In this paper we investigate the efficacy of the score-based martingale posteriors (SMP) (Cui & Walker, 2025; Fong et al., 2023) in the context of modern and large-scale machine learning problems and its potential for meaningful uncertainty quantification. SMPs work with a stochastic gradient ascent-type recursion on the parameter space of stochastic models and construct a martingale on the parameter space. Under simple mathematical assumptions, the recursion can be built so that the parameters form a martingale sequence which possesses a limiting, in time, random variable, the latter of which can be simulated very quickly, in contrast to Monte Carlo-based methods such as Markov chain Monte Carlo. In this expository paper we explore the SMP for inferring the parameters of deep neural networks (DNNs) and, where feasible, compare our results to the state-of-the-art Monte Carlo methods aimed at inferring conventional Bayesian posteriors.

Data-driven motion priors that can guide agents toward producing naturalistic behaviors play a pivotal role in creating life-like virtual characters. Adversarial imitation learning has been a highly effective method for learning motion priors from reference motion data. However, adversarial priors, with few exceptions, need to be retrained for each new controller, thereby limiting their reusability and necessitating the retention of the reference motion data when training on downstream tasks. In this work, we present Score-Matching Motion Priors (SMP), which leverages pre-trained motion diffusion models and score distillation sampling (SDS) to create reusable task-agnostic motion priors. SMPs can be pre-trained on a motion dataset, independent of any control policy or task. Once trained, SMPs can be kept frozen and reused as general-purpose reward functions to train policies to produce naturalistic behaviors for downstream tasks. We show that a general motion prior trained on large-scale datasets can be repurposed into a variety of style-specific priors. Furthermore SMP can compose different styles to synthesize new styles not present in the original dataset. Our method produces high-quality motion comparable to state-of-the-art adversarial imitation learning methods through reusable and modular motion priors. We demonstrate the effectiveness of SMP across a diverse suite of control tasks with physically simulated humanoid characters. Video demo available at https://youtu.be/ravlZJteS20

The proliferation of complex, black-box AI models has intensified the need for techniques that can explain their decisions. Feature attribution methods have become a popular solution for providing post-hoc explanations, yet the field has historically lacked a formal problem definition. This paper addresses this gap by introducing a formal definition for the problem of feature attribution, which stipulates that explanations be supported by an underlying probability distribution represented by the given dataset. Our analysis reveals that many existing model-agnostic methods fail to meet this criterion, while even those that do often possess other limitations. To overcome these challenges, we propose Distributional Feature Attribution eXplanations (DFAX), a novel, model-agnostic method for feature attribution. DFAX is the first feature attribution method to explain classifier predictions directly based on the data distribution. We show through extensive experiments that DFAX is more effective and efficient than state-of-the-art baselines.

We prove the claim by induction. We now shift to the case of SMP . We use an inductive argument. B.3 Extension for attributed graphs It was proven in Theorem 3 that, under the corollary's conditions, the local context (Algorithm 1). We will prove by induction that any Fast SMP layer can be approximated by two blocks of PPGN.

A local-valley (LV) centered approach to assessing the quality of sampling from Restricted Boltzmann Machines (RBMs) was applied to the latest generation of the D-Wave quantum annealer. D-Wave and Gibbs samples from a classically trained RBM were obtained at conditions relevant to the contrastive-divergence-based RBM learning. The samples were compared for the number of the LVs to which they belonged and the energy of the corresponding local minima. No significant (desirable) increase in the number of the LVs has been achieved by decreasing the D-Wave annealing time. At any training epoch, the states sampled by the D-Wave belonged to a somewhat higher number of LVs than in the Gibbs sampling. However, many of those LVs found by the two techniques differed. For high-probability sampled states, the two techniques were (unfavorably) less complementary and more overlapping. Nevertheless, many potentially "important" local minima, i.e., those having intermediate, even if not high, probability values, were found by only one of the two sampling techniques while missed by the other. The two techniques overlapped less at later than earlier training epochs, which is precisely the stage of the training when modest improvements to the sampling quality could make meaningful differences for the RBM trainability. The results of this work may explain the failure of previous investigations to achieve substantial (or any) improvement when using D-Wave-based sampling. However, the results reveal some potential for improvement, e.g., using a combined classical-quantum approach.