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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Joint eigenvector distributions of symmetric random tensors are computed via QFT methods, yielding random matrix forms and universal large-dimension asymptotics governed by tensor geometries.
A tunable microscopic model of network liquids with a liquid-liquid phase transition, analyzed via RFOT theory, predicts nanonucleation near the glass transition and links thermodynamic and kinetic anomalies when matched to water-like conditions.
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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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Joint distributions of eigenvectors of symmetric random tensors
Joint eigenvector distributions of symmetric random tensors are computed via QFT methods, yielding random matrix forms and universal large-dimension asymptotics governed by tensor geometries.
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Polyamorphism in Glassy Network Materials
A tunable microscopic model of network liquids with a liquid-liquid phase transition, analyzed via RFOT theory, predicts nanonucleation near the glass transition and links thermodynamic and kinetic anomalies when matched to water-like conditions.