  Quantifying relevant interactions between neural populations is a prominent
question in the analysis of high-dimensional neural recordings. However,
existing dimension reduction methods often discuss communication in the absence
of a formal framework, while frameworks proposed to address this gap are
impractical in data analysis. This work bridges the formal framework of
M-Information Flow with practical analysis of real neural data. To this end, we
propose Iterative Regression, a message-dependent linear dimension reduction
technique that iteratively finds an orthonormal basis such that each basis
vector maximizes correlation between the projected data and the message. We
then define 'M-forwarding' to formally capture the notion of a message being
forwarded from one neural population to another. We apply our methodology to
recordings we collected from two neural populations in a simplified model of
whisker-based sensory detection in mice, and show that the low-dimensional
M-forwarding structure we infer supports biological evidence of a similar
structure between the two original, high-dimensional populations.
