We study best-of-$N$ for large language models (LLMs) where the selection is based on majority voting. In particular, we analyze the limit $N \to \infty$, which we denote as Best-of-$\infty$. While this approach achieves impressive performance in the limit, it requires an infinite test-time budget. To address this, we propose an adaptive generation scheme that selects $N$ based on answer agreement, thereby efficiently allocating inference-time computation. Beyond adaptivity, we extend the framework to weighted ensembles of multiple LLMs, showing that such mixtures can outperform any individual model. The optimal ensemble weighting is formulated and efficiently computed as a mixed-integer linear program. Extensive experiments demonstrate the effectiveness of our approach.

Biopharmaceutical manufacturing is vital to public health but lacks the agility for rapid, on-demand production of biotherapeutics due to the complexity and variability of bioprocesses. T o overcome this, we introduce RApid PosT eriOR GENerator (RAPTOR-GEN), a mechanism-informed Bayesian learning framework designed to accelerate intelligent digital twin development from sparse and heterogeneous experimental data. This framework is built on a multi-scale probabilistic knowledge graph (pKG), formulated as a stochastic differential equation (SDE)-based foundational model that captures the nonlinear dynamics of bioprocesses. RAPTOR-GEN consists of two ingredients: (i) an interpretable metamodel integrating linear noise approximation (LNA) that exploits the structural information of bioprocessing mechanisms and a sequential learning strategy to fuse heterogeneous and sparse data, enabling inference of latent state variables and explicit approximation of the intractable likelihood function; and (ii) an efficient Bayesian posterior sampling method that utilizes Langevin diffusion (LD) to accelerate posterior exploration by exploiting the gradients of the derived likelihood. It generalizes the LNA approach to circumvent the challenge of step size selection, facilitating robust learning of mechanistic parameters with provable finite-sample performance guarantees. We develop a fast and robust RAPTOR-GEN algorithm with controllable error. Numerical experiments demonstrate its effectiveness in uncovering the underlying regulatory mechanisms of biomanufacturing processes. Funding: This research was supported by National Science Foundation Grant CAREER CMMI-2442970 and National Institute of Standards and T echnology Grant 70NANB21H086.

The analysis of spatial data from biological imaging technology, such as imaging mass spectrometry (IMS) or imaging mass cytometry (IMC), is challenging because of a competitive sampling process which convolves signals from molecules in a single pixel. To address this, we develop a scalable Bayesian framework that leverages natural sparsity in spatial signal patterns to recover relative rates for each molecule across the entire image. Our method relies on the use of a heavy-tailed variant of the graphical lasso prior and a novel hierarchical variational family, enabling efficient inference via automatic differentiation variational inference. Simulation results show that our approach outperforms state-of-the-practice point estimate methodologies in IMS, and has superior posterior coverage than mean-field variational inference techniques. Results on real IMS data demonstrate that our approach better recovers the true anatomical structure of known tissue, removes artifacts, and detects active regions missed by the standard analysis approach.

In scientific applications, predictive modeling is often of limited use without accurate uncertainty quantification (UQ) to indicate when a model may be extrapolating or when more data needs to be collected. Bayesian Neural Networks (BNNs) produce predictive uncertainty by propagating uncertainty in neural network (NN) weights and offer the promise of obtaining not only an accurate predictive model but also accurate UQ. However, in practice, obtaining accurate UQ with BNNs is difficult due in part to the approximations used for practical model training and in part to the need to choose a suitable set of hyperparameters; these hyperparameters outnumber those needed for traditional NNs and often have opaque effects on the results. We aim to shed light on the effects of hyperparameter choices for BNNs by performing a global sensitivity analysis of BNN performance under varying hyperparameter settings. Our results indicate that many of the hyperparameters interact with each other to affect both predictive accuracy and UQ. For improved usage of BNNs in real-world applications, we suggest that global sensitivity analysis, or related methods such as Bayesian optimization, should be used to aid in dimensionality reduction and selection of hyperparameters to ensure accurate UQ in BNNs.

Background/Purpose: Diabetes affects over 537 million people worldwide and is projected to reach 783 million by 2045. Early risk stratification can benefit from machine learning. We compare two hybrid classifiers and assess their generalizability on an external cohort. Methods: Two hybrids were built: (i) XGBoost + Random Forest (XGB-RF) and (ii) Support Vector Machine + Logistic Regression (SVM-LR). A leakage-safe, standardized pipeline (encoding, imputation, min-max scaling; SMOTE on training folds only; probability calibration for SVM) was fit on the primary dataset and frozen. Evaluation prioritized threshold-independent discrimination (AUROC/AUPRC) and calibration (Brier, slope/intercept). External validation used the PIMA cohort (N=768) with the frozen pipeline; any thresholded metrics on PIMA were computed at the default rule tau = 0.5. Results: On the primary dataset (PR baseline = 0.50), XGB-RF achieved AUROC ~0.995 and AUPRC ~0.998, outperforming SVM-LR (AUROC ~0.978; AUPRC ~0.947). On PIMA (PR baseline ~0.349), XGB-RF retained strong performance (AUROC ~0.990; AUPRC ~0.959); SVM-LR was lower (AUROC ~0.963; AUPRC ~0.875). Thresholded metrics on PIMA at tau = 0.5 were XGB-RF (Accuracy 0.960; Precision 0.941; Recall 0.944; F1 0.942) and SVM-LR (Accuracy 0.900; Precision 0.855; Recall 0.858; F1 0.857). Conclusions: Across internal and external cohorts, XGB-RF consistently dominated SVM-LR and exhibited smaller external attenuation on ROC/PR with acceptable calibration. These results support gradient-boosting-based hybridization as a robust, transferable approach for diabetes risk stratification and motivate prospective, multi-site validation with deployment-time threshold selection based on clinical trade-offs.

