Traditional clustering techniques often rely solely on similarity in the input data, limiting their ability to capture structural or semantic constraints that are critical in many domains. We introduce the Domain Aware Rule Triggered Variational Autoencoder (DARTVAE), a rule guided multimodal clustering framework that incorporates domain specific constraints directly into the representation learning process. DARTVAE extends the VAE architecture by embedding explicit rules, semantic representations, and data driven features into a unified latent space, while enforcing constraint compliance through rule consistency and violation penalties in the loss function. Unlike conventional clustering methods that rely only on visual similarity or apply rules as post hoc filters, DARTVAE treats rules as first class learning signals. The rules are generated by LLMs, structured into knowledge graphs, and enforced through a loss function combining reconstruction, KL divergence, consistency, and violation penalties. Experiments on aircraft and automotive datasets demonstrate that rule guided clustering produces more operationally meaningful and interpretable clusters for example, isolating UAVs, unifying stealth aircraft, or separating SUVs from sedans while improving traditional clustering metrics. However, the framework faces challenges: LLM generated rules may hallucinate or conflict, excessive rules risk overfitting, and scaling to complex domains increases computational and consistency difficulties. By combining rule encodings with learned representations, DARTVAE achieves more meaningful and consistent clustering outcomes than purely data driven models, highlighting the utility of constraint guided multimodal clustering for complex, knowledge intensive settings.

The bi-objective shortest-path (BOSP) problem seeks to find paths between start and target vertices of a graph while optimizing two conflicting objective functions. We consider the BOSP problem in the presence of correlated objectives. Such correlations often occur in real-world settings such as road networks, where optimizing two positively correlated objectives, such as travel time and fuel consumption, is common. BOSP is generally computationally challenging as the size of the search space is exponential in the number of objective functions and the graph size. Bounded sub-optimal BOSP solvers such as A*pex alleviate this complexity by approximating the Pareto-optimal solution set rather than computing it exactly (given a user-provided approximation factor). As the correlation between objective functions increases, smaller approximation factors are sufficient for collapsing the entire Pareto-optimal set into a single solution. We leverage this insight to propose an efficient algorithm that reduces the search effort in the presence of correlated objectives. Our approach for computing approximations of the entire Pareto-optimal set is inspired by graph-clustering algorithms. It uses a preprocessing phase to identify correlated clusters within a graph and to generate a new graph representation. This allows a natural generalization of A*pex to run up to five times faster on DIMACS dataset instances, a standard benchmark in the field. To the best of our knowledge, this is the first algorithm proposed that efficiently and effectively exploits correlations in the context of bi-objective search while providing theoretical guarantees on solution quality.

Recently, some works integrate SSL techniques into deep clustering frameworks to enhance image clustering performance. However, they all need pretraining, clustering learning, or a trained clustering model as prerequisites, limiting the flexible and out-of-box application of SSL learners in the image clustering task. This work introduces ASD, an adaptor that enables the cold-start of SSL learners for deep image clustering without any prerequisites. Specifically, we first randomly sample pseudo-labeled data from all unlabeled data, and set an instance-level classifier to learn them with semantically aligned instance-level labels. With the ability of instance-level classification, we track the class transitions of predictions on unlabeled data to extract high-level similarities of instance-level classes, which can be utilized to assign cluster-level labels to pseudo-labeled data. Finally, we use the pseudo-labeled data with assigned cluster-level labels to trigger a general SSL learner trained on the unlabeled data for image clustering. We show the superior performance of ASD across various benchmarks against the latest deep image clustering approaches and very slight accuracy gaps compared to SSL methods using ground-truth, e.g., only 1.33% on CIFAR-10. Moreover, ASD can also further boost the performance of existing SSL-embedded deep image clustering methods.

We introduce $Urania$, a novel framework for generating insights about LLM chatbot interactions with rigorous differential privacy (DP) guarantees. The framework employs a private clustering mechanism and innovative keyword extraction methods, including frequency-based, TF-IDF-based, and LLM-guided approaches. By leveraging DP tools such as clustering, partition selection, and histogram-based summarization, $Urania$ provides end-to-end privacy protection. Our evaluation assesses lexical and semantic content preservation, pair similarity, and LLM-based metrics, benchmarking against a non-private Clio-inspired pipeline (Tamkin et al., 2024). Moreover, we develop a simple empirical privacy evaluation that demonstrates the enhanced robustness of our DP pipeline. The results show the framework's ability to extract meaningful conversational insights while maintaining stringent user privacy, effectively balancing data utility with privacy preservation.

