mlsanityData to 7 Oct 2026

A scale-dependent notion of effective dimension

arXiv 2001.10872 ↗First posted 29 Jan 2020stat.ML cs.LGcited by 17

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Abstract (arXiv)

We introduce a notion of "effective dimension" of a statistical model based on the number of cubes of size 1/√n needed to cover the model space when endowed with the Fisher Information Matrix as metric, n being the number of observations. The number of observations fixes a natural scale or resolution. The effective dimension is then measured via the spectrum of the Fisher Information Matrix regularized using this natural scale.

Key facts. Cited by 17 papers in the map (data through 7 Oct 2026). First posted on arXiv 29 Jan 2020.

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Citing papers per year: 2021: 2; 2022: 5; 2023: 2; 2024: 3; 2025: 4; 2026: 1.

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  1. 2022Hybrid quantum ResNet for car classification and its hyperparameter optimizationcited by 17
  2. 2022Quantum Neural Architecture Search with Quantum Circuits Metric and Bayesian Optimizationcited by 16
  3. 2021Effective dimension of machine learning modelscited by 14
  4. 2022Incremental Data-Uploading for Full-Quantum Classificationcited by 13
  5. 2022Classical versus Quantum: comparing Tensor Network-based Quantum Circuits on LHC datacited by 7
  6. 2023Nav-Q: Quantum Deep Reinforcement Learning for Collision-Free Navigation of Self-Driving Carscited by 6
  7. 2023BCQQ: Batch-Constraint Quantum Q-Learning with Cyclic Data Re-uploadingcited by 3
  8. 2024A Two-Scale Complexity Measure for Deep Learning Modelscited by 3
  9. 2024Quantum Supervised Learningcited by 3
  10. 2025Quantum feature-map learning with reduced resource overheadcited by 1
  11. 2025Macroeconomic Forecasting and Machine Learningcited by 1
  12. 2021Entropic alternatives to initializationcited by 0
5 more
  1. 2022Geometric Regularization from Overparameterizationcited by 0
  2. 2024Exploring Quantum-Enhanced Machine Learning for Computer Vision: Applications and Insights on Noisy Intermediate-Scale Quantum Devicescited by 0
  3. 2025Effective Dimension Aware Fractional-Order Stochastic Gradient Descent for Convex Optimization Problemscited by 0
  4. 2025Hybrid quantum recurrent neural network for remaining useful life prediction of turbofan enginescited by 0
  5. 2026Why Self-Supervised Encoders Want to Be Normalcited by 0