Continuous diffusion models have demonstrated remarkable generative performance across diverse domains but are often constrained by the computational cost of simulating reverse Ornstein–Uhlenbeck processes via SDE/ODE solvers. Existing theoretical results typically establish query complexities that scale polynomially with both the dimension $d$ and the error tolerance $\epsilon$ (e.g., $\tilde{\mathcal{O}}(d/\epsilon)$). This mirrors the limitations of unadjusted Langevin algorithm, where standard first-order score solvers lack access to zeroth-order density information, precluding natural error-correction mechanisms and thus preventing the fast $\ln(1/\epsilon)$ convergence attainable by Metropolis-adjusted methods. In this paper, we develop an improved generative modeling method by introducing Quantized Transition Diffusion (QTD), a framework that reformulates continuous diffusion into a discrete generation problem through spatial quantization and the parameterization of zeroth-order information (e.g., density ratios). To sample from this discrete target, we propose a truncated uniformization algorithm that simulates the underlying continuous-time Markov chain of the discrete diffusion process without discretization error, while eliminating the restrictive bounded-score assumption required by prior uniformization-based approaches. Consequently, QTD attains $\epsilon$-accuracy in total variation distance with a query complexity of $\mathcal{O}(d \ln^2(d/\epsilon))$, yielding a notable improvement in $\epsilon$-dependence compared to existing continuous diffusion samplers. Crucially, our analysis capitalizes on a novel proof technique based on the infinitesimal chain rule of KL divergence, providing a fresh perspective on unifying continuous and discrete diffusion paradigms.

Real-world data often violates the equal-variance assumption (homoscedasticity), making it essential to account for heteroscedastic noise in causal discovery. In this work, we explore heteroscedastic symmetric noise models (HSNMs), where the effect $Y$ is modeled as $Y = f(X) + \sigma(X)N$, with $X$ as the cause and $N$ as independent noise following a symmetric distribution. We introduce a novel criterion for identifying HSNMs based on the skewness of the score (i.e., the gradient of the log density) of the data distribution. This criterion establishes a computationally tractable measurement that is zero in the causal direction but nonzero in the anticausal direction, enabling the causal direction discovery. We extend this skewness-based criterion to the multivariate setting and propose \texttt{SkewScore}, an algorithm that handles heteroscedastic noise without requiring the extraction of exogenous noise. We also conduct a case study on the robustness of \texttt{SkewScore} in a bivariate model with a latent confounder, providing theoretical insights into its performance. Empirical studies further validate the effectiveness of the proposed method.

We propose a framework to convert $(\varepsilon, \delta)$-approximate Differential Privacy (DP) mechanisms into $(\varepsilon', 0)$-pure DP mechanisms under certain conditions, a process we call ``purification.'' This algorithmic technique leverages randomized post-processing with calibrated noise to eliminate the $\delta$ parameter while achieving near-optimal privacy-utility tradeoff for pure DP. It enables a new design strategy for pure DP algorithms: first run an approximate DP algorithm with certain conditions, and then purify. This approach allows one to leverage techniques such as strong composition and propose-test-release that require $\delta>0$ in designing pure-DP methods with $\delta=0$. We apply this framework in various settings, including Differentially Private Empirical Risk Minimization (DP-ERM), stability-based release, and query release tasks. To the best of our knowledge, this is the first work with a statistically and computationally efficient reduction from approximate DP to pure DP. Finally, we illustrate the use of this reduction for proving lower bounds under approximate DP constraints with explicit dependence in $\delta$, avoiding the sophisticated fingerprinting code construction.

Temporal Knowledge Graph (TKG) reasoning has received a growing interest recently, especially in forecasting the future facts based on the historical KG sequences. Existing studies typically utilize a recurrent neural network to learn the evolutional representations of entities for temporal reasoning. However, these methods are hard to capture the complex temporal evolutional patterns such as sequential and repetitive patterns accurately. To tackle this challenge, we propose a novel Sequential and Repetitive Pattern Learning (SRPL) method, which comprehensively captures both the sequential and repetitive patterns. Specifically, a Dependency-aware Sequential Pattern Learning (DSPL) component expresses the temporal dependencies of each historical timestamp as embeddings for accurately capturing the sequential patterns across temporally adjacent facts. A Time-interval guided Repetitive Pattern Learning (TRPL) component models the irregular time intervals between historical repetitive facts for capturing the repetitive patterns. Extensive experiments on four representative benchmarks demonstrate that our proposed method outperforms state-of-the-art methods in all metrics by an obvious margin, especially on GDELT dataset, where performance improvement of MRR reaches up to 18.84%.

Posterior sampling, i.e., exponential mechanism to sample from the posterior distribution, provides $\varepsilon$-pure differential privacy (DP) guarantees and does not suffer from potentially unbounded privacy breach introduced by $(\varepsilon,\delta)$-approximate DP. In practice, however, one needs to apply approximate sampling methods such as Markov chain Monte Carlo (MCMC), thus re-introducing the unappealing $\delta$-approximation error into the privacy guarantees. To bridge this gap, we propose the Approximate SAample Perturbation (abbr. ASAP) algorithm which perturbs an MCMC sample with noise proportional to its Wasserstein-infinity ($W_\infty$) distance from a reference distribution that satisfies pure DP or pure Gaussian DP (i.e., $\delta=0$). We then leverage a Metropolis-Hastings algorithm to generate the sample and prove that the algorithm converges in W$_\infty$ distance. We show that by combining our new techniques with a localization step, we obtain the first nearly linear-time algorithm that achieves the optimal rates in the DP-ERM problem with strongly convex and smooth losses.

