In the high-dimensional limit the spherical Boltzmann machine admits exact equations for training dynamics, Bayesian evidence, and cascades of phase transitions tied to mode alignment with data, which connect to generative phenomena including double descent and out-of-equilibrium biases.
Surprises in High-Dimensional Ridgeless Lea st Squares Interpolation
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Survival models show distinct interpolation behaviors driven by loss functions, so overparametrization does not reliably improve generalization as in regression or classification.
Inflating the min-norm interpolator by a factor >1 reduces generalization error in linear regression with anisotropic covariances when d/n diverges to infinity.
New conditions for support vector proliferation (SVP) in RKHS for bounded orthonormal systems and sub-Gaussian features, yielding generalization bounds for kernel SVMs beyond prior restrictive assumptions.
Single-seed CRPS estimates in limited-data BDL show high variance and peaks for heteroscedastic methods, with local variance correlating above 0.96 to single-seed error.
citing papers explorer
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Spherical Boltzmann machines: a solvable theory of learning and generation in energy-based models
In the high-dimensional limit the spherical Boltzmann machine admits exact equations for training dynamics, Bayesian evidence, and cascades of phase transitions tied to mode alignment with data, which connect to generative phenomena including double descent and out-of-equilibrium biases.
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Understanding Overparametrization in Survival Models through Interpolation
Survival models show distinct interpolation behaviors driven by loss functions, so overparametrization does not reliably improve generalization as in regression or classification.
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Shrinkage to Infinity: Reducing Test Error by Inflating the Minimum Norm Interpolator in Linear Models
Inflating the min-norm interpolator by a factor >1 reduces generalization error in linear regression with anisotropic covariances when d/n diverges to infinity.
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New Equivalences Between Interpolation and SVMs: Kernels and Structured Features
New conditions for support vector proliferation (SVP) in RKHS for bounded orthonormal systems and sub-Gaussian features, yielding generalization bounds for kernel SVMs beyond prior restrictive assumptions.
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A Tale of Two Variances: When Single-Seed Benchmarks Fail in Bayesian Deep Learning
Single-seed CRPS estimates in limited-data BDL show high variance and peaks for heteroscedastic methods, with local variance correlating above 0.96 to single-seed error.