This paper relaxes the restrictive symmetry conditions adopted in [4], [5] and extends their universal feature selection framework to accommodate noisy observations as well as attribute structures that may exhibit directional preferences. We introduce the notion of weak spherical symmetry, quantified by second-moment distances, which allows controlled deviations from rotational invariance. Under this relaxed condition, we develop a universal feature selection framework based on the singular value decomposition of the canonical dependence matrix computed from noisy data. Our main result shows that the selected features achieve asymptotically optimal error exponents up to a residual term that depends on the symmetry deviation $δ$ and the noise levels $η_1, η_2$. When $δ, η_1, η_2$ are relatively small, our result recovers that of [5], thereby demonstrating that exact spherical symmetry is unnecessary. Overall, our findings highlight the robustness of the selection framework against second-moment deviations and observation noise, thereby broadening its applicability across diverse inference tasks and providing a theoretically grounded tool for universal feature selection in practical scenarios.

Solving partial differential equations (PDEs) can be prohibitively expensive using traditional numerical methods. Deep learning-based surrogate models typically specialize in a single PDE with fixed parameters. We present a framework for equation-aware emulation that generalizes to unseen PDEs, conditioning a neural model on a vector encoding representing the terms in a PDE and their coefficients. We present a baseline of four distinct modeling technqiues, trained on a family of 1D PDEs from the APEBench suite. Our approach achieves strong performance on parameter sets held out from the training distribution, with strong stability for rollout beyond the training window, and generalization to an entirely unseen PDE. This work was developed as part of a broader effort exploring AI systems that automate the creation of expert-level empirical software for scorable scientific tasks. The data and codebase are available at https://github.com/google-research/generalized-pde-emulator.

Fitness functions map large combinatorial spaces of biological sequences to properties of interest. Inferring these multimodal functions from experimental data is a central task in modern protein engineering. Global epistasis models are an effective and physically-grounded class of models for estimating fitness functions from observed data. These models assume that a sparse latent function is transformed by a monotonic nonlinearity to emit measurable fitness. Here we demonstrate that minimizing supervised contrastive loss functions, such as the Bradley-Terry loss, is a simple and flexible technique for extracting the sparse latent function implied by global epistasis.

The whiskers extend to 4x the IQR ( Supplementary Figure 1), which is a conservative threshold that ensures only the most extreme variations in PL are classified as outliers (denoted by diamond symbols). Outliers in PL property distributions may indicate experimental errors, sample inconsistencies, or data proces sing anomalies, thus, they are removed from the ML analysis. Data Visualization: PCA orthogonally transforms the original variables into a new set of linearly uncorrelated variables termed principal components (PCs). The first PC captures the maximum variance present in the data, and each subsequent component has the highest variance p ossible under the constraint of being orthogonal to the preceding ones. The methodology involves standardizing the dataset, calculating the covariance matrix, and then extracting the eigenvalues and eigenvectors of this matrix, which, in tur n, dictate the magnitude and direction of the new space, respectively. By projecting the original data along these new axes, PCA provides a means to reduce the dimensionality of the dataset. Supplementary Figure 1A illustrates the distribution of the samples in the space defined by the PCs, with each point representing a single sample's location within this novel coordinate system. Here, the colors indicate the value of each PL property, offering a visual insight into how these factors correlate with the PCs.

Radio-based localization in dynamic environments, such as urban and vehicular settings, requires systems that can efficiently adapt to varying signal conditions and environmental changes. Factors such as multipath interference and obstructions introduce different levels of complexity that affect the accuracy of the localization. Although generalized models offer broad applicability, they often struggle to capture the nuances of specific environments, leading to suboptimal performance in real-world deployments. In contrast, specialized models can be tailored to particular conditions, enabling more precise localization by effectively handling domain-specific variations and noise patterns. However, deploying multiple specialized models requires an efficient mechanism to select the most appropriate one for a given scenario. In this work, we develop an adaptive localization framework that combines shallow attention-based models with a router/switching mechanism based on a single-layer perceptron (SLP). This enables seamless transitions between specialized localization models optimized for different conditions, balancing accuracy, computational efficiency, and robustness to environmental variations. We design three low-complex localization models tailored for distinct scenarios, optimized for reduced computational complexity, test time, and model size. The router dynamically selects the most suitable model based on real-time input characteristics. The proposed framework is validated using real-world vehicle localization data collected from a massive MIMO base station (BS), demonstrating its ability to seamlessly adapt to diverse deployment conditions while maintaining high localization accuracy.

