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.
Generative uncertainty in diffusion models
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Derives closed-form posterior covariance for flow matching from divergence of velocity field, enabling post-hoc uncertainty on pre-trained models including one-step generators.
Replica calculations fully solve spherical Boltzmann machine ensembles and identify regimes where ensemble learning outperforms standard training, particularly for nearly finite-dimensional data.
FMwC computes per-sample confidence scores for flow matching models via closed-form propagation of input-dependent multiplicative noise variance along the sampling ODE, supporting filtering, editing, and adaptive stepping.
SFM improves generalization under distribution shift for scientific imaging tasks while AVUQ supplies sample-efficient epistemic and aleatoric uncertainty estimates plus anomaly scores.
UCD adjusts diffusion-based 3D molecular graph generation to handle epistemic uncertainty, improving sample quality and reaching new benchmark performance.
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Replica Theory of Spherical Boltzmann Machine Ensembles
Replica calculations fully solve spherical Boltzmann machine ensembles and identify regimes where ensemble learning outperforms standard training, particularly for nearly finite-dimensional data.