  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.
