Attractor Topology in Neural Manifolds: A Dynamical Systems Approach

Sánchez-Karhunen identified "unexpected fixed point topologies" in RNN hidden states during intent detection, showing trajectories converge to attractors aligned with output classes. However, the nature of these attractors remains unexplored. This idea leverages exotic smoothness theory (Asselmeyer-Maluga) to classify these attractors as distinct smooth structures on the same underlying 4-manifold. For example, different intent classes could correspond to inequivalent (\mathbb{R}^4). By computing invariants like Casson handles or Donaldson polynomials from neural weights, we could quantify the "exoticity" of neural dynamics. This bridges dynamical systems and 4-manifold topology, offering a new lens for interpretability. Novelty: Uses quantum gravity tools to demystify neural computation beyond classical dynamics.

References:

1. Interpretation of the Intent Detection Problem as Dynamics in a Low-dimensional Space. Eduardo Sánchez-Karhunen, Jose F. Quesada-Moreno, Miguel A. Guti'errez-Naranjo (2024). European Conference on Artificial Intelligence.
2. Smooth quantum gravity: Exotic smoothness and Quantum gravity. T. Asselmeyer-Maluga (2016).