mlsanityData to 14 Oct 2026

Perspectives on Tsallis Statistics for Artificial Intelligence

arXiv 2608.01223 ↗First posted 2 Aug 2026cs.AI cs.CEcited by 1

On the map: Deep reinforcement learning methods → RL theory and sample complexity

Abstract (arXiv)

Tsallis statistics generalizes Boltzmann-Gibbs statistical mechanics through a single real parameter q that controls the weight assigned to rare and frequent events. Originally proposed to describe physical systems with long-range correlations, multifractal geometry, and heavy-tailed fluctuations, the framework has become a recurring ingredient in modern artificial intelligence (AI): it underlies sparse attention mechanisms (textscsparsemax and α-textscentmax), maximum-entropy reinforcement learning with controllable exploration, robust and heavy-tailed probabilistic models, and a family of generalized loss functions and regularizers. This paper offers a structured perspective on where Tsallis statistics meets AI. We first review the mathematical core: q-entropy and its variational (maximum-entropy) foundation, the q-exponential and q-logarithm, the q-central limit theorem, q-Gaussian distributions, and their dynamical origin in superstatistics, emphasizing the properties that matter for machine learning. We then survey applications across softmax generalization, reinforcement learning, sequential and graph neural models, generative and probabilistic modeling, loss design, and optimization, extracting the recurring design pattern in each case: a tunable interpolation between dense/uniform and sparse/peaked behavior governed by q. We further argue that the heavy-tailed weight spectra and gradient-noise statistics empirically observed in deep networks are themselves nonextensive signatures, placing modern learning dynamics within the scope of q-statistics. Finally, we discuss methodological pitfalls, the relationship to information geometry and q-exponential families, and open directions, arguing that q should be treated as a learnable inductive bias rather than a fixed hyperparameter.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods. Builds on 33 of its 70 references that are in the map. First posted on arXiv 2 Aug 2026.

Builds on

33 of 70 references.

References · 33

  1. 2018Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actorcited by 4,885
  2. 2018Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learningcited by 1,102
  3. 2018Generalized Cross Entropy Loss for Training Deep Neural Networks with Noisy Labelscited by 997
  4. 2016From Softmax to Sparsemax: A Sparse Model of Attention and Multi-Label Classificationcited by 341
  5. 2019A Theory of Regularized Markov Decision Processescited by 286
  6. 2018Implicit Self-Regularization in Deep Neural Networks: Evidence from Random Matrix Theory and Implications for Learningcited by 215
  7. 2019A Tail-Index Analysis of Stochastic Gradient Noise in Deep Neural Networkscited by 214
  8. 2019Sparse Sequence-to-Sequence Modelscited by 170
  9. 2019Adaptively Sparse Transformerscited by 155
  10. 2018Tsallis-INF: An Optimal Algorithm for Stochastic and Adversarial Banditscited by 124
  11. 2020The Heavy-Tail Phenomenon in SGDcited by 124
  12. 2019Learning with Fenchel-Young Lossescited by 119
21 more
  1. 2018Solving Statistical Mechanics Using Variational Autoregressive Networkscited by 100
  2. 2020Munchausen Reinforcement Learningcited by 69
  3. 2020Hausdorff Dimension, Heavy Tails, and Generalization in Neural Networkscited by 62
  4. 2019Robust Bi-Tempered Logistic Loss Based on Bregman Divergencescited by 61
  5. 2021Heavy Tails in SGD and Compressibility of Overparametrized Neural Networkscited by 44
  6. 2019Sparse Graph Attention Networkscited by 41
  7. 2024Heavy-Tailed Diffusion Modelscited by 40
  8. 2020Sparse and Continuous Attention Mechanismscited by 39
  9. 2017Sparse Markov Decision Processes with Causal Sparse Tsallis Entropy Regularization for Reinforcement Learningcited by 37
  10. 2018Path Consistency Learning in Tsallis Entropy Regularized MDPscited by 22
  11. 2025Long-Context Generalization with Sparse Attentioncited by 21
  12. 2019Tsallis Reinforcement Learning: A Unified Framework for Maximum Entropy Reinforcement Learningcited by 19
  13. 2024Heavy-Tailed Diffusion with Denoising L'evy Probabilistic Modelscited by 18
  14. 2020Multiplicative noise and heavy tails in stochastic optimizationcited by 17
  15. 2017Two-temperature logistic regression based on the Tsallis divergencecited by 14
  16. 2021Sparse Continuous Distributions and Fenchel-Young Lossescited by 14
  17. 2021Predicting Attention Sparsity in Transformerscited by 13
  18. 2023Star-Shaped Denoising Diffusion Probabilistic Modelscited by 13
  19. 2025AdaSplash: Adaptive Sparse Flash Attentioncited by 12
  20. 2022Clustering above Exponential Families with Tempered Exponential Measurescited by 6
  21. 2025Applications of Entropy in Data Analysis and Machine Learning: A Reviewcited by 3

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Generalized Graph Variational Autoencoders: Bounded Divergences Control Posterior Collapsecited by 0

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