Point signatures based on the Laplacian operators on graphs, point clouds, and manifolds have become popular tools in machine learning for graphs, clustering, and shape analysis. In this work, we propose a novel point signature, the power spectrum signature, a measure on $\mathbb{R}$ defined as the squared graph Fourier transform of a graph signal. Unlike eigenvectors of the Laplacian from which it is derived, the power spectrum signature is invariant under graph automorphisms. We show that the power spectrum signature is stable under perturbations of the input graph with respect to the Wasserstein metric. We focus on the signature applied to classes of indicator functions, and its applications to generating descriptive features for vertices of graphs. To demonstrate the practical value of our signature, we showcase several applications in characterizing geometry and symmetries in point cloud data, and graph regression problems.

Test-time training (TTT) methods explicitly update the weights of a model to adapt to the specific test instance, and they have found success in a variety of settings, including most recently language modeling and reasoning. To demystify this success, we investigate a gradient-based TTT algorithm for in-context learning, where we train a transformer model on the in-context demonstrations provided in the test prompt. Specifically, we provide a comprehensive theoretical characterization of linear transformers when the update rule is a single gradient step. Our theory (i) delineates the role of alignment between pretraining distribution and target task, (ii) demystifies how TTT can alleviate distribution shift, and (iii) quantifies the sample complexity of TTT including how it can significantly reduce the eventual sample size required for in-context learning. As our empirical contribution, we study the benefits of TTT for TabPFN, a tabular foundation model. In line with our theory, we demonstrate that TTT significantly reduces the required sample size for tabular classification (3 to 5 times fewer) unlocking substantial inference efficiency with a negligible training cost.

Active learning (AL), which iteratively queries the most informative examples from a large pool of unlabeled candidates for model training, faces significant challenges in the presence of open-set classes. Existing methods either prioritize query examples likely to belong to known classes, indicating low epistemic uncertainty (EU), or focus on querying those with highly uncertain predictions, reflecting high aleatoric uncertainty (AU). However, they both yield suboptimal performance, as low EU corresponds to limited useful information, and closed-set AU metrics for unknown class examples are less meaningful. In this paper, we propose an Energy-based Active Open-set Annotation (EAOA) framework, which effectively integrates EU and AU to achieve superior performance. EAOA features a $(C+1)$-class detector and a target classifier, incorporating an energy-based EU measure and a margin-based energy loss designed for the detector, alongside an energy-based AU measure for the target classifier. Another crucial component is the target-driven adaptive sampling strategy. It first forms a smaller candidate set with low EU scores to ensure closed-set properties, making AU metrics meaningful. Subsequently, examples with high AU scores are queried to form the final query set, with the candidate set size adjusted adaptively. Extensive experiments show that EAOA achieves state-of-the-art performance while maintaining high query precision and low training overhead. The code is available at https://github.com/chenchenzong/EAOA.

The multivariate generalized Pareto distribution (mGPD) is a common method for modeling extreme threshold exceedance probabilities in environmental and financial risk management. Despite its broad applicability, mGPD faces challenges due to the infinite possible parametrizations of its dependence function, with only a few parametric models available in practice. To address this limitation, we introduce GPDFlow, an innovative mGPD model that leverages normalizing flows to flexibly represent the dependence structure. Unlike traditional parametric mGPD approaches, GPDFlow does not impose explicit parametric assumptions on dependence, resulting in greater flexibility and enhanced performance. Additionally, GPDFlow allows direct inference of marginal parameters, providing insights into marginal tail behavior. We derive tail dependence coefficients for GPDFlow, including a bivariate formulation, a $d$-dimensional extension, and an alternative measure for partial exceedance dependence. A general relationship between the bivariate tail dependence coefficient and the generative samples from normalizing flows is discussed. Through simulations and a practical application analyzing the risk among five major US banks, we demonstrate that GPDFlow significantly improves modeling accuracy and flexibility compared to traditional parametric methods.

How can we rely on an end-to-end autonomous vehicle's complex decision-making system during deployment? One common solution is to have a ``fallback layer'' that checks the planned trajectory for rule violations and replaces it with a pre-defined safe action if necessary. Another approach involves adjusting the planner's decisions to minimize a pre-defined ``cost function'' using additional system predictions such as road layouts and detected obstacles. However, these pre-programmed rules or cost functions cannot learn and improve with new training data, often resulting in overly conservative behaviors. In this work, we propose Centaur (Cluster Entropy for Test-time trAining using Uncertainty) which updates a planner's behavior via test-time training, without relying on hand-engineered rules or cost functions. Instead, we measure and minimize the uncertainty in the planner's decisions. For this, we develop a novel uncertainty measure, called Cluster Entropy, which is simple, interpretable, and compatible with state-of-the-art planning algorithms. Using data collected at prior test-time time-steps, we perform an update to the model's parameters using a gradient that minimizes the Cluster Entropy. With only this sole gradient update prior to inference, Centaur exhibits significant improvements, ranking first on the navtest leaderboard with notable gains in safety-critical metrics such as time to collision. To provide detailed insights on a per-scenario basis, we also introduce navsafe, a challenging new benchmark, which highlights previously undiscovered failure modes of driving models.

