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.
Conference on Uncertainty in Artificial Intelligence (UAI) , year =
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An exact closed-form posterior covariance for flow matching is derived from the divergence of the velocity field and is computable on any pre-trained model.
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.
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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Divergence is Uncertainty: A Closed-Form Posterior Covariance for Flow Matching
An exact closed-form posterior covariance for flow matching is derived from the divergence of the velocity field and is computable on any pre-trained model.
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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.
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Flowing with Confidence
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.
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Uncertainty-Aware Distribution-to-Distribution Flow Matching for Scientific Imaging
SFM improves generalization under distribution shift for scientific imaging tasks while AVUQ supplies sample-efficient epistemic and aleatoric uncertainty estimates plus anomaly scores.