Graph Neural Networks learn on graph-structured data by iteratively aggregating local neighborhood information. While this local message passing paradigm imparts a powerful inductive bias and exploits graph sparsity, it also yields three key challenges: (i) oversquashing of long-range information, (ii) oversmoothing of node representations, and (iii) limited expressive power. In this work we inject randomized global embeddings of node features, which we term \textit{Sketched Random Features}, into standard GNNs, enabling them to efficiently capture long-range dependencies. The embeddings are unique, distance-sensitive, and topology-agnostic -- properties which we analytically and empirically show alleviate the aforementioned limitations when injected into GNNs. Experimental results on real-world graph learning tasks confirm that this strategy consistently improves performance over baseline GNNs, offering both a standalone solution and a complementary enhancement to existing techniques such as graph positional encodings. Our source code is available at \href{https://github.com/ryienh/sketched-random-features}{https://github.com/ryienh/sketched-random-features}.

Ensuring the privacy of sensitive training data is crucial in privacy-preserving machine learning. However, in practical scenarios, privacy protection may be required for only a subset of features. For instance, in ICU data, demographic attributes like age and gender pose higher privacy risks due to their re-identification potential, whereas raw lab results are generally less sensitive. Traditional DP-SGD enforces privacy protection on all features in one sample, leading to excessive noise injection and significant utility degradation. We propose FusionDP, a two-step framework that enhances model utility under feature-level differential privacy. First, FusionDP leverages large foundation models to impute sensitive features given non-sensitive features, treating them as external priors that provide high-quality estimates of sensitive attributes without accessing the true values during model training. Second, we introduce a modified DP-SGD algorithm that trains models on both original and imputed features while formally preserving the privacy of the original sensitive features. We evaluate FusionDP on two modalities: a sepsis prediction task on tabular data from PhysioNet and a clinical note classification task from MIMIC-III. By comparing against privacy-preserving baselines, our results show that FusionDP significantly improves model performance while maintaining rigorous feature-level privacy, demonstrating the potential of foundation model-driven imputation to enhance the privacy-utility trade-off for various modalities.

Recently, the concept of ``compression as intelligence'' has provided a novel informatics metric perspective for language models (LMs), emphasizing that highly structured representations signify the intelligence level of LMs. However, from a geometric standpoint, the word representation space of highly compressed LMs tends to degenerate into a highly anisotropic state, which hinders the LM's ability to comprehend instructions and directly impacts its performance. We found this compression-anisotropy synchronicity is essentially the ``Compression Hacking'' in LM representations, where noise-dominated directions tend to create the illusion of high compression rates by sacrificing spatial uniformity. Based on this, we propose three refined compression metrics by incorporating geometric distortion analysis and integrate them into a self-evaluation pipeline. The refined metrics exhibit strong alignment with the LM's comprehensive capabilities, achieving Spearman correlation coefficients above 0.9, significantly outperforming both the original compression and other internal structure-based metrics. This confirms that compression hacking substantially enhances the informatics interpretation of LMs by incorporating geometric distortion of representations.

This study evaluates a 40-item mathematics placement examination administered to 198 students using a multi-method framework combining Classical Test Theory, machine learning, and unsupervised clustering. Classical Test Theory analysis reveals that 55\% of items achieve excellent discrimination ($D \geq 0.40$) while 30\% demonstrate poor discrimination ($D < 0.20$) requiring replacement. Question 6 (Graph Interpretation) emerges as the examination's most powerful discriminator, achieving perfect discrimination ($D = 1.000$), highest ANOVA F-statistic ($F = 4609.1$), and maximum Random Forest feature importance (0.206), accounting for 20.6\% of predictive power. Machine learning algorithms demonstrate exceptional performance, with Random Forest and Gradient Boosting achieving 97.5\% and 96.0\% cross-validation accuracy. K-means clustering identifies a natural binary competency structure with a boundary at 42.5\%, diverging from the institutional threshold of 55\% and suggesting potential overclassification into remedial categories. The two-cluster solution exhibits exceptional stability (bootstrap ARI = 0.855) with perfect lower-cluster purity. Convergent evidence across methods supports specific refinements: replace poorly discriminating items, implement a two-stage assessment, and integrate Random Forest predictions with transparency mechanisms. These findings demonstrate that multi-method integration provides a robust empirical foundation for evidence-based mathematics placement optimization.

This paper presents evomap, a Python package for dynamic mapping. Mapping methods are widely used across disciplines to visualize relationships among objects as spatial representations, or maps. However, most existing statistical software supports only static mapping, which captures objects' relationships at a single point in time and lacks tools to analyze how these relationships evolve. evomap fills this gap by implementing the dynamic mapping framework EvoMap, originally proposed by Matthe, Ringel, and Skiera (2023), which adapts traditional static mapping methods for dynamic analyses. The package supports multiple mapping techniques, including variants of Multidimensional Scaling (MDS), Sammon Mapping, and t-distributed Stochastic Neighbor Embedding (t-SNE). It also includes utilities for data preprocessing, exploration, and result evaluation, offering a comprehensive toolkit for dynamic mapping applications. This paper outlines the foundations of static and dynamic mapping, describes the architecture and functionality of evomap, and illustrates its application through an extensive usage example.

