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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Sub-network Laplace approximations always underestimate full-model predictive variance, and two new gradient-based and greedy selection rules provide theoretically grounded improvements.
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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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Optimality of Sub-network Laplace Approximations: New Results and Methods
Sub-network Laplace approximations always underestimate full-model predictive variance, and two new gradient-based and greedy selection rules provide theoretically grounded improvements.