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.