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  • Gradient Descent Algorithm
  • Gradient Descent Algorithm
  • Stochastic Gradient
  • Stochastic Gradient

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  • New
  • Research Article
  • 10.1177/1540658x261429312
Indolizine Compound Selection for HPV Anticancer Active Prediction Using CNN Classifier with ADME Descriptors.
  • Jul 1, 2026
  • Assay and drug development technologies
  • Sangeeta Mahaur + 1 more

Despite the significant progress made in developing different in silico methodology for structure activity research over the past few decades. The ability to predict correlation structure activity (CSA) from absorption distribution metabolism excretion (ADME) descriptors to select indolizine compounds for human papilloma virus (HPV) anticancer activity continues to pose a challenge. This study employed five machine learning (ML) algorithms for classification, viz., stochastic gradient descent (SGD), random forest (RF), support vector machine (SVM), convolutional neural network (CNN), and logistic regression (LR), to perform the classification based on ADME-related physiochemical descriptors of 8,900 indolizine compounds to predict the CSA. The present study focuses on 26 well-known parameters to optimize the results, which are utilized for ML models SGD, RF, SVM, CNN, and LR for classification. The CNN achieved the best results with the highest overall accuracy and average loss values of 98.33% and 0.16, respectively. On the other hand, the SGD, RF, SVM, and LR recorded the accuracy values of 95.32%, 93.23%, 96.03%, 94.03%, and loss values of 0.046, 0.067, 0.039, and 0.059, respectively. It is stated that from the obtained results, the CNN is performing better compared to other methods. The cross-validation and results are done with the relationship of descriptors, viz., accuracy, correlation, distribution, area under the receiver operating characteristic, area under the precision recall curve, and bootstrap error analysis. This study demonstrated the utility of ML to facilitate early prediction of indolizine compounds for HPV anticancer activity in preclinical development.

  • New
  • Research Article
  • 10.1016/j.neunet.2026.108758
A hybrid adaptive preconditioned gradient method with momentum for deep learning.
  • Jul 1, 2026
  • Neural networks : the official journal of the International Neural Network Society
  • Zhiyang Zhou + 2 more

A hybrid adaptive preconditioned gradient method with momentum for deep learning.

  • New
  • Research Article
  • 10.1007/s11356-026-37943-1
Comparative evaluation of machine learning for prediction ofwater quality index in constructed wetlands.
  • Jun 24, 2026
  • Environmental science and pollution research international
  • Abdolsamad Davoodi + 2 more

Constructed wetlands play a crucial role in urban runoff treatment, enhancing water quality and maintaining ecosystem health, while the water quality index (WQI) serves as a key parameter for evaluating their performance. This study provides a comprehensive assessment of WQI prediction in a constructed wetland at Universiti Sains Malaysia, using 442 samples and 11 physicochemical parameters evaluated across six input scenarios. Feature selection was performed using Pearson correlation and feature-importance rankings from extreme gradient boosting (XGBoost) and categorical boosting (CatBoost) to create reduced-input combinations. SHapley Additive exPlanations (SHAP) analysis further indicated that WQI predictions were mainly driven by organic/solid load and nitrogen-related variables (e.g., chemical oxygen demand (COD), total suspended solids (TSS), and ammoniacal nitrogen (AN)). Fourteen ML models, including adaptive boosting (AdaBoost), adaptive neuro-fuzzy inference system, artificial neural network (ANN), CatBoost, extreme learning machine, gradient boosting regressor, histogram gradient boosting (HGB), Huber regressor, multiple linear regression, ridge regression, stochastic gradient descent regressor (SGD), support vector regression (SVR), XGBoost, and a hybrid Grey Wolf Optimizer-ANN, were developed and evaluated using four statistical metrics such as root mean square error (RMSE), coefficient of determination (R2), percent bias (PBIAS), and mean absolute relative error (MARE), complemented by LP-based multi-metric ranking. Across all scenarios (mean LP; lower is better), CatBoost (0.44) and HGB (0.46) achieved the best overall performance, while SGD (0.91) and SVR (0.75) ranked worst. Notably, several top-performing models maintained competitive performance under reduced inputs (e.g., CatBoost's LP value of 0.56 in the four-feature scenario), supporting practical WQI estimation when monitoring variables are limited or costly. These findings highlight the critical role of both input selection and model choice in developing robust, scalable frameworks for WQI prediction.

  • New
  • Research Article
  • 10.1016/j.tiv.2026.106273
Integration of label-free electrochemical sensing, differential privacy deep learning, and blockchain for secure cytotoxicity monitoring.
  • Jun 18, 2026
  • Toxicology in vitro : an international journal published in association with BIBRA
  • Hasret Turkmen + 2 more

Integration of label-free electrochemical sensing, differential privacy deep learning, and blockchain for secure cytotoxicity monitoring.

