We give a sufficient criterion to ensure that the problem is well-conditioned.

Current perceptual similarity metrics operate at the level of pixels and patches.

Now, we can exactly derive that q (G) = ˆ p( G|I) . The definitions of potential function φ and ψ follow those in JM-SGG model. Figure 1: The scene graphs generated by JM-SGG model. In these examples, factor update is able to correct some wrong relation labels ( e.g.

We carefully design the potential functions to enable relational reasoning among different objects according to knowledge graph embedding methods.

Class imbalance significantly degrades classification performance, yet its effects are rarely analyzed from a unified theoretical perspective. We propose a principled framework based on three fundamental scales: the imbalance coefficient $η$, the sample--dimension ratio $κ$, and the intrinsic separability $Δ$. Starting from the Gaussian Bayes classifier, we derive closed-form Bayes errors and show how imbalance shifts the discriminant boundary, yielding a deterioration slope that predicts four regimes: Normal, Mild, Extreme, and Catastrophic. Using a balanced high-dimensional genomic dataset, we vary only $η$ while keeping $κ$ and $Δ$ fixed. Across parametric and non-parametric models, empirical degradation closely follows theoretical predictions: minority Recall collapses once $\log(η)$ exceeds $Δ\sqrtκ$, Precision increases asymmetrically, and F1-score and PR-AUC decline in line with the predicted regimes. These results show that the triplet $(η,κ,Δ)$ provides a model-agnostic, geometrically grounded explanation of imbalance-induced deterioration.

Knowledge graph reasoning, which aims at predicting missing facts through reasoning with observed facts, is critical for many applications. Such a problem has been widely explored by traditional logic rule-based approaches and recent knowledge graph embedding methods. A principled logic rule-based approach is the Markov Logic Network (MLN), which is able to leverage domain knowledge with first-order logic and meanwhile handle uncertainty. However, the inference in MLNs is usually very difficult due to the complicated graph structures.

Knowledge graph (KG) embedding is well-known in learning representations of KGs. Many models have been proposed to learn the interactions between entities and relations of the triplets. However, long-term information among multiple triplets is also important to KG. In this work, based on the relational paths, which are composed of a sequence of triplets, we define the Interstellar as a recurrent neural architecture search problem for the short-term and long-term information along the paths. First, we analyze the difficulty of using a unified model to work as the Interstellar. Then, we propose to search for recurrent architecture as the Interstellar for different KG tasks. A case study on synthetic data illustrates the importance of the defined search problem. Experiments on real datasets demonstrate the effectiveness of the searched models and the efficiency of the proposed hybrid-search algorithm.