On the Equivalence of Random Network Distillation, Deep Ensembles, and Bayesian Inference

Uncertainty quantification is central to safe and efficient deployments of deep learning models, yet many computationally practical methods lack lacking rigorous theoretical motivation. Random network distillation (RND) is a lightweight technique that measures novelty via prediction errors against a fixed random target. While empirically effective, it has remained unclear what uncertainties RND measures and how its estimates relate to other approaches, e.g. Bayesian inference or deep ensembles. This paper establishes these missing theoretical connections by analyzing RND within the neural tangent kernel framework in the limit of infinite network width. Our analysis reveals two central findings in this limit: (1) The uncertainty signal from RND -- its squared self-predictive error -- is equivalent to the predictive variance of a deep ensemble. (2) By constructing a specific RND target function, we show that the RND error distribution can be made to mirror the centered posterior predictive distribution of Bayesian inference with wide neural networks. Based on this equivalence, we moreover devise a posterior sampling algorithm that generates i.i.d. samples from an exact Bayesian posterior predictive distribution using this modified \textit{Bayesian RND} model. Collectively, our findings provide a unified theoretical perspective that places RND within the principled frameworks of deep ensembles and Bayesian inference, and offer new avenues for efficient yet theoretically grounded uncertainty quantification methods.

Discover Important Paths in the Knowledge Graph Based on Dynamic Relation Confidence

Most of the existing knowledge graphs are not usually complete and can be complemented by some reasoning algorithms. The reasoning method based on path features is widely used in the field of knowledge graph reasoning and completion on account of that its have strong interpretability. However, reasoning methods based on path features still have several problems in the following aspects: Path search isinefficient, insufficient paths for sparse tasks and some paths are not helpful for reasoning tasks. In order to solve the above problems, this paper proposes a method called DC-Path that combines dynamic relation confidence and other indicators to evaluate path features, and then guide path search, finally conduct relation reasoning. Experimental result show that compared with the existing relation reasoning algorithm, this method can select the most representative features in the current reasoning task from the knowledge graph and achieve better performance on the current relation reasoning task.