Physics-informed machine learning (PIML) integrates partial differential equations (PDEs) into machine learning models to solve inverse problems, such as estimating coefficient functions (e.g., the Hamiltonian function) that characterize physical systems. This framework enables data-driven understanding and prediction of complex physical phenomena. While coefficient functions in PIML are typically estimated on the basis of predictive performance, physics as a discipline does not rely solely on prediction accuracy to evaluate models. For example, Kepler's heliocentric model was favored owing to small discrepancies in planetary motion, despite its similar predictive accuracy to the geocentric model. This highlights the inherent uncertainties in data-driven model inference and the scientific importance of selecting physically meaningful solutions. In this paper, we propose a framework to quantify and analyze such uncertainties in the estimation of coefficient functions in PIML. We apply our framework to reduced model of magnetohydrodynamics and our framework shows that there are uncertainties, and unique identification is possible with geometric constraints. Finally, we confirm that we can estimate the reduced model uniquely by incorporating these constraints.

--The phenomenon of linear mode connectivity (LMC) links several aspects of deep learning, including training stability under noisy stochastic gradients, the smoothness and generalization of local minima (basins), the similarity and functional diversity of sampled models, and architectural effects on data processing. In this work, we experimentally study LMC under data shifts and identify conditions that mitigate their impact. We interpret data shifts as an additional source of stochastic gradient noise, which can be reduced through small learning rates and large batch sizes. These parameters influence whether models converge to the same local minimum or to regions of the loss landscape with varying smoothness and generalization. Although models sampled via LMC tend to make similar errors more frequently than those converging to different basins, the benefit of LMC lies in balancing training efficiency against the gains achieved from larger, more diverse ensembles. Code and supplementary materials will be made publicly available at https://github.com/DLR-KI/LMC in due course. ODE connectivity refers to a phenomenon, when stochastic gradient descent (SGD) solutions or modes are connected via a path of low loss in neural networks parameter space [1], [2]. So every solution along such path exhibits similar performance and generalization as those solutions, between which the path is constructed. Moreover, such paths were shown to be embedded in a multi-dimensional manifold of low loss [3]. When a connecting path is linear the phenomenon is referred to as linear mode connectivity (LMC) [4]. LMC was investigated under different perspectives: (1) conditions affecting LMC [4], [5], (2) connectivity of layers, features or different types of solutions [6], [7], [8] and (3) so-called "re-basin" approaches, that "transport" a solution from one local minimum From a practical view point, LMC is expected to improve ensemble methods, in particular in federated learning setting, robustness of fine-tuned models, distributed optimization and model pruning [13], [9]. This work focuses on LMC from the perspective of data shifts [14], which are ever-present in real world applications. In particular, when training is performed on multiple training datasets separately and ensembles of models are employed.

A formal link between regression and classification has been tenuous. Even though the margin maximization term $\|w\|$ is used in support vector regression, it has at best been justified as a regularizer. We show that a regression problem with $M$ samples lying on a hyperplane has a one-to-one equivalence with a linearly separable classification task with $2M$ samples. We show that margin maximization on the equivalent classification task leads to a different regression formulation than traditionally used. Using the equivalence, we demonstrate a ``regressability'' measure, that can be used to estimate the difficulty of regressing a dataset, without needing to first learn a model for it. We use the equivalence to train neural networks to learn a linearizing map, that transforms input variables into a space where a linear regressor is adequate.

Deep learning models achieve strong performance across various domains but often rely on spurious correlations, making them vulnerable to distribution shifts. This issue is particularly severe in subpopulation shift scenarios, where models struggle in underrepresented groups. While existing methods have made progress in mitigating this issue, their performance gains are still constrained. They lack a rigorous theoretical framework connecting the embedding space representations with worst-group error. To address this limitation, we propose Spurious Correlation-Aware Embedding Regularization for Worst-Group Robustness (SCER), a novel approach that directly regularizes feature representations to suppress spurious cues. We show theoretically that worst-group error is influenced by how strongly the classifier relies on spurious versus core directions, identified from differences in group-wise mean embeddings across domains and classes. By imposing theoretical constraints at the embedding level, SCER encourages models to focus on core features while reducing sensitivity to spurious patterns. Through systematic evaluation on multiple vision and language, we show that SCER outperforms prior state-of-the-art studies in worst-group accuracy. Our code is available at \href{https://github.com/MLAI-Yonsei/SCER}{https://github.com/MLAI-Yonsei/SCER}.

Differentially private in-context learning (DP-ICL) has recently become an active research topic due to the inherent privacy risks of in-context learning. However, existing approaches overlook a critical component of modern large language model (LLM) pipelines: the similarity search used to retrieve relevant context data. In this work, we introduce a DP framework for in-context learning that integrates nearest neighbor search of relevant examples in a privacy-aware manner. Our method outperforms existing baselines by a substantial margin across all evaluated benchmarks, achieving more favorable privacy-utility trade-offs. To achieve this, we employ nearest neighbor retrieval from a database of context data, combined with a privacy filter that tracks the cumulative privacy cost of selected samples to ensure adherence to a central differential privacy budget. Experimental results on text classification and document question answering show a clear advantage of the proposed method over existing baselines.