Abstract-- In previous work, we introduced a 2D localization algorithm called CLAP, Clustering to Localize Across n Possibilities, which was used during our championship win in RoboCup 2024, an international autonomous humanoid soccer competition. CLAP is particularly recognized for its robustness against outliers, where clustering is employed to suppress noise and mitigate against erroneous feature matches. This clustering-based strategy provides an alternative to traditional outlier rejection schemes such as RANSAC, in which candidates are validated by reprojection error across all data points. In this paper, CLAP is extended to a more general framework beyond 2D localization, specifically to 3D localization and image stitching. We also show how CLAP, RANSAC, and Hough transforms are related. The generalization of CLAP is widely applicable to many different fields and can be a useful tool to deal with noise and uncertainty.

We study the oracle complexity of finding $\varepsilon$-Pareto stationary points in smooth multiobjective optimization with $m$ objectives. The progress metric is the Pareto stationarity gap $\mathcal{G}(x)$ (the norm of an optimal convex combination of gradients). Our contributions are fourfold. (i) For strongly convex objectives, any span first-order method (iterates lie in the span of past gradients) exhibits linear convergence no faster than $\exp(-Θ(T/\sqrtκ))$ after $T$ oracle calls, where $κ$ is the condition number, implying $Θ(\sqrtκ\log(1/\varepsilon))$ iterations; this matches classical accelerated upper bounds. (ii) For convex problems and oblivious one-step methods (a fixed scalarization with pre-scheduled step sizes), we prove a lower bound of order $1/T$ on the best gradient norm among the first $T$ iterates. (iii) Although accelerated gradient descent is outside this restricted class, it is an oblivious span method and attains the same $1/T$ upper rate on a fixed scalarization. (iv) For convex problems and general span methods with adaptive scalarizations, we establish a universal lower bound of order $1/T^{2}$ on the gradient norm of the final iterate after $T$ steps, highlighting a gap between known upper bounds and worst-case guarantees. All bounds hold on non-degenerate instances with distinct objectives and non-singleton Pareto fronts; rates are stated up to universal constants and natural problem scaling.

The U.S. Federal Open Market Committee (FOMC) regularly discusses and sets monetary policy, affecting the borrowing and spending decisions of millions of people. In this work, we release Op-Fed, a dataset of 1044 human-annotated sentences and their contexts from FOMC transcripts. We faced two major technical challenges in dataset creation: imbalanced classes -- we estimate fewer than 8% of sentences express a non-neutral stance towards monetary policy -- and inter-sentence dependence -- 65% of instances require context beyond the sentence-level. To address these challenges, we developed a five-stage hierarchical schema to isolate aspects of opinion, monetary policy, and stance towards monetary policy as well as the level of context needed. Second, we selected instances to annotate using active learning, roughly doubling the number of positive instances across all schema aspects. Using Op-Fed, we found a top-performing, closed-weight LLM achieves 0.80 zero-shot accuracy in opinion classification but only 0.61 zero-shot accuracy classifying stance towards monetary policy -- below our human baseline of 0.89. We expect Op-Fed to be useful for future model training, confidence calibration, and as a seed dataset for future annotation efforts.

Chemists in search of structure-property relationships face great challenges due to limited high quality, concordant datasets. Machine learning (ML) has significantly advanced predictive capabilities in chemical sciences, but these modern data-driven approaches have increased the demand for data. In response to the growing demand for explainable AI (XAI) and to bridge the gap between predictive accuracy and human comprehensibility, we introduce LAMeL - a Linear Algorithm for Meta-Learning that preserves interpretability while improving the prediction accuracy across multiple properties. While most approaches treat each chemical prediction task in isolation, LAMeL leverages a meta-learning framework to identify shared model parameters across related tasks, even if those tasks do not share data, allowing it to learn a common functional manifold that serves as a more informed starting point for new unseen tasks. Our method delivers performance improvements ranging from 1.1- to 25-fold over standard ridge regression, depending on the domain of the dataset. While the degree of performance enhancement varies across tasks, LAMeL consistently outperforms or matches traditional linear methods, making it a reliable tool for chemical property prediction where both accuracy and interpretability are critical.

Neural surrogates and operator networks for solving partial differential equation (PDE) problems have attracted significant research interest in recent years. However, most existing approaches are limited in their ability to generalize solutions across varying non-parametric geometric domains. In this work, we address this challenge in the context of Polyethylene Terephthalate (PET) bottle buckling analysis, a representative packaging design problem conventionally solved using computationally expensive finite element analysis (FEA). We introduce a hybrid DeepONet-Transolver framework that simultaneously predicts nodal displacement fields and the time evolution of reaction forces during top load compression. Our methodology is evaluated on two families of bottle geometries parameterized by two and four design variables. Training data is generated using nonlinear FEA simulations in Abaqus for 254 unique designs per family. The proposed framework achieves mean relative $L^{2}$ errors of 2.5-13% for displacement fields and approximately 2.4% for time-dependent reaction forces for the four-parameter bottle family. Point-wise error analyses further show absolute displacement errors on the order of $10^{-4}$-$10^{-3}$, with the largest discrepancies confined to localized geometric regions. Importantly, the model accurately captures key physical phenomena, such as buckling behavior, across diverse bottle geometries. These results highlight the potential of our framework as a scalable and computationally efficient surrogate, particularly for multi-task predictions in computational mechanics and applications requiring rapid design evaluation.

