An algebraic theory to discriminate qualia in the brain

The mind-brain problem is to bridge relations between in higher-level mental events and in lower-level neural events. To address this, some mathematical models have been proposed to explain how the brain can represent the discriminative structure of qualia, but they remain unresolved due to a lack of validation methods. To understand the qualia discrimination mechanism, we need to ask how the brain autonomously develops such a mathematical structure using the constructive approach. In unsupervised representation learning, independence between axes is generally used to constrain the latent vector but independence between axes cannot explain qualia type discrimination because independent axes cannot distinguish between inter-qualia type independence (e.g., vision and touch) and intra-qualia type independence (e.g., green and red). We hypothesised that inter-axis independence must be weakened in order to discriminate qualia types. To solve the problem, we formulate an algebraic independence to link it to the other-qualia-type invariant transformations, whose transformation value is a vector space rather than a scalar. In addition, we show that a brain model that learns to satisfy the algebraic independence between neural networks separates the latent space into multiple metric spaces corresponding to qualia types, suggesting that our theory can contribute to the further development of the mathematical theory of consciousness.