However, existing deep constrained clustering (DCC) methods are either limited by anchors inherent in end-to-end modeling or struggle with learning discriminative Euclidean embedding, restricting their scalability and real-world applicability. To avoid their respective pitfalls, we propose a novel angular constraint embedding approach for DCC, termed SpherePair. Using the SpherePair loss with a geometric formulation, our method faithfully encodes pairwise constraints and leads to embeddings that are clustering-friendly in angular space, effectively separating representation learning from clustering. SpherePair preserves pairwise relations without conflict, removes the need to specify the exact number of clusters, generalizes to unseen data, enables rapid inference of the number of clusters, and is supported by rigorous theoretical guarantees. Comparative evaluations with stateof-the-art DCC methods on diverse benchmarks, along with empirical validation of theoretical insights, confirm its superior performance, scalability, and overall real-world effectiveness. Code is available at our repository.

Spatial transcriptomics (ST) technologies provide gene expression measurements with spatial resolution, enabling the dissection of tissue structure and function. A fundamental challenge in ST analysis is clustering spatial spots into coherent functional regions. While existing models effectively integrate expression and spatial signals, they largely overlook sequence-level biological priors encoded in the DNA sequences of expressed genes. To bridge this gap, we propose SAINT (Sequence-Aware Integration for Nucleotide-informed Transcriptomics), a unified framework that augments spatial representation learning with nucleotide-derived features. We construct sequence-augmented datasets across 14 tissue sections from three widely used ST benchmarks (DLPFC, HBC, and MBA), retrieving reference DNA sequences for each expressed gene and encoding them using a pretrained Nucleotide Transformer. For each spot, gene-level embeddings are aggregated via expression-weighted and attention-based pooling, then fused with spatial-expression representations through a late fusion module. Extensive experiments demonstrate that SAINT consistently improves clustering performance across multiple datasets.

Due to its powerful capability of self-supervised representation learning and clustering, contrastive attributed graph clustering (CAGC) has achieved great success, which mainly depends on effective data augmentation and contrastive objective setting. However, most CAGC methods utilize edges as auxiliary information to obtain node-level embedding representation and only focus on node-level embedding augmentation. This approach overlooks edge-level embedding augmentation and the interactions between node-level and edge-level embedding augmentations across various granularity. Moreover, they often treat all contrastive sample pairs equally, neglecting the significant differences between hard and easy positivenegative sample pairs, which ultimately limits their discriminative capability. To tackle these issues, a novel robust attributed graph clustering (RAGC), incorporating hybrid-collaborative augmentation (HCA) and contrastive sample adaptivedifferential awareness (CSADA), is proposed. First, node-level and edge-level embedding representations and augmentations are simultaneously executed to establish a more comprehensive similarity measurement criterion for subsequent contrastive learning.

Current Large Language Models (LLMs) are confronted with overwhelming information volume when comprehending long-form documents. This challenge raises the imperative of a cohesive memory module, which can elevate vanilla LLMs into autonomous reading agents. Despite the emergence of some heuristic approaches, a systematic design principle remains absent. To fill this void, we draw inspiration from Jean Piaget's Constructivist Theory, illuminating three traits of the agentic memory--structured schemata, flexible assimilation, and dynamic accommodation.

Large language models (LLMs) have enabled agents to perform complex reasoning and decision-making through free-form language interactions. However, in openended language action environments (e.g., negotiation or question-asking games), the action space can be formulated as a joint distribution over tokens, resulting in an exponentially large action space. Sampling actions in such a space can lead to extreme reward sparsity, which brings large reward variance, hindering effective reinforcement learning (RL). To address this, we propose ARIA, a method that Aggregates Rewards in Intention space to enable efficient and effective language Agents training. ARIA aims to project natural language actions from the highdimensional joint token distribution space into a low-dimensional intention space, where semantically similar actions are clustered and assigned shared rewards. This intention-aware reward aggregation reduces reward variance by densifying reward signals, fostering better policy optimization. Extensive experiments demonstrate that ARIA not only significantly reduces policy gradient variance, but also delivers substantial performance gains of an average of 9.95% across four downstream tasks, consistently outperforming offline and online RL baselines.

