arXiv AI
Predicting kernel regression learning curves from only raw data statistics
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On Kernel Eigen-alignments of KRR: Reconstruction and Generalization
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Breaking Data Symmetry is Needed For Generalization in Feature Learning Kernels
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Generalization, memorization, and overfitting for diffusion models trained in the lazy high-dimensional regime
The paper investigates diffusion models trained in a lazy high‑dimensional regime, extending benign overfitting theory to generative settings. By analyzing denoising score matching in a vector‑valued RKHS with an inner‑product kernel, the authors derive exact risk trajectories under gradient flow when the number of samples scales proportionally with dimensionality. These trajectories reveal three distinct phases—spectral generalization, noise‑dominated interpolation, and empirical Bayes memorization—whose interplay shapes the distribution of generated samples.
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Deep kernel hedging
arXiv:2609.34474v2 Announce Type: replace Abstract: We introduce a deep kernel hedging framework that combines the flexibility of deep learning with the structural inductive bias of kernel methods. T...
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Into the danger zone: stable extrapolation in high-dimensional function and operator learning
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The Sample Complexity of Learning Lipschitz Operators with respect to Gaussian Measures
The paper investigates how many linear samples are needed to learn Lipschitz operators under Gaussian measures. It establishes both lower and upper bounds on the Hermite polynomial approximation error and shows that the minimal worst‑case error cannot converge algebraically with the number of samples. However, if the covariance operator of the Gaussian measure decays rapidly, convergence rates arbitrarily close to any algebraic rate can be achieved.