Graph Contrastive Learning (GCL) is a powerful self-supervised learning framework that performs data augmentation through graph perturbations, with growing applications in the analysis of biological networks such as Gene Regulatory Networks (GRNs). The artificial perturbations commonly used in GCL, such as node dropping, induce structural changes that can diverge from biological reality. This concern has contributed to a broader trend in graph representation learning toward augmentation-free methods, which view such structural changes as problematic and to be avoided. However, this trend overlooks the fundamental insight that structural changes from biologically meaningful perturbations are not a problem to be avoided but a rich source of information, thereby ignoring the valuable opportunity to leverage data from real biological experiments. Motivated by this insight, we propose SupGCL (Supervised Graph Contrastive Learning), a new GCL method for GRNs that directly incorporates biological perturbations from gene knockdown experiments as supervision. SupGCL is a probabilistic formulation that continuously generalizes conventional GCL, linking artificial augmentations with real perturbations measured in knockdown experiments and using the latter as explicit supervisory signals. To assess effectiveness, we train GRN representations with SupGCL and evaluate their performance on downstream tasks. The evaluation includes both node-level tasks, such as gene function classification, and graph-level tasks on patient-specific GRNs, such as patient survival hazard prediction. Across 13 tasks built from GRN datasets derived from patients with three cancer types, SupGCL consistently outperforms state-of-the-art baselines. Graph representation learning has recently attracted attention in various fields to learn a meaningful latent space to represent the connectivity and attributes in given graphs (Ju et al., 2024). The application of graph representation learning to Gene Regulatory Networks (GRNs), which contain information about intracellular functions and processes, is particularly important in the fields of biology and drug discovery. It is expected to contribute to the identification of therapeutic targets and the elucidation of disease mechanisms. Representation learning for GRNs has been applied to tasks such as transcription factor inference (Y u et al., 2025) and predicting drug responses in cancer cell lines (Liu et al., 2022). Advances in gene expression measurement and analysis technologies have enabled the construction of patient-specific GRNs, highlighting gene regulation patterns that differ from the population as a whole (Nakazawa et al., 2021). Hereafter, this paper will refer to such individualized networks simply as GRNs.

--Inherent in virtually every iterative machine learning algorithm is the problem of hyper-parameter tuning which includes three major design parameters: (a) the complexity of the model, e.g., the number of neurons in a neural network, (b) the initial conditions, which heavily affect the behavior of the algorithm, and (c) the dissimilarity measure used to quantify its performance. We introduce an online prototype-based learning algorithm that can be viewed as a progressively growing competitive-learning neural network architecture for classification and clustering. The learning rule of the proposed approach is formulated as an online gradient-free stochastic approximation algorithm that solves a sequence of appropriately defined optimization problems, simulating an annealing process. The annealing nature of the algorithm contributes to avoiding poor local minima, offers robustness with respect to the initial conditions, and provides a means to progressively increase the complexity of the learning model, through an intuitive bifurcation phenomenon. The proposed approach is interpretable, requires minimal hyper-parameter tuning, and allows online control over the performance-complexity trade-off. Finally, we show that Bregman divergences appear naturally as a family of dissimilarity measures that play a central role in both the performance and the computational complexity of the learning algorithm. EARNING from data samples has become an important component of artificial intelligence. While virtually all learning problems can be formulated as constrained stochastic optimization problems, the optimization methods can be intractable, typically dealing with mixed constraints and very large, or even infinite-dimensional spaces [1]. For this reason, feature extraction, model selection and design, and analysis of optimization methods, have been the cornerstone of machine learning algorithms from their genesis until today. Deep learning methods, currently dominating the field of machine learning due to their performance in multiple applications, attempt to learn feature representations from data, using biologically-inspired models in artificial neural networks [2], [3]. Manuscript published in the IEEE Transactions on Neural Networks and Learning Systems (TNNLS).

A deep dive into the open literature shows that there are t hree fundamental limitations to current ML approaches, namely blackbox brittleness (which renders models uninterpretable and unreliable under distribution shift [2]), causal blindness (which conflates correlation with causation [3]), and alignment failures (which produce systems optimizing objectives misaligned with human values [4]) . These deficiencies stem from a profound philosophical poverty in how ML conceptualizes knowledge, reasoning, and values. The first fundamental limitation, b lackbox brittleness, manifests when trained models fail on seemingly trivial variations of their training distribution. For example, a vision model that accurately identifies stop signs under normal conditions might misclassify them entirely when small adversarial perturbations are applied [5] . Not surprisingly, t h e same brittleness extends beyond adversarial examples to everyday distribution shifts (e.g., natural language processing models exhibit performance degradation when processing text from different cultural contexts, etc.) [6] .