Natural physical environments constantly fluctuate across multiple timescales, often following a scale-free ($1/f^alpha$) pattern where $alpha = 0.5$ governs the fractional adaptation dynamics citep{drew2006, lundstrom2008}. Here, we demonstrate how a multi-timescale sensory model successfully tracks these long-term trends to maintain stable encoding. Using an event-based Generalized Leaky Integrate-and-Fire (GLIF) paradigm, we found that a fast-adapting, single-exponential model with a short time constant $tau le 31.6~text{ms}$ quickly crashes into complete refractory saturation when faced with large, low-frequency environmental shifts. In contrast, introducing a deep fractional memory tail of $1000.0~text{ms}$ acts as an automated, high-pass balancing mechanism that continuously tracks and subtracts slow environmental variance. This predictive balancing prevents sensory collapse, anchors the mean firing rate to a steady homeostatic baseline, and maximizes coding efficiency for rapid, localized signals. Our results show that while a simple single-pole exponential model fails to retain history, a parallel bank of physiological relaxation processes converging on a target fractional profile $t^{-0.5}$ provides the necessary historical memory to safely navigate natural stimulus fluctuations. Comfortingly, even a simplified three-pole approximation captures the bulk of this homeostatic benefit, making efficient fractional adaptation biologically viable at the sensory periphery without requiring infinite historical storage.
Bleeck, S.
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