Studying how embeddings are organized in space not only enhances model interpretability but also uncovers factors that drive downstream task performance. In this paper, we present a comprehensive analysis of topological and geometric measures across a wide set of text embedding models and datasets. We find a high degree of redundancy among these measures and observe that individual metrics often fail to sufficiently differentiate embedding spaces. Building on these insights, we introduce Unified Topological Signatures (UTS), a holistic framework for characterizing embedding spaces. We show that UTS can predict model-specific properties and reveal similarities driven by model architecture. Further, we demonstrate the utility of our method by linking topological structure to ranking effectiveness and accurately predicting document retrievability. We find that a holistic, multi-attribute perspective is essential to understanding and leveraging the geometry of text embeddings.

Graph Neural Networks (GNNs) address two key challenges in applying deep learning to graph-structured data: they handle varying size input graphs and ensure invariance under graph isomorphism. While GNNs have demonstrated broad applicability, understanding their expressive power remains an important question. In this paper, we propose GNN architectures that correspond precisely to prominent fragments of first-order logic (FO), including various modal logics as well as more expressive two-variable fragments. To establish these results, we apply methods from finite model theory of first-order and modal logics to the domain of graph representation learning. Our results provide a unifying framework for understanding the logical expressiveness of GNNs within FO.

As Artificial Intelligence (AI) is increasingly promoted and used in qualitative research, it also raises profound methodological issues. This position paper critically interrogates the role of generative AI (genAI) in the context of qualitative coding methodologies. Despite widespread hype and claims of efficiency, we propose that genAI is not methodologically valid within qualitative inquiries, and its use risks undermining the robustness and trustworthiness of qualitative research. The lack of meaningful documentation, commercial opacity, and the inherent tendencies of genAI systems to produce incorrect outputs all contribute to weakening methodological rigor. Overall, the balance between risk and benefits does not support the use of genAI in qualitative research, and our position paper cautions researchers to put sound methodology before technological novelty.

The expressive power of graph neural networks (GNNs) is typically understood through their correspondence with graph isomorphism tests such as the Weisfeiler-Leman (WL) hierarchy. While more expressive GNNs can distinguish a richer set of graphs, they are also observed to suffer from higher generalization error. This work provides a theoretical explanation for this trade-off by linking expressivity and generalization through the lens of coloring algorithms. Specifically, we show that the number of equivalence classes induced by WL colorings directly bounds the GNNs Rademacher complexity -- a key data-dependent measure of generalization. Our analysis reveals that greater expressivity leads to higher complexity and thus weaker generalization guarantees. Furthermore, we prove that the Rademacher complexity is stable under perturbations in the color counts across different samples, ensuring robustness to sampling variability across datasets. Importantly, our framework is not restricted to message-passing GNNs or 1-WL, but extends to arbitrary GNN architectures and expressivity measures that partition graphs into equivalence classes. These results unify the study of expressivity and generalization in GNNs, providing a principled understanding of why increasing expressive power often comes at the cost of generalization.

While Graph Neural Networks (GNNs) have proven highly effective at modeling relational data, pairwise connections cannot fully capture multi-way relationships naturally present in complex real-world systems. In response to this, Topological Deep Learning (TDL) leverages more general combinatorial representations -- such as simplicial or cellular complexes -- to accommodate higher-order interactions. Existing TDL methods often extend GNNs through Higher-Order Message Passing (HOMP), but face critical \emph{scalability challenges} due to \textit{(i)} a combinatorial explosion of message-passing routes, and \textit{(ii)} significant complexity overhead from the propagation mechanism. This work presents HOPSE (Higher-Order Positional and Structural Encoder), an alternative method to solve tasks involving higher-order interactions \emph{without message passing}. Instead, HOPSE breaks \emph{arbitrary higher-order domains} into their neighborhood relationships using a Hasse graph decomposition. This method shows that decoupling the representation learning of neighborhood topology from that of attributes results in lower computational complexity, casting doubt on the need for HOMP. The experiments on molecular graph tasks and topological benchmarks show that HOPSE matches performance on traditional TDL datasets and outperforms HOMP methods on topological tasks, achieving up to $7\times$ speedups over HOMP-based models, opening a new path for scalable TDL.

Buildings account for a significant share of global energy consumption and emissions, making it critical to operate them efficiently. As electricity grids become more volatile with renewable penetration, buildings must provide flexibility to support grid stability. Building automation plays a key role in enhancing efficiency and flexibility via centralized operations, but it must prioritize occupant-centric strategies to balance energy and comfort targets. However, incorporating occupant information into large-scale, centralized building operations remains challenging due to data limitations. We investigate the potential of using whole-building smart meter data to infer both occupancy and system operations. Integrating these insights into data-driven building energy analysis allows more occupant-centric energy-saving and flexibility at scale. Specifically, we propose OccuEMBED, a unified framework for occupancy inference and system-level load analysis. It combines two key components: a probabilistic occupancy profile generator, and a controllable and interpretable load disaggregator supported by Kolmogorov-Arnold Networks (KAN). This design embeds knowledge of occupancy patterns and load-occupancy-weather relationships into deep learning models. We conducted comprehensive evaluations to demonstrate its effectiveness across synthetic and real-world datasets compared to various occupancy inference baselines. OccuEMBED always achieved average F1 scores above 0.8 in discrete occupancy inference and RMSE within 0.1-0.2 for continuous occupancy ratios. We further demonstrate how OccuEMBED integrates with building load monitoring platforms to display occupancy profiles, analyze system-level operations, and inform occupant-responsive strategies. Our model lays a robust foundation in scaling occupant-centric building management systems to meet the challenges of an evolving energy system.

Understanding the internal mechanisms of large language models (LLMs) remains a challenging and complex endeavor. Even fundamental questions, such as how fine-tuning affects model behavior, often require extensive empirical evaluation. In this paper, we introduce a novel perspective based on the geometric properties of contextual latent embeddings to study the effects of training and fine-tuning. To that end, we measure the local dimensions of a contextual language model's latent space and analyze their shifts during training and fine-tuning. We show that the local dimensions provide insights into the model's training dynamics and generalization ability. Specifically, the mean of the local dimensions predicts when the model's training capabilities are exhausted, as exemplified in a dialogue state tracking task, overfitting, as demonstrated in an emotion recognition task, and grokking, as illustrated with an arithmetic task. Furthermore, our experiments suggest a practical heuristic: reductions in the mean local dimension tend to accompany and predict subsequent performance gains. Through this exploration, we aim to provide practitioners with a deeper understanding of the implications of fine-tuning on embedding spaces, facilitating informed decisions when configuring models for specific applications. The results of this work contribute to the ongoing discourse on the interpretability, adaptability, and generalizability of LLMs by bridging the gap between intrinsic model mechanisms and geometric properties in the respective embeddings.

We propose multi-agent reinforcement learning as a new method for modeling fake news in social networks. This method allows us to model human behavior in social networks both in unaccustomed populations and in populations that have adapted to the presence of fake news. In particular the latter is challenging for existing methods. We find that a fake-news attack is more effective if it targets highly connected people and people with weaker private information. Attacks are more effective when the disinformation is spread across several agents than when the disinformation is concentrated with more intensity on fewer agents. Furthermore, fake news spread less well in balanced networks than in clustered networks. We test a part of our findings in a human-subject experiment. The experimental evidence provides support for the predictions from the model, suggesting that the model is suitable to analyze the spread of fake news in social networks.