Introduces the Patnaik-Pearson intrinsic dimension estimator, proves some of its properties, relates it to HTSR/SETOL for Pareto spectra, and applies it to track embedding dimension evolution in BERT-base and DeepSeek-R1-Distill-Qwen-1.
S.,Note on an approximation to the distribution of noncentralχ 2.Biometrika, 46(3/4), (1959) 364
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A review summarizing definitions, canonical forms, exact and approximate distributions, numerical methods, applications, and open problems for quadratic forms in real and complex Gaussian variables, including multiforms and ratios.
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Patnaik-Pearson intrinsic dimension for internal representations of neural networks
Introduces the Patnaik-Pearson intrinsic dimension estimator, proves some of its properties, relates it to HTSR/SETOL for Pareto spectra, and applies it to track embedding dimension evolution in BERT-base and DeepSeek-R1-Distill-Qwen-1.
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Quadratic Forms in Gaussian Random Variables Theoretical Results and Applications
A review summarizing definitions, canonical forms, exact and approximate distributions, numerical methods, applications, and open problems for quadratic forms in real and complex Gaussian variables, including multiforms and ratios.