propagation, and the distance to the BMU is computed in the same wave thanks to this finding: "When a data is iteratively propagated through a grid network, the propagation time is equivalent to the Manhattan distance between the source and each receiver" [21].…”

“…The SOM implementation on the IG proposed in Reference [21] has to be adapted to fit the needs of the multimodal association: (1) we add the WMU activity needed for the activities min-max normalization in the convergence step, and (2) we use the Gaussian kernel in Equation (1) to transform the euclidean distances into activities. Therefore, the BMU is the neuron with the maximum activity and the WMU the neuron with the minimum one.…”

“…Section 2 describes the Reentry framework of Edelman [19] and the Convergence Divergence Zone framework of Damasio [20], two different theories in neuroscience for modeling multimodal association in the brain, and then review some of their recent computational models and applications. Section 3 details the proposed ReSOM multimodal learning and inference algorithms, while Section 4 presents an extension of the Iterative Grid (IG) [21] which is applied to distribute the systems's computation in a cellular neuromorphic architecture for FPGA implementations. Then, Section 5 presents the databases, experiments and results with the different case studies.…”