aiqbench analysis
This research proposes a method to selectively determine which parameters in Bayesian neural networks should remain stochastic versus deterministic by factorizing prior scales. The approach successfully sparsifies uncertainty without sacrificing universal conditional density approximation capabilities, achieving performance comparable to fully stochastic models while reducing the number of stochastic parameters by half. This work advances the theoretical understanding of Bayesian inference efficiency and offers practical improvements for model calibration and computational cost in machine learning systems.
Sparsifying Stochasticity, Not Capacity: Partial Stochasticity via Deep Weight Factorization of Prior Scales
arXiv:2610.09886v1 Announce Type: cross Abstract: Bayesian neural networks need not be fully stochastic to be universal conditional density approximators, but it remains open which parameters should be stochastic. We learn this split by applying deep weight factorization to the prior scales, which are the standard deviations of the parameter priors, while fitting the functional prior to a Gaussian process with a maximum mean discrepancy objective. A parameter whose prior scale falls below a cutoff becomes deterministic and is optimized during inference, so the regularizer sparsifies stochasticity rather than capacity. We give a certificate for universal conditional density approximation that is checkable in linear time, together with a minimal repair when it fails. We further show that the common hybrid scheme of sampling some parameters and optimizing the others is stochastic approximation for a type-II maximum a posteriori objective, and that coupled step sizes can leave a tracking error that does not vanish as the step size shrinks. On a bimodal target, the learned split stays close to an unconstrained reference across all budgets and is insensitive to the cutoff, while random masks that distribute the same prior scales across layers are worse by up to two orders of magnitude. On UCI benchmarks, our method performs on par with a fully stochastic network while keeping about half of its parameters deterministic.
Abstract:Bayesian neural networks need not be fully stochastic to be universal conditional density approximators, but it remains open which parameters should be stochastic. We learn this split by applying deep weight factorization to the prior scales, which are the standard deviations of the parameter priors, while fitting the functional prior to a Gaussian process with a maximum mean discrepancy objective. A parameter whose prior scale falls below a cutoff becomes deterministic and is optimized during inference, so the regularizer sparsifies stochasticity rather than capacity. We give a certificate for universal conditional density approximation that is checkable in linear time, together with a minimal repair when it fails. We further show that the common hybrid scheme of sampling some parameters and optimizing the others is stochastic approximation for a type-II maximum a posteriori objective, and that coupled step sizes can leave a tracking error that does not vanish as the step size shrinks. On a bimodal target, the learned split stays close to an unconstrained reference across all budgets and is insensitive to the cutoff, while random masks that distribute the same prior scales across layers are worse by up to two orders of magnitude. On UCI benchmarks, our method performs on par with a fully stochastic network while keeping about half of its parameters deterministic.
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:2610.09886 [stat.ML]
(or arXiv:2610.09886v1 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2610.09886 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 312 words
