Where cognitive-state information lives depends on brain-dynamics complexity: working memory rides trajectories, relational reasoning rides time averages

The information that distinguishes cognitive conditions is not fixed in time-averaged connectivity; it migrates between time averages and trajectory geometry as chronnectome complexity changes. Earlier work characterized time-varying connectivity descriptively, summarizing which connectivity states occur and how they change, without modeling the rules governing their evolution or identifying whether discriminative information sits in time-averaged connectivity or in trajectory geometry. On the cortical atlas of the Human Connectome Project young adult cohort, the full model reached 97.4% accuracy across eight conditions against a 12.5% chance level; with the time-averaged representation zeroed, trajectory-only accuracy was 93.4% for Working Memory and 0.0% for Relational Reasoning, the latter indistinguishable from the label-permutation null.

A graph attention network encodes each window's connectivity matrix into a latent vector, and a neural ordinary differential equation learns a continuous trajectory through that latent space starting from the first latent vector, so both representations come from one learned dynamical system. Earlier deep learning models entangled time-averaged and dynamic information so the two could not be separated, while latent dynamical models were used mainly to reconstruct or forecast activity rather than to identify which part of the dynamics distinguishes cognitive conditions. On the cortical atlas of the young adult cohort the full model reached 97.4% accuracy; with subcortical regions added it reached 94.2%, and in the aging cohort 92.22% on the cortical atlas and 92.29% on the cortico-subcortical atlas.

Adding subcortical regions changes trajectory-carried information in a condition-specific way, indicating an observability boundary for conditions that depend on subcortical circuits. With the cortical atlas alone, the Emotion condition had limited trajectory information; extending the atlas raised its trajectory contribution markedly, while Gambling moved in the opposite direction. In the young adult cohort, Emotion trajectory-only accuracy rose from 28.4% to 67.3% and Gambling fell from 65.0% to 38.8%; in the aging cohort Visuomotor Tracking gained 12.4 percentage points while Face-Name Memory changed little.

Results come from eight conditions in the Human Connectome Project young adult cohort and four conditions in the aging cohort, evaluated under a cortical atlas and an atlas extended with subcortical regions, all on held-out test sets partitioned at the subject level; the two cohorts were modeled by separately trained models, so aging was assessed through comparisons within the aging cohort.

The ergodicity gap is a model-derived proxy for ergodic breakdown rather than a formal test of ergodicity, and its interpretation depends on how strongly the fitting loss couples the trajectory to the observed embeddings; zeroing a representation at inference produces inputs outside the training distribution that can affect the result, which was mitigated by label-permutation testing and linear probes; the subcortical extension identifies circuit-level contributions without isolating specific nuclei.