Abstract--Motion prediction is critical for autonomous vehicles to effectively navigate complex environments and accurately anticipate the behaviors of other traffic participants. As autonomous driving continues to evolve, the need to assimilate new and varied driving scenarios necessitates frequent model updates through retraining. To address these demands, we introduce DECODE, a novel continual learning framework that begins with a pretrained generalized model and incrementally develops specialized models for distinct domains. Unlike existing continual learning approaches that attempt to develop a unified model capable of generalizing across diverse scenarios, DECODE uniquely balances specialization with generalization, dynamically adjusting to real-time demands. The proposed framework leverages a hypernetwork to generate model parameters, significantly reducing storage requirements, and incorporates a normalizing flow mechanism for real-time model selection based on likelihood estimation. This integration ensures optimal performance in familiar conditions while maintaining robustness in unfamiliar scenarios. Extensive evaluations confirm the effectiveness of the framework, achieving a notably low forgetting rate of 0.044 and an average minADE of 0.584 m, significantly surpassing traditional learning strategies and demonstrating adaptability across a wide range of driving OTION prediction has attracted significant attention in recent years, finding applications across a wide array of fields. It plays a critical role in the development of autonomous vehicles, enabling them to understand complex scenarios and data [10]-[15], yielding successful performances on several anticipate the future behaviors of other traffic participants [1]- prominent open datasets [16]-[18].

Effective management and early detection of BPSD are crucial to reduce the stress and burden on caregivers and healthcare systems. Despite the advancements in machine learning for dementia prediction, there is a considerable gap in utilizing these methods for BPSD prediction. This study aims to fill this gap by presenting a novel personalized framework for BPSD prediction, utilizing physiological signals from smart wearable devices. Our personalized fine-grained BPSD prediction method accurately predicts BPSD occurrences by extracting individual behavioral patterns, while the generalized models identify diverse patterns and differentiate between various BPSD symptoms. Detailed comparisons between the proposed personalized method and conventional generalized methods reveals substantial improvements across all performance metrics, including a 16.0% increase in AUC. These results demonstrate the potential of our proposed method in advancing dementia care by enabling proactive interventions and improving patient outcomes in real-world scenarios. To the best of our knowledge, this is the first study that leverages physiological signals from smart wearable devices to predict BPSD, marking a significant stride in dementia care research.

Recent research has indicated a substantial rise in interest in understanding Nesterov's accelerated gradient methods via their continuous-time models. However, most existing studies focus on specific classes of Nesterov's methods, which hinders the attainment of an in-depth understanding and a unified perspective. To address this deficit, we present generalized continuous-time models that cover a broad range of Nesterov's methods, including those previously studied under existing continuous-time frameworks. Our key contributions are as follows. First, we identify the convergence rates of the generalized models, eliminating the need to determine the convergence rate for any specific continuous-time model derived from them. Second, we show that six existing continuous-time models are special cases of our generalized models, thereby positioning our framework as a unifying tool for analyzing and understanding these models. Third, we design a restart scheme for Nesterov's methods based on our generalized models and show that it ensures a monotonic decrease in objective function values. Owing to the broad applicability of our models, this scheme can be used to a broader class of Nesterov's methods compared to the original restart scheme. Fourth, we uncover a connection between our generalized models and gradient flow in continuous time, showing that the accelerated convergence rates of our generalized models can be attributed to a time reparametrization in gradient flow. Numerical experiment results are provided to support our theoretical analyses and results.

Improper pain management can lead to severe physical or mental consequences, including suffering, and an increased risk of opioid dependency. Assessing the presence and severity of pain is imperative to prevent such outcomes and determine the appropriate intervention. However, the evaluation of pain intensity is challenging because different individuals experience pain differently. To overcome this, researchers have employed machine learning models to evaluate pain intensity objectively. However, these efforts have primarily focused on point estimation of pain, disregarding the inherent uncertainty and variability present in the data and model. Consequently, the point estimates provide only partial information for clinical decision-making. This study presents a neural network-based method for objective pain interval estimation, incorporating uncertainty quantification. This work explores three algorithms: the bootstrap method, lower and upper bound estimation (LossL) optimized by genetic algorithm, and modified lower and upper bound estimation (LossS) optimized by gradient descent algorithm. Our empirical results reveal that LossS outperforms the other two by providing a narrower prediction interval. As LossS outperforms, we assessed its performance in three different scenarios for pain assessment: (1) a generalized approach (single model for the entire population), (2) a personalized approach (separate model for each individual), and (3) a hybrid approach (separate model for each cluster of individuals). Our findings demonstrate the hybrid approach's superior performance, with notable practicality in clinical contexts. It has the potential to be a valuable tool for clinicians, enabling objective pain intensity assessment while taking uncertainty into account. This capability is crucial in facilitating effective pain management and reducing the risks associated with improper treatment.