Stochastic Neighbor Embedding (SNE) algorithms like UMAP and tSNE often produce visualizations that do not preserve the geometry of noisy and high dimensional data. In particular, they can spuriously separate connected components of the underlying data submanifold and can fail to find clusters in well-clusterable data. To address these limitations, we propose EmbedOR, a SNE algorithm that incorporates discrete graph curvature. Our algorithm stochastically embeds the data using a curvature-enhanced distance metric that emphasizes underlying cluster structure. Critically, we prove that the EmbedOR distance metric extends consistency results for tSNE to a much broader class of datasets. We also describe extensive experiments on synthetic and real data that demonstrate the visualization and geometry-preservation capabilities of EmbedOR. We find that, unlike other SNE algorithms and UMAP, EmbedOR is much less likely to fragment continuous, high-density regions of the data. Finally, we demonstrate that the EmbedOR distance metric can be used as a tool to annotate existing visualizations to identify fragmentation and provide deeper insight into the underlying geometry of the data.

--Federated learning (FL) effectively promotes collaborative training among distributed clients with privacy considerations in the Internet of Things (IoT) scenarios. Despite of data heterogeneity, FL clients may also be constrained by limited energy and availability budgets. Therefore, effective selection of clients participating in training is of vital importance for the convergence of the global model and the balance of client contributions. In this paper, we discuss the performance impact of client availability with time-series data on federated learning. We set up three different scenarios that affect the availability of time-series data and propose FedDeCAB, a novel, semi-decentralized client selection method applying probabilistic rankings of available clients. When a client is disconnected from the server, FedDeCAB allows obtaining partial model parameters from the nearest neighbor clients for joint optimization, improving the performance of offline models and reducing communication overhead. Experiments based on real-world large-scale taxi and vessel trajectory datasets show that FedDeCAB is effective under highly heterogeneous data distribution, limited communication budget, and dynamic client offline or rejoining. Traditional machine learning (ML) requires the central server to gather data from various node devices for model training. However, the access to personal data from edge devices is usually subject to privacy restrictions and the large scale of local data in common edge computing environments or scenarios with a large number of Internet of Things (IoT) devices.

Large Language Models (LLMs) are prone to critical failure modes, including \textit{intrinsic faithfulness hallucinations} (also known as confabulations), where a response deviates semantically from the provided context. Frameworks designed to detect this, such as Semantic Divergence Metrics (SDM), rely on identifying latent topics shared between prompts and responses, typically by applying geometric clustering to their sentence embeddings. This creates a disconnect, as the topics are optimized for spatial proximity, not for the downstream information-theoretic analysis. In this paper, we bridge this gap by developing a principled topic identification method grounded in the Deterministic Information Bottleneck (DIB) for geometric clustering. Our key contribution is to transform the DIB method into a practical algorithm for high-dimensional data by substituting its intractable KL divergence term with a computationally efficient upper bound. The resulting method, which we dub UDIB, can be interpreted as an entropy-regularized and robustified version of K-means that inherently favors a parsimonious number of informative clusters. By applying UDIB to the joint clustering of LLM prompt and response embeddings, we generate a shared topic representation that is not merely spatially coherent but is fundamentally structured to be maximally informative about the prompt-response relationship. This provides a superior foundation for the SDM framework and offers a novel, more sensitive tool for detecting confabulations.

Context: Utilization of operating theaters is a major cost driver in hospitals. Optimizing this variable through optimized surgery schedules may significantly lower cost and simultaneously improve medical outcomes. Previous studies proposed various complex models to predict the duration of procedures, the key ingredient to optimal schedules. They did so perusing large amounts of data. Goals: We aspire to create an effective and efficient model to predict operation durations based on only a small amount of data. Ideally, our model is also simpler in structure, and thus easier to use. Methods: We immerse ourselves in the application domain to leverage practitioners expertise. This way, we make the best use of our limited supply of clinical data, and may conduct our data analysis in a theory-guided way. We do a combined factor analysis and develop regression models to predict the duration of the perioperative process. Findings: We found simple methods of central tendency to perform on a par with much more complex methods proposed in the literature. In fact, they sometimes outperform them. We conclude that combining expert knowledge with data analysis may improve both data quality and model performance, allowing for more accurate forecasts. Conclusion: We yield better results than previous researchers by integrating conventional data science methods with qualitative studies of clinical settings and process structure. Thus, we are able to leverage even small datasets.

We extend the ReLU Transition Graph (RTG) framework into a comprehensive graph-theoretic model for understanding deep ReLU networks. In this model, each node represents a linear activation region, and edges connect regions that differ by a single ReLU activation flip, forming a discrete geometric structure over the network's functional behavior. We prove that RTGs at random initialization exhibit strong expansion, binomial degree distributions, and spectral properties that tightly govern generalization. These structural insights enable new bounds on capacity via region entropy and on generalization via spectral gap and edge-wise KL divergence. Empirically, we construct RTGs for small networks, measure their smoothness and connectivity properties, and validate theoretical predictions. Our results show that region entropy saturates under overparameterization, spectral gap correlates with generalization, and KL divergence across adjacent regions reflects functional smoothness. This work provides a unified framework for analyzing ReLU networks through the lens of discrete functional geometry, offering new tools to understand, diagnose, and improve generalization.

