A fundamental problem in neuroscience is to understand the different ways in which brain areas can interact to encode information. When two brain areas interact with a third, what fraction of the mutual information between the former and the latter can be attributed uniquely to each of the former? What fraction is redundant between them, and what fraction is synergistic? These “partial information” components quantify how different brain areas interact, which can help us understand the efficiency of various neural coding or communication schemes. Information-theoretic measures called partial information decompositions (PIDs) have previously been used to quantify partial information components. However, the practical application of PID methods has faced challenges: measures that capture uniqueness, redundancy and synergy precisely require a complex optimization, and do not scale to high-dimensional neural data, while measures that do scale are often less precise and tend to conflate two or more partial information terms. Here, we present the Gaussian Partial Information Decomposition (GPID): starting with a non-conflationary PID measure, we approximate it under a Gaussian parameterization. The parameterization exponentially reduces the space of the optimization, while the approximation makes it a convex problem—allowing for a more precise PID estimator that scales to high dimensions. We first validate GPID on simulated neural data, through comparisons with alternative estimators at lower dimensions, and observing intuitive trends at higher dimensions. We also apply GPID to high-dimensional spiking data from mouse visual cortex and thalamus recorded using Neuropixels probes, from the Allen Brain Observatory. GPID reveals differences in how cortico-thalamic regions share information, relative to cortico-cortical regions, and provides a new approach: using simulations, we can map different computational motifs to specific PID profiles. By comparing these to PID profiles estimated from data, we can formulate hypotheses about how different regions compute or communicate.