LabStats

  1. Why metastability is a natural language for gaze behavior The idea that perception, attention, and neural activity evolve through transiently stable states has deep roots in cognitive science and neuroscience. Concepts such as attractors , basins , noise‑induced transitions , and escape times appear in work on perceptual switching, decision‑making, and neural population dynamics (Kelso, 1995; Rabinovich et al., 2008; Deco & Jirsa, 2012). Eye movements, especially the alternation between fixations and saccades ,   fit remarkably well into this metastable picture. The Freidlin–Wentzell theory of rare events (Freidlin & Wentzell, 2012) provides a rigorous mathematical language for these intuitions. 2. Fixations as metastable states  Consider the gaze position X t as the state of a stochastic dynamical system. During a fixation the  gaze remains confined to a small region, microsaccades and noise generate small fluctuations, and the gaze tends to return...

Large-deviation theory provides a powerful mathematical framework for quantifying the probability of rare events in stochastic systems. Among its foundational results, Sanov’s theorem plays a central role: it characterizes the exponential decay of probabilities associated with atypical empirical distributions. This perspective is deeply connected to information theory, statistical mechanics, and the analysis of stochastic processes. 1. Introduction Many stochastic systems, ranging from molecular dynamics to neural activity, exhibit fluctuations that are typically small but occasionally produce rare, high-impact deviations. Understanding the probability of these deviations requires tools that go beyond classical variance-based approximations. Sanov’s theorem provides exactly such a tool: a geometric and information-theoretic description of rarity. This post introduces the theorem, its intuition, and its connection to diffusion processes through discrete approximations and c...