Excitable networks for finite state computation with continuous time recurrent neural networks

Area of Science:

• Computational neuroscience
• Machine learning theory
• Dynamical systems

Background:

• Continuous time recurrent neural networks (CTRNNs) are valuable models for understanding computation and learning in both biological and artificial systems.
• Existing methods for realizing finite state computations on CTRNNs can be complex and lack direct constructive approaches.

Purpose of the Study:

• To present a direct constructive method for implementing finite state input-dependent computations on arbitrary directed graphs using CTRNNs.
• To analyze the dynamics of the resulting CTRNN systems, focusing on network attractors and state transition behaviors.

Main Methods:

• Developed a direct constructive method to realize finite state computations on CTRNNs.
• Utilized ordinary differential equations to model the network dynamics.
• Investigated network attractors and intermittent dynamics, including excitable and spontaneous state transitions.

Main Results:

• Successfully demonstrated a method for constructing CTRNNs capable of finite state input-dependent computations.
• Observed intermittent dynamics characterized by long steady-state periods and rapid state transitions.
• Showcased that transitions can be either excitable (requiring input/noise threshold) or spontaneous.
• Proved that the excitability threshold can be made arbitrarily sensitive.

Conclusions:

• The proposed constructive method enables the realization of complex computations in CTRNNs.
• The intermittent and excitable dynamics offer a biologically plausible mechanism for information processing.
• This work provides a foundation for designing more sophisticated CTRNN models for learning and computation.