This perspective paper surveys how Tsallis statistics, parameterized by q, appears across AI. It reviews q-entropy, q-exponentials, q-Gaussians, the q-central limit theorem, and superstatistics, then connects them to sparsemax and α-entmax, maximum-entropy reinforcement learning, neural sequence and graph models, heavy-tailed probabilistic modeling, losses, and optimization. The authors identify a recurring interpolation between dense or uniform and sparse or peaked behavior. They further interpret heavy-tailed neural weight spectra and gradient noise as possible nonextensive signatures and propose treating q as a learnable inductive bias.
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