Hierarchical relations are prevalent and indispensable for organizing human knowledge captured by a knowledge graph (KG). The key property of hierarchical relations is that they induce a partial ordering over the entities, which needs to be modeled in order to allow for hierarchical reasoning.

Instead, we show that searching over input mixture distributions using validation loss results in the recovery of the true model(withrespecttothevalidation,Proposition1).

We consider the problem of regret minimization in non-parametric stochastic bandits. When the rewards are known to be bounded from above, there exists asymptotically optimal algorithms, with asymptotic regret depending on an infi-mum of Kullback-Leibler divergences (KL).

Our VB-LoRA achieves higher scores with significantly smaller number ofstoredparameters.

Neural Architecture Search (NAS) can automatically design promising neural architectures without artificial experience. Though itachievesgreat success, prohibitively high search cost is required to find a high-performance architecture, whichblocksitspractical implementation.

We also consider in detail the specific case where the summary is the Fréchet mean of data residing on a manifold.