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An elementary introduction to information geometry

arXiv 1808.08271 ↗First posted 17 Aug 2018cs.LG cs.IT math.ITcited by 76

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Abstract (arXiv)

In this survey, we describe the fundamental differential-geometric structures of information manifolds, state the fundamental theorem of information geometry, and illustrate some use cases of these information manifolds in information sciences. The exposition is self-contained by concisely introducing the necessary concepts of differential geometry, but proofs are omitted for brevity.

Key facts. Cited by 76 papers in the map (data through 7 Oct 2026). First posted on arXiv 17 Aug 2018.

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Citing papers per year: 2021: 9; 2022: 11; 2023: 10; 2024: 9; 2025: 15; 2026: 22.

76 papers.

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  1. 2021Merging Models with Fisher-Weighted Averagingcited by 613
  2. 2024Fisher Flow Matching for Generative Modeling over Discrete Datacited by 68
  3. 2022Loss Minimization through the Lens of Outcome Indistinguishabilitycited by 61
  4. 2025All Roads Lead to Likelihood: The Value of Reinforcement Learning in Fine-Tuningcited by 58
  5. 2024Wasserstein Flow Matching: Generative modeling over families of distributionscited by 27
  6. 2023Improved Regret Bounds of (Multinomial) Logistic Bandits via Regret-to-Confidence-Set Conversioncited by 24
  7. 2021Pulling back information geometrycited by 23
  8. 2021On the Properties of Kullback-Leibler Divergence Between Multivariate Gaussian Distributionscited by 22
  9. 2021On the Variance of the Fisher Information for Deep Learningcited by 22
  10. 2022Designing Universal Causal Deep Learning Models: The Geometric (Hyper)Transformercited by 22
  11. 2023Bayesian Renormalizationcited by 13
  12. 2024Learning to Assist Humans without Inferring Rewardscited by 12
38 more
  1. 2022FIT: A Metric for Model Sensitivitycited by 10
  2. 2025Foundations of Top-k Decoding For Language Modelscited by 10
  3. 2021Model-centric Data Manifold: the Data Through the Eyes of the Modelcited by 9
  4. 2022A Class of Geometric Structures in Transfer Learning: Minimax Bounds and Optimalitycited by 9
  5. 2024Bayesian RG Flow in Neural Network Field Theoriescited by 9
  6. 2026The Information Geometry of Softmax: Probing and Steeringcited by 9
  7. 2023Language Model Decoding as Direct Metrics Optimizationcited by 8
  8. 2021On the Importance of Firth Bias Reduction in Few-Shot Classificationcited by 7
  9. 2024NCoder -- A Quantum Field Theory approach to encoding datacited by 7
  10. 2022Adversarial attacks on neural networks through canonical Riemannian foliationscited by 5
  11. 2022Geometric Methods for Sampling, Optimisation, Inference and Adaptive Agentscited by 5
  12. 2022Phase2vec: Dynamical systems embedding with a physics-informed convolutional networkcited by 5
  13. 2023The Fisher-Rao geometry of CES distributionscited by 5
  14. 2025Enforcing Latent Euclidean Geometry in Single-Cell VAEs for Manifold Interpolationcited by 5
  15. 2026AEM: Adaptive Entropy Modulation for Multi-Turn Agentic Reinforcement Learningcited by 5
  16. 2021A Unifying and Canonical Description of Measure-Preserving Diffusionscited by 4
  17. 2025Does Low Rank Adaptation Lead to Lower Robustness against Training-Time Attacks?cited by 4
  18. 2021Fast approximations of the Jeffreys divergence between univariate Gaussian mixture models via exponential polynomial densitiescited by 3
  19. 2022Variational Representations of Annealing Paths: Bregman Information under Monotonic Embeddingcited by 3
  20. 2023Towards Optimal Compression: Joint Pruning and Quantizationcited by 3
  21. 2023Neural FIM for learning Fisher Information Metrics from point cloud datacited by 3
  22. 2023Divergences induced by dual subtractive and divisive normalizations of exponential families and their convex deformationscited by 2
  23. 2025AMiD: Knowledge Distillation for LLMs with α-mixture Assistant Distributioncited by 2
  24. 2021Principal component analysis for Gaussian process posteriorscited by 1
  25. 2022Unsupervised Learning Discriminative MIG Detectors in Nonhomogeneous Cluttercited by 1
  26. 2023Spherical and Hyperbolic Toric Topology-Based Codes On Graph Embedding for Ising MRF Models: Classical and Quantum Topology Machine Learningcited by 1
  27. 2023Information Geometry for the Working Information Theoristcited by 1
  28. 2024Sequential transport maps using SoS density estimation and α-divergencescited by 1
  29. 2024Cartan moving frames and the data manifoldscited by 1
  30. 2025Federated Generalised Variational Inference: A Robust Probabilistic Federated Learning Frameworkcited by 1
  31. 2025Squared families: Searching beyond regular probability modelscited by 1
  32. 2025Near-Optimal Clustering in Mixture of Markov Chainscited by 1
  33. 2025Wasserstein Gradient Flows for Scalable and Regularized Barycenter Computationcited by 1
  34. 2026Relaxed Triangle Inequality for Kullback-Leibler Divergence Between Multivariate Gaussian Distributionscited by 1
  35. 2026Statistical Properties of the King Wen Sequence: An Anti-Habituation Structure That Does Not Improve Neural Network Trainingcited by 1
  36. 2022On the Kullback-Leibler divergence between pairwise isotropic Gaussian-Markov random fieldscited by 0
  37. 2022Properties of the Concrete distributioncited by 0
  38. 2023Asymptotically Optimal Pure Exploration for Infinite-Armed Banditscited by 0

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