Temporal knowledge graph reasoning (TKGR) is crucial for capturing dynamic relational dependencies and inferring evolving facts. However, existing embedding-based and diffusion-based methods primarily rely on Euclidean point embeddings and face two limitations: (1) sparse entities may suffer from embedding crowding and norm-sensitive scoring, especially under limited supervision in long-tail temporal knowledge graphs; (2) uniform noise schedules in diffusion models ignore temporal heterogeneity and instance-level prediction difficulty. To address these challenges, we propose SimDiff-DNS (Simplex Diffusion with Dynamic Noise Scheduling), a simplex-anchored logit diffusion framework for TKGR. First, we represent entity states as probability distributions on the simplex and obtain continuous embeddings as convex combinations of learnable entity basis vectors. This simplex-coordinate parameterization provides a probabilistic view of uncertainty and alleviates norm-sensitive ranking behavior for sparse entities. Second, we introduce a difficulty-aware dynamic noise scheduling strategy for the training corruption process, which adjusts the noise applied to target-entity logits according to a bounded difficulty score. Extensive experiments on three TKGR datasets show that SimDiff-DNS consistently improves over the diffusion-based baseline (improving MRR by 3.25 points on ICEWS14) and achieves competitive or state-of-the-art results on several metrics. Additional diagnostic analyses further demonstrate its benefits for long-tail entities, calibration, and ranking stability.

Temporal knowledge graph (TKG) forecasting aims to predict future facts based on historical temporal information and still faces key challenges such as event sparsity and complex long-term dependencies. While graph-based methods effectively capture relational structure, they often fail to model nuanced long-range temporal patterns. Alternatively, standard Transformers, while potent for sequence modeling, are fundamentally time-agnostic; their generic positional encodings overlook critical TKG-specific temporal dynamics. As a result, many approaches struggle to capture fine-grained temporal patterns, limiting their effectiveness in forecasting sparse or complex events. To address these limitations, we propose HTA (Hybrid Transformer Architecture). HTA first constructs a query-specific Attention-Ready Temporal Sequence (ARTS) by aggregating historical context along a query-centered temporal reasoning path. This atomic sequence represents timestamps as dedicated temporal tokens that are contextualized together with their associated relation and entity tokens. At its core, HTA employs a stack of hybrid Attention-Mixer Transformer Blocks that combine bidirectional self-attention for capturing long-range dependencies with MLP-based layers for efficient feature refinement. Extensive experiments on four diverse benchmarks show that HTA achieves state-of-the-art performance. Notably, on the sparse and challenging GDELT dataset, HTA achieves an absolute MRR improvement of over 18 points, demonstrating its superior ability to model complex and noisy temporal dynamics.

Multi-modal Knowledge Graph Completion (MKGC) aims to infer missing links in multimodal knowledge graphs by leveraging structured triples together with auxiliary modalities such as text and images. Existing MKGC methods typically train with all modalities available, implicitly assuming consistent complementarity; however, this practice often induces modality dependence and modality competition under heterogeneous noise, which can hinder robust multi-modal fusion and limit overall performance.To address these issues, we propose MDBGF, a Modality Dropout and Bidirectional Gated Fusion framework for MKGC. MDBGF introduces a dynamic, probability-based modality dropout schedule. When the dropout is activated, MDBGF drops either the textual or visual modality during training while always preserving the structural information, encouraging the model to reduce over-reliance on any single auxiliary modality and to learn complementary cues under missing-modality conditions. When the dropout is not activated (i.e., all modalities are present), we further design a bidirectional gated fusion mechanism that enables mutual modulation between textual and visual modalities, enhancing cross-modal interaction and flexible fusion. In addition, we propose an adaptive proportional hybrid negative sampling strategy to strengthen MDBGF’s discriminative ability on hard negatives. Experiments on three benchmarks show that MDBGF consistently outperforms existing baselines and achieves new state-of-the-art results. Our code is available at https://anonymous.4open.science/r/MDBGF-AHNS.

Temporal knowledge graph (TKG) forecasting aims to infer future facts from historical observations in time-evolving graphs. Traditional rule-based methods often rely on statistical co-occurrences and extensive path enumeration, suffering from rule sparsity and search-space explosion, while recent LLM-based rule reasoning can produce linguistically plausible rules that are weakly constrained by graph evidence and thus may reflect spurious correlations or violate temporal constraints.To address these challenges, we propose Critic-Guided Rule Induction (CRI), which treats temporal rules as rule hypotheses to be examined and adopts a decoupled Generation-Discrimination pipeline to induce rules that are both high-coverage and high-precision. CRI first mines seed rules and path evidence from the historical graph and uses an LLM-based generator to abstract and generalize them into broader raw rule hypotheses. It then introduces a Fact-Grounded Rule Evaluator to perform fact-grounded discrimination of rule hypotheses from complementary perspectives together with necessary temporal and statistical constraints. Finally, CRI performs symbolic reasoning over the refined rule set to produce forecasts with traceable reasoning evidence. Experiments on three benchmarks show that CRI outperforms strong baselines, achieving state-of-the-art performance on TKG forecasting.

Temporal knowledge graph (TKG) reasoning, a central task in temporal knowledge representation, focuses on predicting future facts by leveraging historical temporal contexts. However, current approaches face two major challenges: limited generalization to unseen facts and insufficient interpretability of reasoning processes. To address these challenges, this paper proposes the Denoising Logic-based Temporal Knowledge Graph (DLTKG) framework, which employs a denoising diffusion process to complete reasoning tasks by introducing a noise source and a historical conditionguiding mechanism. Specifically, DLTKG constructs fuzzy entity representations by treating historical facts as noise sources, thereby enhancing the semantic associations between entities and the generalization ability for unseen facts. Additionally, the condition-based guidance mechanism, rooted in the relationship evolutionary paths, is designed to improve the interpretability of the reasoning process. Furthermore, we introduce a fine-tuning strategy that optimizes the denoising process by leveraging shortest path information between the head entity and candidate entities. Experimental results on three benchmark datasets demonstrate that DLTKG outperforms state-of-the-art methods across multiple evaluation metrics. Our code is available at: https://github.com/NEU-IDKE/DLTKG