Principal bundle geometry of qualia: Understanding the quality of consciousness from symmetry.

Qualia, the subjective qualities of experience, pose a fundamental challenge to scientific explanation. A promising approach is to characterize qualia by their relational structures rather than their intrinsic nature. Assuming the structure of qualia is characterized by the geometry of neural representations, we posit that this geometry is fundamentally organized by symmetry. We propose that the principal bundle, induced by a symmetry group G acting on a neural network's state space, is the essential mathematical object uniquely characterizing this geometric structure. The core mathematical principle is that, for a G-equivariant network, its state space partitions into a quotient space Q and orbits induced by the group G. This framework reveals a three-level hierarchy for characterizing qualia. First, the choice of symmetry group G constrains the fundamental nature of the qualia modality (e.g. vision vs. audition). Second, we identify a qualia signature with a point in the quotient space Q (e.g. "cat"), representing the invariant identity of a percept. Third, we identify a qualia attribute with a position on a specific orbit (e.g. the cat's location), representing its continuous variations. This framework uncovers a powerful duality: the geometry of the orbits is rigid, inheriting the structure of the group G, which explains the stable relational structure of qualia attributes. In contrast, quotient-space geometry is plastic, allowing the relationships between qualia signatures to be shaped by learning. This geometric hierarchy provides a unified language for explaining the structure of perceptual experience. Furthermore, our framework generates empirical predictions and a clear research strategy for characterizing qualia and comparing qualia across individuals.