Abstract
Foundational models are trained on extensive datasets to capture the general trends of a domain. However, in medical imaging, the scarcity of data makes pre-training for every domain, modality, or task challenging. Continual learning offers a solution by fine-tuning a model sequentially on different domains or tasks, enabling it to integrate new knowledge without requiring large datasets for each training phase. In this paper, we propose UNIfied CONtinual Learning for Medical Foundational Models (UNICON), a framework that enables the seamless adaptation of foundation models to diverse domains, tasks, and modalities. Unlike conventional adaptation methods that treat these changes in isolation, UNICON provides a unified, perpetually expandable framework. Through careful integration, we show that foundation models can dynamically expand across imaging modalities, anatomical regions, and clinical objectives without catastrophic forgetting or task interference. Empirically, we validate our approach by adapting a chest CT foundation model initially trained for classification to a prognosis and segmentation task. Our results show improved performance across both additional tasks. Furthermore, we continually incorporated PET scans and achieved a 5\% improvement in Dice score compared to respective baselines. These findings establish that foundation models are not inherently constrained to their initial training scope but can evolve, paving the way toward generalist AI models for medical imaging.

Abstract
Continual learning (CL) is crucial for the adaptation of neural network models to new environments. Although outperforming weight-space regularisation approaches, the functional regularisation-based CL methods suffer from high computational costs and large linear approximation errors. In this work, we present a new functional regularisation CL framework, called MCFRCL, which approximates model prediction distributions by Monte Carlo (MC) sampling. Moreover, three continuous distributions are leveraged to capture the statistical characteristics of the MC samples via moment-based methods. Additionally, both the Wasserstein distance and the Kullback-Leibler (KL) distance are employed to construct the regularisation function. The proposed MCFRCL is evaluated against multiple benchmark methods on the MNIST and CIFAR datasets, with simulation results highlighting its effectiveness in both prediction accuracy and training efficiency.

Abstract
Information Ecosystem Reengineering (IER) -- the technological reconditioning of information sources, services, and systems within a complex information ecosystem -- is a foundational challenge in the digital transformation of public sector services and smart governance platforms. From a semantic knowledge management perspective, IER becomes especially entangled due to the potentially infinite number of possibilities in its conceptualization, namely, as a result of manifoldness in the multi-level mix of perception, language and conceptual interlinkage implicit in all agents involved in such an effort. This paper proposes a novel approach -- Representation Disentanglement -- to disentangle these multiple layers of knowledge representation complexity hindering effective reengineering decision making. The approach is based on the theoretically grounded and implementationally robust ontology-driven conceptual modeling paradigm which has been widely adopted in systems analysis and (re)engineering. We argue that such a framework is essential to achieve explainability, traceability and semantic transparency in public sector knowledge representation and to support auditable decision workflows in governance ecosystems increasingly driven by Artificial Intelligence (AI) and data-centric architectures.

Abstract
Table understanding is key to addressing challenging downstream tasks such as table-based question answering and fact verification. Recent works have focused on leveraging Chain-of-Thought and question decomposition to solve complex questions requiring multiple operations on tables. However, these methods often suffer from a lack of explicit long-term planning and weak inter-step connections, leading to miss constraints within questions. In this paper, we propose leveraging the long-term planning capabilities of large language models (LLMs) to enhance table understanding. Our approach enables the execution of a long-term plan, where the steps are tightly interconnected and serve the ultimate goal, an aspect that methods based on Chain-of-Thought and question decomposition lack. In addition, our method effectively minimizes the inclusion of unnecessary details in the process of solving the next short-term goals, a limitation of methods based on Chain-of-Thought. Extensive experiments demonstrate that our method outperforms strong baselines and achieves state-of-the-art performance on WikiTableQuestions and TabFact datasets.