Inverse problems (IPs) involve reconstructing signals from noisy observations. Recently, diffusion models (DMs) have emerged as a powerful framework for solving IPs, achieving remarkable reconstruction performance. However, existing DM-based methods frequently encounter issues such as heavy computational demands and suboptimal convergence. In this work, building upon the idea of the recent work DMPlug, we propose two novel methods, DMILO and DMILO-PGD, to address these challenges. Our first method, DMILO, employs intermediate layer optimization (ILO) to alleviate the memory burden inherent in DMPlug. Additionally, by introducing sparse deviations, we expand the range of DMs, enabling the exploration of underlying signals that may lie outside the range of the diffusion model. We further propose DMILO-PGD, which integrates ILO with projected gradient descent (PGD), thereby reducing the risk of suboptimal convergence. We provide an intuitive theoretical analysis of our approaches under appropriate conditions and validate their superiority through extensive experiments on diverse image datasets, encompassing both linear and nonlinear IPs. Our results demonstrate significant performance gains over state-of-the-art methods, highlighting the effectiveness of DMILO and DMILO-PGD in addressing common challenges in DM-based IP solvers.

The flexibility of a power generation unit determines how quickly and often it can ramp up or down. In energy models, it depends on assumptions on the technical characteristics of the unit, such as its installed capacity or turbine technology. In this paper, we learn the empirical flexibility of gas units from their electricity generation, revealing how real-world limitations can lead to substantial differences between units with similar technical characteristics. Using a novel deep clustering approach, we transform 5 years (2019-2023) of unit-level hourly generation data for 49 German units from 100 MWp of installed capacity into low-dimensional embeddings. Our unsupervised approach identifies two clusters of peaker units (high flexibility) and two clusters of non-peaker units (low flexibility). The estimated ramp rates of non-peakers, which constitute half of the sample, display a low empirical flexibility, comparable to coal units. Non-peakers, predominantly owned by industry and municipal utilities, show limited response to low residual load and negative prices, generating on average 1.3 GWh during those hours. As the transition to renewables increases market variability, regulatory changes will be needed to unlock this flexibility potential.

Despite the tremendous success of graph-based learning systems in handling structural data, it has been widely investigated that they are fragile to adversarial attacks on homophilic graph data, where adversaries maliciously modify the semantic and topology information of the raw graph data to degrade the predictive performances. Motivated by this, a series of robust models are crafted to enhance the adversarial robustness of graph-based learning systems on homophilic graphs. However, the security of graph-based learning systems on heterophilic graphs remains a mystery to us. To bridge this gap, in this paper, we start to explore the vulnerability of graph-based learning systems regardless of the homophily degree, and theoretically prove that the update of the negative classification loss is negatively correlated with the pairwise similarities based on the powered aggregated neighbor features. The theoretical finding inspires us to craft a novel robust graph structural learning strategy that serves as a useful graph mining module in a robust model that incorporates a dual-kNN graph constructions pipeline to supervise the neighbor-similarity-preserved propagation, where the graph convolutional layer adaptively smooths or discriminates the features of node pairs according to their affluent local structures. In this way, the proposed methods can mine the ``better" topology of the raw graph data under diverse graph homophily and achieve more reliable data management on homophilic and heterophilic graphs.

Using standard preference elicitation methods, researchers and practitioners build models of human decisions and judgments, which are then used to align AI behavior with that of humans. However, models commonly used in such elicitation processes often do not capture the true cognitive processes of human decision making, such as when people use heuristics to simplify information associated with a decision problem. As a result, models learned from people's decisions often do not align with their cognitive processes, and can not be used to validate the learning framework for generalization to other decision-making tasks. To address this limitation, we take an axiomatic approach to learning cognitively faithful decision processes from pairwise comparisons. Building on the vast literature characterizing the cognitive processes that contribute to human decision-making, and recent work characterizing such processes in pairwise comparison tasks, we define a class of models in which individual features are first processed and compared across alternatives, and then the processed features are then aggregated via a fixed rule, such as the Bradley-Terry rule. This structured processing of information ensures such models are realistic and feasible candidates to represent underlying human decision-making processes. We demonstrate the efficacy of this modeling approach in learning interpretable models of human decision making in a kidney allocation task, and show that our proposed models match or surpass the accuracy of prior models of human pairwise decision-making.

Comparison of fine-tuning models with reinforcement learning (RL) and supervised fine-tuning (SFT) reveals that, despite similar performance at a new task, RL preserves prior knowledge and capabilities significantly better. We find that the degree of forgetting is determined by the distributional shift, measured as the KL-divergence between the fine-tuned and base policy evaluated on the new task. Our analysis reveals that on-policy RL is implicitly biased towards KL-minimal solutions among the many that solve the new task, whereas SFT can converge to distributions arbitrarily far from the base model. We validate these findings through experiments with large language models and robotic foundation models and further provide theoretical justification for why on-policy RL updates lead to a smaller KL change. We term this principle $\textit{RL's Razor}$: among all ways to solve a new task, RL prefers those closest in KL to the original model.