Deep multi-modal clustering (DMC) aims to explore the correlated information from different modalities to improve the clustering performance. Most existing DMCs attempt to investigate the consistency or/and complementarity information by fusing all modalities, but this will lead to the following challenges: 1) Information conflicts between modalities emerge.

Model-based clustering integrated with variable selection is a powerful tool for uncovering latent structures within complex data. However, its effectiveness is often hindered by challenges such as identifying relevant variables that define heterogeneous subgroups and handling data that are missing not at random, a prevalent issue in fields like transcriptomics. While several notable methods have been proposed to address these problems, they typically tackle each issue in isolation, thereby limiting their flexibility and adaptability. This paper introduces a unified framework designed to address these challenges simultaneously. Our approach incorporates a data-driven penalty matrix into penalized clustering to enable more flexible variable selection, along with a mechanism that explicitly models the relationship between missingness and latent class membership. We demonstrate that, under certain regularity conditions, the proposed framework achieves both asymptotic consistency and selection consistency, even in the presence of missing data. This unified strategy significantly enhances the capability and efficiency of model-based clustering, advancing methodologies for identifying informative variables that define homogeneous subgroups in the presence of complex missing data patterns. The performance of the framework, including its computational efficiency, is evaluated through simulations and demonstrated using both synthetic and real-world transcriptomic datasets.

Greedy k-means++ is a generalization of k-means++ where, in each iteration, a new seed is greedily chosen among multiple ℓ 2points sampled, as opposed to a single seed being sampled in k-means++. While empirical studies consistently show the superior performance of greedy k-means++, making it a preferred method in practice, a discrepancy exists between theory and practice. No theoretical justification currently explains this improved performance. Indeed, the prevailing theory suggests that greedy k-means++ exhibits worse performance than k-means++ in worst-case scenarios. This paper presents an analysis demonstrating the outperformance of the greedy algorithm compared to k-means++ for a natural class of well-separated instances with exponentially decaying distributions, such as Gaussian, specifically when ℓ = lnk +Θ(1), a common parameter setting in practical applications.

The Unaligned Multi-view Clustering (UMC) aims to learn a discriminative cluster structure from unaligned multi-view data, where the features of samples are not completely aligned across multiple views. Most existing methods usually prioritize employing various alignment strategies to align sample representations across views and then conduct cross-view fusion on aligned representations for subsequent clustering. However, due to the heterogeneity of representations across different views, these alignment strategies often fail to achieve ideal view-alignment results, inevitably leading to unreliable alignment-based fusion. To address this issue, we propose an alignment-free consistency fusion framework named AF-UMC, which bypasses the traditional view-alignment operation and directly extracts consistent representations from each view to perform global cross-view consistency fusion. Specifically, we first construct a cross-view consistent basis space by a cross-view reconstruction loss and a designed Structural Clarity Regularization (SCR), where autoencoders extract consistent representations from each view through projecting view-specific data to the constructed basis space. Afterwards, these extracted representations are globally pulled together for further cross-view fusion according to a designed Instance Global Contrastive Fusion (IGCF). Compared with previous methods, AF-UMC directly extracts consistent representations from each view for global fusion instead of alignment for fusion, which significantly mitigates the degraded fusion performance caused by undesired view-alignment results while greatly reducing algorithm complexity and enhancing its efficiency. Extensive experiments on various datasets demonstrate that our AF-UMC exhibits superior performance against other state-of-the-art methods.

Brain atlases are essential for reducing the dimensionality of neuroimaging data and enabling interpretable analysis. However, most existing atlases are predefined, group-level templates with limited flexibility and resolution.