Abstract
One of the essential issues in decision problems and preference modeling is the number of comparisons and their pattern to ask from the decision maker. We focus on the optimal patterns of pairwise comparisons and the sequence including the most (close to) optimal cases based on the results of a color selection experiment. In the test, six colors (red, green, blue, magenta, turquoise, yellow) were evaluated with pairwise comparisons as well as in a direct manner, on color-calibrated tablets in ISO standardized sensory test booths of a sensory laboratory. All the possible patterns of comparisons resulting in a connected representing graph were evaluated against the complete data based on 301 individual's pairwise comparison matrices (PCMs) using the logarithmic least squares weight calculation technique. It is shown that the empirical results, i.e., the empirical distributions of the elements of PCMs, are quite similar to the former simulated outcomes from the literature. The obtained empirically optimal patterns of comparisons were the best or the second best in the former simulations as well, while the sequence of comparisons that contains the most (close to) optimal patterns is exactly the same. In order to enhance the applicability of the results, besides the presentation of graph of graphs, and the representing graphs of the patterns that describe the proposed sequence of comparisons themselves, the recommendations are also detailed in a table format as well as in a Java application.

Abstract
Word-representable graphs are a class of graphs that can be represented by words, where edges and non-edges are determined by the alternation of letters in those words. Several papers in the literature have explored the word-representability of split graphs, in which the vertices can be partitioned into a clique and an independent set. In this paper, we initiate the study of the word-representability of graphs in which the vertices can be partitioned into two cliques. We provide a complete characterization of such word-representable graphs in terms of forbidden subgraphs when one of the cliques has a size of at most four. In particular, if one of the cliques is of size four, we prove that there are seven minimal non-word-representable graphs.

Abstract
Due to regulations like the Right to be Forgotten, there is growing demand for removing training data and its influence from models. Since full retraining is costly, various machine unlearning methods have been proposed. In this paper, we firstly present an efficient knowledge graph (KG) unlearning algorithm. We remark that KG unlearning is nontrivial due to the distinctive structure of KG and the semantic relations between entities. Also, unlearning by estimating the influence of removed components incurs significant computational overhead when applied to large-scale knowledge graphs. To this end, we define an influence function for KG unlearning and propose to approximate the model's sensitivity without expensive computation of first-order and second-order derivatives for parameter updates. Specifically, we use Taylor expansion to estimate the parameter changes caused by data removal. Given that the first-order gradients and second-order derivatives dominate the computational load, we use the Fisher matrices and zeroth-order optimization to approximate the inverse-Hessian vector product without constructing the computational graphs. Our experimental results demonstrate that the proposed method outperforms other state-of-the-art graph unlearning baselines significantly in terms of unlearning efficiency and unlearning quality. Our code is released at https://github.com/NKUShaw/ZOWFKGIF.

Abstract
Understanding dataset complexity is fundamental to evaluating and comparing link prediction models on knowledge graphs (KGs). While the Cumulative Spectral Gradient (CSG) metric, derived from probabilistic divergence between classes within a spectral clustering framework, has been proposed as a classifier agnostic complexity metric purportedly scaling with class cardinality and correlating with downstream performance, it has not been evaluated in KG settings so far. In this work, we critically examine CSG in the context of multi relational link prediction, incorporating semantic representations via transformer derived embeddings. Contrary to prior claims, we find that CSG is highly sensitive to parametrisation and does not robustly scale with the number of classes. Moreover, it exhibits weak or inconsistent correlation with standard performance metrics such as Mean Reciprocal Rank (MRR) and Hit@1. To deepen the analysis, we introduce and benchmark a set of structural and semantic KG complexity metrics. Our findings reveal that global and local relational ambiguity captured via Relation Entropy, node level Maximum Relation Diversity, and Relation Type Cardinality exhibit strong inverse correlations with MRR and Hit@1, suggesting these as more faithful indicators of task difficulty. Conversely, graph connectivity measures such as Average Degree, Degree Entropy, PageRank, and Eigenvector Centrality correlate positively with Hit@10. Our results demonstrate that CSGs purported stability and generalization predictive power fail to hold in link prediction settings and underscore the need for more stable, interpretable, and task-aligned measures of dataset complexity in knowledge driven learning.