Manaoj Aravind

Invertible logic is a powerful new unconventional computing paradigm, providing bidirectional operations between inputs and outputs. It has found applications in important critical problems, such as integer factorization and machine learning. Here we propose a network of interconnected nonlinear systems that serve as our probabilistic bits (“p-bits”) to implement invertible logic in the presence of a noise floor. In the forward (or directed) mode, the inputs are fixed in our network, yielding outputs in accordance with and, or, nand, and nor logic functions. In the reverse (inverted) mode the output is clamped in the network, and the input nodes fluctuate among all possible logical input values consistent with the different logic functions. So the system acts as a unique invertible logic circuit by exploiting the probabilistic transitions between the dynamical states of the coupled noisy nonlinear systems. Interestingly, both the directed and the inverted mode are most robust and reliable in an optimal band of moderate noise, reminiscent of stochastic resonance. The concept is verified in proof-of-principle electronic circuit experiments, demonstrating the robustness of the architecture and the potential of this idea to be realized in a wide range of physical situations.

Heteroclinic dynamics provide a suitable framework for describing transient dynamics such as cognitive processes in the brain. It is appreciated for being well reproducible and at the same time highly sensitive to external input. It is supposed to capture features of switching statistics between metastable states in the brain. Beyond the high sensitivity, a further desirable feature of these dynamics is to enable a fast adaptation to new external input. In view of this, we analyze relaxation times of heteroclinic motion toward a new resting state, when oscillations in heteroclinic networks are arrested by a quench of a bifurcation parameter from a parameter regime of oscillations to a regime of equilibrium states. As it turns out, the relaxation is underdamped and depends on the nesting of the attractor space, the size of the attractor’s basin of attraction, the depth of the quench, and the level of noise. In the case of coupled heteroclinic units, it depends on the coupling strength, the coupling type, and synchronization between different units. Depending on how these factors are combined, finite relaxation times may support or impede a fast switching to new external input. Our results also shed some light on the discussion of how the stability of a system changes with its complexity.