Generative diffusion and flow models are constructed to remain exactly on the Lorentz-invariant massless N-particle phase space manifold during sampling for particle physics applications.
Trajectory of mini-batch momentum: Batch size saturation and convergence in high dimensions,
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Ridge regression in high dimensions exhibits power-law scalings because covariance fluctuations renormalize the ridge parameter, allowing closed-form error expressions and bias-variance decompositions for random feature models via free probability.
DNNs succeed by capturing high-order correlation structures in datasets, similar to mesoscale methods in physics.
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Generative models on phase space
Generative diffusion and flow models are constructed to remain exactly on the Lorentz-invariant massless N-particle phase space manifold during sampling for particle physics applications.
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Scaling and renormalization in high-dimensional regression
Ridge regression in high dimensions exhibits power-law scalings because covariance fluctuations renormalize the ridge parameter, allowing closed-form error expressions and bias-variance decompositions for random feature models via free probability.
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DNNs, Dataset Statistics, and Correlation Functions
DNNs succeed by capturing high-order correlation structures in datasets, similar to mesoscale methods in physics.