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Description
Brain computations arise from interactions between neuronal populations distributed across regions. Communication subspaces have become a standard tool to map these interactions with cellular resolution, capturing the additive coupling between a source and a target population of many neurons through a small number of activity patterns. However, interactions are not static: they are reshaped by behavioral state, task context, or the activity of other populations. A long line of work has proposed that many neural interactions are multiplicatively gated by modulatory variables that can themselves be high-dimensional. Yet no existing method explicitly captures how such a modulator reconfigures source–target population interactions.
Here we introduce Multiplicative Interaction Channels (MICs), extending the communication-subspace framework to quantify this modulation. We model the modulator-induced perturbation of the source–target mapping as a low-rank three-way tensor, parameterized via a Canonical Polyadic decomposition and derived as a bilinear perturbation of reduced-rank regression. Each MIC is a triplet of source, target, and modulator activity patterns in which the modulator gates the source-target interaction. We provide a cross-validated hierarchical fitting pipeline and a closed-form geometric decomposition that quantifies whether modulation reshapes the baseline interaction, recruits private dimensions of either population, or opens new interaction pathways. In simulations, MICs reliably recover the presence and geometry of ground-truth modulation in the high-dimensional, low-sample regime, outperforming full-rank bilinear tensor regression at small sample sizes.
Applying MICs to new dual-color two-photon recordings of prefrontal (ACA) axons and VIP interneurons in mouse visual cortex, with behavioral state (pupil, locomotion) as modulator, we find that state asymmetrically modulates top-down interactions: it reconfigures the prefrontal projection patterns that interact with a comparatively stable set of interneuron activity patterns, possibly reflecting state-dependent routing of distinct top-down signals through a stable local interface. Altogether, MICs enable asking how high-dimensional variables shape interactions between neuronal populations.
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