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This study combines Neuropixels recordings across six mouse visual areas with mechanistic circuit modeling to identify a novel dynamical regime, the adaptive fractional (AF) state, characterized by heavy-tailed superdiffusive fluctuations and long-range temporal dependence. An effective mean-field theory formalizes this state using spatial and temporal fractional derivatives, revealing that dynamical exponents shift systematically across the visual hierarchy, with higher areas exhibiting weaker superdiffusion and stronger temporal memory due to progressively weaker effective inhibition. These findings establish a hierarchy of dynamical regimes, extending the classical hierarchy of timescales, and suggest the AF state enables cortical areas to balance rapid responses with long-term temporal integration.
Cortical areas dynamically balance rapid responses and long-term memory through an "adaptive fractional" state, whose superdiffusion and temporal memory strength systematically shift across the visual hierarchy.
Cortical circuits must respond flexibly to new inputs while integrating information about the past, yet the way in which neural activity reconciles these competing demands remains unclear. Combining Neuropixels recordings from six mouse visual areas with mechanistic circuit modeling, we identify a dynamical regime in which heavy-tailed superdiffusive fluctuations coexist with long-range temporal dependence and oscillations. We formalize this regime as the adaptive fractional (AF) state, using an effective mean-field theory in which spatial and temporal fractional derivatives capture heavy-tailed excursions and long-range memory, respectively. We find that dynamical exponents characterizing the AF state vary systematically across the visual hierarchy: higher visual areas exhibit weaker superdiffusion and stronger temporal memory. In the circuit model, this hierarchical shift emerges from a progressive weakening of effective inhibition. These findings extend the classical hierarchy of timescales to a hierarchy of dynamical regimes and suggest that the AF state allows cortical areas to jointly express rapid responses and long-term temporal integration.