# Spectral Initialization and Scheduled Graph Smoothness for Uncertain Knowledge Graph Completion

arXiv: https://arxiv.org/abs/2609.02519 · HTML: https://mlsanity.com/paper/2609.02519/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 22 references that are in the map.
- First posted on arXiv 2 Sep 2026.

## Builds on (most cited first, 11 of 11)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Composition-based Multi-Relational Graph Convolutional Networks](https://mlsanity.com/paper/1911.03082/) (2019)
- [Knowledge-aware Graph Neural Networks with Label Smoothness Regularization for Recommender Systems](https://mlsanity.com/paper/1905.04413/) (2019)
- [Dirichlet Energy Constrained Learning for Deep Graph Neural Networks](https://mlsanity.com/paper/2107.02392/) (2021)
- [Probabilistic Entity Representation Model for Reasoning over Knowledge Graphs](https://mlsanity.com/paper/2110.13522/) (2021)
- [Deep Insights into Noisy Pseudo Labeling on Graph Data](https://mlsanity.com/paper/2310.01634/) (2023)
- [Generalizing Knowledge Graph Embedding with Universal Orthogonal Parameterization](https://mlsanity.com/paper/2405.08540/) (2024)
- [BANGS: Game-Theoretic Node Selection for Graph Self-Training](https://mlsanity.com/paper/2410.09348/) (2024)
- [Uncertain Knowledge Graph Completion via Semi-Supervised Confidence Distribution Learning](https://mlsanity.com/paper/2510.16601/) (2025)
- [Data Imputation from the Perspective of Graph Dirichlet Energy](https://mlsanity.com/paper/2304.04474/) (2023)
- [Joint Feature and Differentiable  k -NN Graph Learning using Dirichlet Energy](https://mlsanity.com/paper/2305.12396/) (2023)

## Abstract (arXiv)

Uncertain knowledge graphs (UKGs) extend knowledge graphs by assigning each triple a continuous confidence score. Since most possible triples lack observed confidences, recent methods rely on semi-supervised learning to generate pseudo-labels. These methods initialize entity embeddings without using the confidence-weighted graph, discarding its global community and hub structure. We introduce QUEST, which adds no trainable parameters to the standard confidence-distribution learning pipeline. First, QUEST initializes entity embeddings using the smallest non-trivial eigenvectors of the confidence-weighted graph Laplacian, incorporating community and hub structure before training. Second, QUEST applies an unbiased mini-batch Dirichlet energy regularizer to enforce early-stage structural consistency. On two UKG datasets, QUEST improves confidence prediction and link prediction on six of eight metric-dataset pairs over prior methods and matches the previous best on the remaining two, while removing the instability spike observed on dense graphs. These results indicate that spectral structural priors combined with a graph Dirichlet energy regularizer improve accuracy, training stability, and checkpoint reliability in UKG completion.