The effectiveness of machine learning models, particularly in unbalanced classification tasks, is often hindered by the failure to differentiate between critical instances near the decision boundary and redundant samples concentrated in the core of the data distribution. In this paper, we propose a method to systematically identify and differentiate between these two types of data. Through extensive experiments on multiple benchmark datasets, we show that the boundary data oversampling method improves the F1 score by up to 10\% on 96\% of the datasets, whereas our core-aware reduction method compresses datasets up to 90\% while preserving their accuracy, making it 10 times more powerful than the original dataset. Beyond imbalanced classification, our method has broader implications for efficient model training, particularly in computationally expensive domains such as Large Language Model (LLM) training. By prioritizing high-quality, decision-relevant data, our approach can be extended to text, multimodal, and self-supervised learning scenarios, offering a pathway to faster convergence, improved generalization, and significant computational savings. This work paves the way for future research in data-efficient learning, where intelligent sampling replaces brute-force expansion, driving the next generation of AI advancements. Our code is available as a Python package at https://pypi.org/project/adaptive-resampling/ .

Outdoor intelligent autonomous robotic operation relies on a sufficiently expressive map of the environment. Classical geometric mapping methods retain essential structural environment information, but lack a semantic understanding and organization to allow high-level robotic reasoning. 3D scene graphs (3DSGs) address this limitation by integrating geometric, topological, and semantic relationships into a multi-level graph-based map. Outdoor autonomous operations commonly rely on terrain information either due to task-dependence or the traversability of the robotic platform. We propose a novel approach that combines indoor 3DSG techniques with standard outdoor geometric mapping and terrain-aware reasoning, producing terrain-aware place nodes and hierarchically organized regions for outdoor environments. Our method generates a task-agnostic metric-semantic sparse map and constructs a 3DSG from this map for downstream planning tasks, all while remaining lightweight for autonomous robotic operation. Our thorough evaluation demonstrates our 3DSG method performs on par with state-of-the-art camera-based 3DSG methods in object retrieval and surpasses them in region classification while remaining memory efficient. We demonstrate its effectiveness in diverse robotic tasks of object retrieval and region monitoring in both simulation and real-world environments.

We address temporal failures in RAG systems using two methods on cybersecurity data. A simple recency prior achieved an accuracy of 1.00 on freshness tasks. In contrast, a clustering heuristic for topic evolution failed (0.08 F1-score), showing trend detection requires methods beyond simple heuristics.

The rapid growth of scientific literature demands efficient methods to organize and synthesize research findings. Existing taxonomy construction methods, leveraging unsupervised clustering or direct prompting of large language models (LLMs), often lack coherence and granularity. We propose a novel context-aware hierarchical taxonomy generation framework that integrates LLM-guided multi-aspect encoding with dynamic clustering. Our method leverages LLMs to identify key aspects of each paper (e.g., methodology, dataset, evaluation) and generates aspect-specific paper summaries, which are then encoded and clustered along each aspect to form a coherent hierarchy. In addition, we introduce a new evaluation benchmark of 156 expert-crafted taxonomies encompassing 11.6k papers, providing the first naturally annotated dataset for this task. Experimental results demonstrate that our method significantly outperforms prior approaches, achieving state-of-the-art performance in taxonomy coherence, granularity, and interpretability.

The well-known graph-based clustering methods, including spectral clustering, symmetric non-negative matrix factorization, and doubly stochastic normalization, can be viewed as relaxations of the kernel $k$-means approach. However, we posit that these methods excessively relax their inherent low-rank, nonnegative, doubly stochastic, and orthonormal constraints to ensure numerical feasibility, potentially limiting their clustering efficacy. In this paper, guided by our theoretical analyses, we propose \textbf{Lo}w-\textbf{R}ank \textbf{D}oubly stochastic clustering (\textbf{LoRD}), a model that only relaxes the orthonormal constraint to derive a probabilistic clustering results. Furthermore, we theoretically establish the equivalence between orthogonality and block diagonality under the doubly stochastic constraint. By integrating \textbf{B}lock diagonal regularization into LoRD, expressed as the maximization of the Frobenius norm, we propose \textbf{B-LoRD}, which further enhances the clustering performance. To ensure numerical solvability, we transform the non-convex doubly stochastic constraint into a linear convex constraint through the introduction of a class probability parameter. We further theoretically demonstrate the gradient Lipschitz continuity of our LoRD and B-LoRD enables the proposal of a globally convergent projected gradient descent algorithm for their optimization. Extensive experiments validate the effectiveness of our approaches. The code is publicly available at https://github.com/lwl-learning/LoRD.