The detection of anomalies in automotive cabin sounds is critical for ensuring vehicle quality and maintaining passenger comfort. In many real-world settings, this task is more appropriately framed as an unsupervised learning problem rather than the supervised case due to the scarcity or complete absence of labeled faulty data. In such an unsupervised setting, the model is trained exclusively on healthy samples and detects anomalies as deviations from normal behavior. However, in the absence of labeled faulty samples for validation and the limited reliability of commonly used metrics, such as validation reconstruction error, effective model selection remains a significant challenge. To overcome these limitations, a domain-knowledge-informed approach for model selection is proposed, in which proxy-anomalies engineered through structured perturbations of healthy spectrograms are used in the validation set to support model selection. The proposed methodology is evaluated on a high-fidelity electric vehicle dataset comprising healthy and faulty cabin sounds across five representative fault types viz., Imbalance, Modulation, Whine, Wind, and Pulse Width Modulation. This dataset, generated using advanced sound synthesis techniques, and validated via expert jury assessments, has been made publicly available to facilitate further research. Experimental evaluations on the five fault cases demonstrate the selection of optimal models using proxy-anomalies, significantly outperform conventional model selection strategies.

Utilizing recently developed abstract notions of sectional curvature, we introduce a method for constructing a curvature-based geometric profile of discrete metric spaces. The curvature concept that we use here captures the metric relations between triples of points and other points. More significantly, based on this curvature profile, we introduce a quantitative measure to evaluate the effectiveness of data representations, such as those produced by dimensionality reduction techniques. Furthermore, Our experiments demonstrate that this curvature-based analysis can be employed to estimate the intrinsic dimensionality of datasets. We use this to explore the large-scale geometry of empirical networks and to evaluate the effectiveness of dimensionality reduction techniques.

Recent advances in spatial omics technologies have revolutionized our ability to study biological systems with unprecedented resolution. By preserving the spatial context of molecular measurements, these methods enable comprehensive mapping of cellular het erogeneity, tissue architecture, and dynamic biological processes in developmental biology, neuroscience, oncology, and evolutionary studies . This review highlights a systematic overview of the continuous advancements in both technology and computational a lgorithms that are paving the way for a deeper, more systematic comprehension of the structure and mechanisms of mammalian tissues and organs by using spatial multi - omics . Our viewpoint demonstrates how advanced machine learning algorithms and multi - omics integrative modeling can decode complex biological processes, including the spatial organization and topological relationships of cells during organ development, as well as key molecular signatures and regulatory networks underlying tumorigenesis and metas tasis . Finally, we outline future directions for technological innovation and modeling insights of spatial omics in precision medicine.

Thermal energy storage (TES) is an effective method for load shifting and demand response in buildings. Optimal TES control and management are essential to improve the performance of the cooling system. Most existing TES systems operate on a fixed schedule, which cannot take full advantage of its load shifting capability, and requires extensive investigation and optimization. This study proposed a novel integrated load prediction and optimized control approach for ice-based TES in commercial buildings. A cooling load prediction model was developed and a mid-day modification mechanism was introduced into the prediction model to improve the accuracy. Based on the predictions, a rule-based control strategy was proposed according to the time-of-use tariff; the mid-day control adjustment mechanism was introduced in accordance with the mid-day prediction modifications. The proposed approach was applied in the ice-based TES system of a commercial complex in Beijing, and achieved a mean absolute error (MAE) of 389 kW and coefficient of variance of MAE of 12.5 %. The integrated prediction-based control strategy achieved an energy cost saving rate of 9.9 %. The proposed model was deployed in the realistic building automation system of the case building and significantly improved the efficiency and automation of the cooling system.

We introduce a unified framework for evaluating dimensionality reduction techniques in spatial transcriptomics beyond standard PCA approaches. We benchmark six methods PCA, NMF, autoencoder, VAE, and two hybrid embeddings on a cholangiocarcinoma Xenium dataset, systematically varying latent dimensions ($k$=5-40) and clustering resolutions ($ρ$=0.1-1.2). Each configuration is evaluated using complementary metrics including reconstruction error, explained variance, cluster cohesion, and two novel biologically-motivated measures: Cluster Marker Coherence (CMC) and Marker Exclusion Rate (MER). Our results demonstrate distinct performance profiles: PCA provides a fast baseline, NMF maximizes marker enrichment, VAE balances reconstruction and interpretability, while autoencoders occupy a middle ground. We provide systematic hyperparameter selection using Pareto optimal analysis and demonstrate how MER-guided reassignment improves biological fidelity across all methods, with CMC scores improving by up to 12\% on average. This framework enables principled selection of dimensionality reduction methods tailored to specific spatial transcriptomics analyses.