From nonlinear dynamics to proof of concept for Heteroclinic Computing
Final Report Abstract
Despite the detailed analysis of the collective nonlinear dynamics of systems exhibiting heteroclinic networks and the several theoretical suggestions about their computational capabilities, no complete concept for a computational system based on the dynamics near heteroclinic network structures existed at the start of the project. By combining analytical insights, circuit simulations and hardware tests, we have laid the foundations on dynamical systems knowledge about spiking neural networks and their complex computing capabilities. We focused on dynamics guided by heteroclinic networks, and after discovering a novel link to stable systems with analogous features on multi-stable dynamics in circuits with proportional inhibition. We proposed and analyzed a two layer feed-forward read-out that by design requires only linearly many (2N) additional units for a N-neuron recurrent computing network and in addition uses only a few spikes per neuron for read-out processing. The read-out is also robust against perturbations, self-correcting, and decodes all desired complex periodic orbits. We presented and studied basic neuron motif networks that act as basic entities providing volatile memory, a prerequisite for more complex computational device concepts and for any implementation of heteroclinic(-like) computations in hardware. We integrated knowledge from the first two work packages as well as additional insights about the influence of noise in spiking systems with heteroclinic and related dynamics to realize computational function in real hardware, integrating real environmental noise and perturbations, basic memory, decoding, and direct motion control. Already in the early phases of this project, when working on decoding and noise, we discovered an analogy of computational features in systems with stable instead of heteroclinic (saddle-driven) dynamics. The insights led to a new form of noise-robust, reconfigurable spiking neural circuits. In the future, the new features may help designing self-adapting systems that also become robust against complete failures or removal of units or communication channels, opening up a novel paradigm for spike-based computing. Mathematically and conceptually, the link between systems with proportional inhibition (and thus multiplicative coupling) to systems with heteroclinic dynamics (and additive coupling) is fundamental. Considering the progress jointly in the light of the rapidly evolving field of spiking neural networks as well as their hardware implementation options, these results substantially advance the state of the art in theory and specifically offer new perspective on how to design spiking circuits for engineering applications.
Publications
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Reconfigurable Computation in Spiking Neural Networks. IEEE Access, 8, 179648-179655.
Neves, Fabio Schittler & Timme, Marc
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Bio-inspired computing by nonlinear network dynamics—a brief introduction. Journal of Physics: Complexity, 2(4), 045019.
S., Neves Fabio & Timme, Marc
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Decoding complex state space trajectories for neural computing. Chaos: An Interdisciplinary Journal of Nonlinear Science, 31(12).
Schittler, Neves Fabio & Timme, Marc
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Stochastic facilitation in heteroclinic communication channels. Chaos: An Interdisciplinary Journal of Nonlinear Science, 31(9).
Sirio, Carmantini Giovanni; Schittler, Neves Fabio; Timme, Marc & Rodrigues, Serafim
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Equivalence of Additive and Multiplicative Coupling in Spiking Neural Networks. IEEE Access, 11, 145503-145515.
Börner, Georg; Neves, Fabio Schittler & Timme, Marc
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Volatile Memory Motifs: Minimal Spiking Neural Networks. IEEE Access, 11, 88649-88655.
Schittler, Neves Fabio & Timme, Marc
