To prove Theorem 1, we need to consider the two directions of the iff conditions. If we are given h(c1,X1) = h(c2,X2), we are able to prove that the conditions mentioned in the theorem are necessary by showing contradictions occur when they are not satisfied. As Eq. (4) equals Eq. (6), we have: X Obviously, the above equation does not hold as the terms in the summation operator are positive. We may now assume S1 = S2 = S. Eliminating the irrational terms in Eq. (4), we have: X Eq. (9) can be simplified and rewritten as: µ1(x) µ2(x) = However, the RHS of Eq. (10) can be an irrational number. It is obvious that the above equality does not hold as the RHS is an irrational number, while LHS is a rational number.

Graph Neural Networks have achieved remarkable accuracy in semi-supervised node classification tasks. However, these results lack reliable uncertainty estimates. Conformal prediction methods provide a theoretical guarantee for node classification tasks, ensuring that the conformal prediction set contains the ground-truth label with a desired probability (e.g., 95\%). In this paper, we empirically show that for each node, aggregating the non-conformity scores of nodes with the same label can improve the efficiency of conformal prediction sets while maintaining valid marginal coverage. This observation motivates us to propose a novel algorithm named $\textit{Similarity-Navigated Adaptive Prediction Sets}$ (SNAPS), which aggregates the non-conformity scores based on feature similarity and structural neighborhood. The key idea behind SNAPS is that nodes with high feature similarity or direct connections tend to have the same label. By incorporating adaptive similar nodes information, SNAPS can generate compact prediction sets and increase the singleton hit ratio (correct prediction sets of size one). Moreover, we theoretically provide a finite-sample coverage guarantee of SNAPS. Extensive experiments demonstrate the superiority of SNAPS, improving the efficiency of prediction sets and singleton hit ratio while maintaining valid coverage.

Based on our definitions, we identify and analyze six real-world benchmarks spanning from homophilic to heterophilic link prediction settings, with graphs containing up to 30M edges.

However, these results lack reliable uncertainty estimates.

Conversely, the opposite scenario is relatively benign.

Based on our definitions, we identify and analyze six real-world benchmarks spanning from homophilic to heterophilic link prediction settings, with graphs containing up to 30M edges.

However, these results lack reliable uncertainty estimates.

We study the problem of named entity recognition (NER) based on demonstration learning in low-resource scenarios. We identify two issues in demonstration construction and model training . Firstly, existing methods for selecting demonstration examples primarily rely on semantic similarity; We show that feature similarity can provide significant performance improvement. Secondly, we show that the NER tagger's ability to reference demonstration examples is generally inadequate. We propose a demonstration and training approach that effectively addresses these issues. For the first issue, we propose to select examples by dual similarity, which comprises both semantic similarity and feature similarity. For the second issue, we propose to train an NER model with adversarial demonstration such that the model is forced to refer to the demonstrations when performing the tagging task. We conduct comprehensive experiments in low-resource NER tasks, and the results demonstrate that our method outperforms a range of methods.