Hypothesis Generation (HG) aims to expedite biomedical researches by generating novel hypotheses from existing scientific literature. Most existing studies focused on modeling static snapshots of the corpus, neglecting the temporal evolution of scientific terms. Despite recent efforts to learn term evolution from Knowledge Bases (KBs) for HG, the temporal information from multi-source KBs is still overlooked, which contains important, up-to-date knowledge. In this paper, an innovative Temporal Contrastive Learning (TCL) framework is introduced to uncover latent associations between entities by jointly modeling their co-evolution across multi-source temporal KBs. Specifically, we first construct a temporal relation graph based on PubMed papers and a biomedical relation database (such as Comparative Toxicogenomics Database (CTD)). Then the constructed temporal relation graph and a temporal concept graph (such as Medical Subject Headings (MeSH)) are used to train two GCN-based recurrent networks for learning the entity temporal evolutional embeddings, respectively. Finally, a cross-view temporal prediction task is designed for learning knowledge enriched temporal embeddings by contrasting the temporal embeddings learned from the two Temporal Knowledge Graphs (TKGs). Findings from experiments conducted on three real-world biomedical term relationship datasets demonstrate that the proposed approach is clearly superior to approaches based on single TKG, achieving the state-of-the-art performance.

Knowledge Graph (KG) reasoning has been an interesting topic in recent decades. Most current researches focus on predicting the missing facts for incomplete KG. Nevertheless, Temporal KG (TKG) reasoning, which is to forecast future facts, still faces with a dilemma due to the complex interactions between entities over time. This article proposes a novel intricate Spatiotemporal Dependency learning Network (STDN) based on Graph Convolutional Network (GCN) to capture the underlying correlations of an entity at different timestamps. Specifically, we first learn an adaptive adjacency matrix to depict the direct dependencies from the temporally adjacent facts of an entity, obtaining its previous context embedding. Then, a Spatiotemporal feature Encoding GCN (STE-GCN) is proposed to capture the latent spatiotemporal dependencies of the entity, getting the spatiotemporal embedding. Finally, a time gate unit is used to integrate the previous context embedding and the spatiotemporal embedding at the current timestamp to update the entity evolutional embedding for predicting future facts. STDN could generate the more expressive embeddings for capturing the intricate spatiotemporal dependencies in TKG. Extensive experiments on WIKI, ICEWS14, and ICEWS18 datasets prove our STDN has the advantage over state-of-the-art baselines for the temporal reasoning task.

BACKGROUND: Biomedical named entity recognition is one of the most essential tasks in biomedical information extraction. Previous studies suffer from inadequate annotated datasets, especially the limited knowledge contained in them. METHODS: To remedy the above issue, we propose a novel Biomedical Named Entity Recognition (BioNER) framework with label re-correction and knowledge distillation strategies, which could not only create large and high-quality datasets but also obtain a high-performance recognition model. Our framework is inspired by two points: (1) named entity recognition should be considered from the perspective of both coverage and accuracy; (2) trustable annotations should be yielded by iterative correction. Firstly, for coverage, we annotate chemical and disease entities in a large-scale unlabeled dataset by PubTator to generate a weakly labeled dataset. For accuracy, we then filter it by utilizing multiple knowledge bases to generate another weakly labeled dataset. Next, the two datasets are revised by a label re-correction strategy to construct two high-quality datasets, which are used to train two recognition models, respectively. Finally, we compress the knowledge in the two models into a single recognition model with knowledge distillation. RESULTS: Experiments on the BioCreative V chemical-disease relation corpus and NCBI Disease corpus show that knowledge from large-scale datasets significantly improves the performance of BioNER, especially the recall of it, leading to new state-of-the-art results. CONCLUSIONS: We propose a framework with label re-correction and knowledge distillation strategies. Comparison results show that the two perspectives of knowledge in the two re-corrected datasets respectively are complementary and both effective for BioNER.

BACKGROUND: Automatic extraction of chemical-disease relations (CDR) from unstructured text is of essential importance for disease treatment and drug development. Meanwhile, biomedical experts have built many highly-structured knowledge bases (KBs), which contain prior knowledge about chemicals and diseases. Prior knowledge provides strong support for CDR extraction. How to make full use of it is worth studying. RESULTS: This paper proposes a novel model called "Knowledge-guided Convolutional Networks (KCN)" to leverage prior knowledge for CDR extraction. The proposed model first learns knowledge representations including entity embeddings and relation embeddings from KBs. Then, entity embeddings are used to control the propagation of context features towards a chemical-disease pair with gated convolutions. After that, relation embeddings are employed to further capture the weighted context features by a shared attention pooling. Finally, the weighted context features containing additional knowledge information are used for CDR extraction. Experiments on the BioCreative V CDR dataset show that the proposed KCN achieves 71.28% F1-score, which outperforms most of the state-of-the-art systems. CONCLUSIONS: This paper proposes a novel CDR extraction model KCN to make full use of prior knowledge. Experimental results demonstrate that KCN could effectively integrate prior knowledge and contexts for the performance improvement.

Automatically extracting the relationships between chemicals and diseases is significantly important to various areas of biomedical research and health care. Biomedical experts have built many large-scale knowledge bases (KBs) to advance the development of biomedical research. KBs contain huge amounts of structured information about entities and relationships, therefore plays a pivotal role in chemical-disease relation (CDR) extraction. However, previous researches pay less attention to the prior knowledge existing in KBs. This paper proposes a neural network-based attention model (NAM) for CDR extraction, which makes full use of context information in documents and prior knowledge in KBs. For a pair of entities in a document, an attention mechanism is employed to select important context words with respect to the relation representations learned from KBs. Experiments on the BioCreative V CDR dataset show that combining context and knowledge representations through the attention mechanism, could significantly improve the CDR extraction performance while achieve comparable results with state-of-the-art systems.