The minima of modern neural network loss functions are typically not isolated, rather they form connected components of reparameterization invariant solutions on the training data. Analytically characterizing these solutions is a hard problem, but sampling approaches are feasible. By construction, existing methods either spread over low-loss regions, and thus do not sample reparameterization invariant solutions exactly, or are inherently local, which limits exploration of other minima valleys. We propose sampling such reparameterization invariant models using a dynamical system based on kinetic energy, subject to a gravitational pull and a friction term that dissipates energy from the system. Our proposed sampler, DIMS, is guaranteed to sample exactly from the minimum level sets and depends on physically motivated hyperparameters which allows control over the exploration capabilities of the sampler. We consider uncertainty quantification in Bayesian inference as the motivating problem and observe improved performance compared to previously proposed approaches.

Recent works have shown the promise of learning pre-trained models for 3D molecular representation. However, existing pre-training models focus predominantly on equilibrium data and largely overlook off-equilibrium conformations. It is challenging to extend these methods to off-equilibrium data because their training objective relies on assumptions of conformations being the local energy minima. We address this gap by proposing a force-centric pretraining model for 3D molecular conformations covering both equilibrium and off-equilibrium data. For off-equilibrium data, our model learns directly from their atomic forces.

Over decades, Markov chain Monte Carlo (MCMC) methods have been widely studied, with a typical application being the quantification of posterior uncertainties in Bayesian system identification of structural dynamic models. To address the issue of excessively low sampling efficiency in generic MCMC methods when applied to specific problems, researchers developed several MCMC algorithms that integrate trainable neural networks to replace and enhance their critical components. Later, meta-learning MCMC methods emerged to reduce training time. However, they require considerable similarity between test and training tasks, while their sampling efficiency is constrained by trade-off-simplified network designs. This paper proposes the Adaptive Principal-Component (PC) Meta-learning Stochastic Gradient Hamiltonian Monte Carlo (APM-SGHMC) algorithm. It adaptively rotates coordinate axes in the parameter space to align with the PC directions of the current posterior samples, ensuring rotation-invariance of sampling performance with respect to the posterior distribution. By incorporating translation-invariance, scale-invariance, and rotation-invariance in a unified framework, APM-SGHMC enables universal samplers to acquire generalizable knowledge across diverse Bayesian system identification tasks using minimalistic tasks while eliminating the constraints imposed by network design trade-offs on sampling efficiency. Practical feasibility issues are also addressed. Two Bayesian system identification case studies demonstrate its effectiveness and universality: our method overcomes the case-by-case limitations of traditional data-driven approaches, achieving zero-shot generalization across structurally distinct models without retraining and maintaining consistent superior performance across all scenarios.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/