Testing Structured Dependence in Decodable Brain-State Representations: Higher-Order Information and Temporal Topology in fMRI

Decoding models can identify brain regions predictive of cognitive states, but they do not directly test how the information carried by these regions is organized. We formulate post-decoding analysis of task-fMRI representations as a set of structured hypothesis-testing problems. Building on an interpretable decoding pipeline, we test whether brain regions identified as important for classifying cognitive states differ from less classifier-relevant regions, and characterize how their information is organized using tools from information theory and topology. We find that classifier-selected regions exhibit higher pairwise mutual information than matched low-weight controls, with a significant shift in the empirical distributions under a two-sample Kolmogorov--Smirnov test. Compact and distributed brain-state regimes also show distinct O-information profiles: compact states have near-zero O-information, whereas distributed states exhibit redundancy-dominated higher-order structure. Surrogate analyses further suggest that delay-coordinate topology is not explained by marginal signal values alone, but is constrained by the temporal ordering of the fMRI signals.