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Attractors in Neural Network Circuits: Beauty and Chaos
- Attractors represent long-term behavioral patterns of dynamical systems, towards which systems tend to evolve from diverse initial conditions.
- Neural networks can also be interpreted as dynamical systems, whose trajectories are influenced by network weights, biases, and activation functions.
- Feedback loops in neural networks lead to recurrent systems with diverse temporal dynamics, producing attractors ranging from simple convergence to chaotic patterns.
- Different types of attractors include point attractors, limit cycles, toroidal attractors, and strange chaotic attractors, each showcasing unique system behaviors.
- A neural attractor model with feedback loops can generate attractors through nonlinear activation functions, random weight initializations, and scaling factors.
- Lyapunov exponents can measure the stability or instability of dynamical systems, with positive values indicating chaos and negative values indicating convergence or stability.
- Visualizing attractors through trajectories of hidden neurons in neural networks can display stable limit cycles, toroidal attractors, and chaotic strange attractors.
- Increasing the scaling factor in neural attractors can lead to transitions from stable patterns to chaotic behaviors, demonstrating the edge of chaos where systems exhibit both complexity and coherence.
- The aesthetics of attractors in neural networks highlight the mathematical beauty found at the intersection of ordered structures and unpredictability.
- The project draws inspiration from the work of J.C. Sprott and provides an interactive widget for visualizing and exploring attractors in neural network circuits.
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