In the current work, we connect token-level uncertainty in causal language modeling to two types of training objectives: 1) masked maximum likelihood (MLE), 2) self-distillation. We show that masked MLE is effective in reducing epistemic uncertainty, and serve as an effective token-level automatic curriculum learning technique. However, masked MLE is prone to overfitting and requires self-distillation regularization to improve or maintain performance on out-of-distribution tasks. We demonstrate significant performance gain via the proposed training objective - combined masked MLE and self-distillation - across multiple architectures (Gemma, LLaMA, Phi) and datasets (Alpaca, ShareGPT, GSM8K), mitigating overfitting while maintaining adaptability during post-training. Our findings suggest that uncertainty-aware training provides an effective mechanism for enhancing language model training.

Coronary artery disease remains one of the leading causes of mortality globally. Despite advances in revascularization treatments like PCI and CABG, postoperative stroke is inevitable. This study aims to develop and evaluate a sophisticated machine learning prediction model to assess postoperative stroke risk in coronary revascularization patients.This research employed data from the MIMIC-IV database, consisting of a cohort of 7023 individuals. Study data included clinical, laboratory, and comorbidity variables. To reduce multicollinearity, variables with over 30% missing values and features with a correlation coefficient larger than 0.9 were deleted. The dataset has 70% training and 30% test. The Random Forest technique interpolated residual dataset missing values. Numerical values were normalized, whereas categorical variables were one-hot encoded. LASSO regularization selected features, and grid search found model hyperparameters. Finally, Logistic Regression, XGBoost, SVM, and CatBoost were employed for predictive modeling, and SHAP analysis assessed stroke risk for each variable. AUC of 0.855 (0.829-0.878) showed that SVM model outperformed logistic regression and CatBoost models in prior research. SHAP research showed that the Charlson Comorbidity Index (CCI), diabetes, chronic kidney disease, and heart failure are significant prognostic factors for postoperative stroke. This study shows that improved machine learning reduces overfitting and improves model predictive accuracy. Models using the CCI alone cannot predict postoperative stroke risk as accurately as those using independent comorbidity variables. The suggested technique provides a more thorough and individualized risk assessment by encompassing a wider range of clinically relevant characteristics, making it a better reference for preoperative risk assessments and targeted intervention.

This evolution indicates an expansion from industrial uses into diverse fields, including healthcare [61], [59]. The core functionalities of digital twins include an accurate mirroring of their physical counterparts, capturing all associated processes in a data-driven manner, maintaining a continuous connection that synchronizes with the real-time state of their physical twins, and simulating physical behavior for predictive analysis [85]. In the context of healthcare, a novel extension of this technology manifests in the form of Human Digital Twins (HDTs), designed to provide a comprehensive digital mirror of individual patients. HDTs not only represent physical attributes but also integrate dynamic changes across molecular, physiological, and behavioral dimensions. This advancement is aligned with a shift toward personalized healthcare (PH) paradigms, enabling tailored treatment strategies based on a patient's unique health profile, thereby enhancing preventive, diagnostic, and therapeutic processes in clinical settings [44], [50]. The personalization aspect of HDTs underscores their potential to revolutionize healthcare by facilitating precise and individualized treatment plans that optimize patient outcomes [72]. Although the potential of digital twins in healthcare has garnered much attention, practical applications remain newly developing, with critical literature highlighting that many implementations are still in exploratory stages [59]. Notably, institutions like the IEEE Computer Society and Gartner recognize this technology as a pivotal component in the ongoing evolution of healthcare systems that emphasize both precision and personalization [31], [89].

We revisit the problem of secure aggregation of high-dimensional vectors in a two-server system such as Prio. These systems are typically used to aggregate vectors such as gradients in private federated learning, where the aggregate itself is protected via noise addition to ensure differential privacy. Existing approaches require communication scaling with the dimensionality, and thus limit the dimensionality of vectors one can efficiently process in this setup. We propose PREAMBLE: Private Efficient Aggregation Mechanism for BLock-sparse Euclidean Vectors. PREAMBLE is a novel extension of distributed point functions that enables communication- and computation-efficient aggregation of block-sparse vectors, which are sparse vectors where the non-zero entries occur in a small number of clusters of consecutive coordinates. We then show that PREAMBLE can be combined with random sampling and privacy amplification by sampling results, to allow asymptotically optimal privacy-utility trade-offs for vector aggregation, at a fraction of the communication cost. When coupled with recent advances in numerical privacy accounting, our approach incurs a negligible overhead in noise variance, compared to the Gaussian mechanism used with Prio.

We prove a convergence theorem for stochastic gradient descents on manifolds with adaptive learning rate and apply it to the weighted low-rank approximation problem.