  • Research Article
  • 10.1080/00401706.2026.2689970
Generative multi-scale modeling via spatial autoregressive transport maps
  • Jun 15, 2026
  • Technometrics
  • Alejandro Calle-Saldarriaga + 2 more

Spatial fields in the Earth and environmental sciences are often available at multiple scales or resolutions. While coarse-scale data (e.g., from global circulation models) are often abundant, they lack the local detail provided by fine-scale data (e.g., from regional climate models), which are typically computationally expensive to generate. Statistical downscaling and multi-scale data fusion address this challenge by predicting high-resolution fields from low-resolution or related inputs. We propose a highly scalable Bayesian approach that can learn the joint non-Gaussian distribution and nonlinear dependence structure of nonstationary spatial fields across multiple scales from a small number of training samples. Our method employs scale-aware autoregressive Gaussian processes with suitably chosen regularization-inducing priors to model the conditional distribution of fine-scale fields given coarse-scale data. Exploiting conjugacy, the integrated likelihood is available in closed form, enabling efficient parameter optimization via stochastic gradient descent. Once trained, the method provides a closed-form characterization of the posterior distribution of fine-scale fields given coarse-scale inputs. In numerical comparisons, we demonstrate that our approach substantially outperforms existing methods and effectively characterizes and simulates fine-scale climate behavior based on output from coarse global circulation models.

  • Research Article
  • 10.1109/tpami.2026.3703395
Dataset Pruning: Reducing Training Data by Examining SGD-Influence.
  • Jun 15, 2026
  • IEEE transactions on pattern analysis and machine intelligence
  • Shuo Yang + 5 more

The great success of deep learning relies heavily on ever-increasing amounts of training data, which incurs enormous computational and infrastructural costs. This raises crucial questions: Does all training data contribute equally to a model's performance? How much does each individual training sample or sub-training set affect the model's generalization, and how can we construct the smallest proxy training set without significantly sacrificing performance? To address these questions, we propose dataset pruning, an optimization-based sample selection method that (1) examines the influence of removing particular training samples on the model's generalization ability with high computational efficiency and theoretical guarantees, and (2) constructs the smallest subset of training data that yields a strictly constrained generalization gap. The empirically observed generalization gap achieved by dataset pruning is largely consistent with our theoretical expectations. To estimate each sample's influence, we develop an SGD-Influence method that tracks parameter changes during stochastic gradient descent, effectively overcoming the convexity and optimality assumptions required by traditional influence function approaches. Complementing this, our distributed discrete optimization partitions the dataset into manageable buckets, allowing for efficient sample selection without sacrificing quality. Extensive experiments on three datasets of varying scale and complexity demonstrate that our approach not only aligns well with theoretical expectations but also outperforms state-of-the-art methods. Notably, compared to our previous work, the proposed method achieves a 61.26% reduction in computational cost while delivering higher accuracy.

  • Research Article
  • 10.1016/j.ultramic.2026.114404
Optically modulated free-electron computational ghost imaging for long-working-distance surface characterization.
  • Jun 6, 2026
  • Ultramicroscopy
  • Zhe Yu + 5 more

Optically modulated free-electron computational ghost imaging for long-working-distance surface characterization.

  • Research Article
  • 10.2196/78931
Advancing Gastrointestinal Cancer Risk Prediction With Patient-Centered Machine Learning: Machine Learning Modeling Study
  • Jun 4, 2026
  • JMIR Medical Informatics
  • Daina Baublyte + 3 more

BackgroundGastrointestinal (GI) cancers are a significant health concern in South Korea. Recently, machine learning (ML) models have emerged as powerful tools to support early screening efforts and identify people at risk before disease onset. However, the low incidence of GI malignancies in prospective cohorts leads to severe class imbalance, often causing ML models to favor the majority “healthy” class at the expense of clinical sensitivity.ObjectiveThis study aimed to evaluate class imbalance mitigation strategies and develop ML-based GI cancer risk prediction models using noninvasive and minimally invasive predictors linked to modifiable behavioral and metabolic risk factors.MethodsWe analyzed a prospective cohort (n=7652) with 156 incident GI cancer cases (2%) identified over a 14-year follow-up period. The data were randomly split into training (5356/7652, 70%) and testing (2296/7652, 30%) sets. To address class imbalance while preserving observed population structure, we developed a patient-centered undersampling technique (PCUSTe) based on the logic of frequency-matched case-control studies. PCUSTe was compared with commonly used resampling approaches, including synthetic minority oversampling (SMOTE), adaptive synthetic sampling (ADASYN), and SMOTE with edited nearest neighbors (ENN). Six classifiers were implemented, including both batch and incremental training variants. To account for the prior shift introduced by resampling, probability correction was applied. Model performance was evaluated on the independent test set using a classification threshold equal to the observed event proportion (cumulative incidence) in the training data and then across thresholds reflecting incidence values between 1% and 5%. Primary performance metrics included sensitivity, specificity, Matthews correlation coefficient, and area under the receiver operating characteristic curve (AUC).ResultsModels trained using PCUSTe demonstrated improved sensitivity compared with standard resampling techniques, particularly for more complex classifiers. The incrementally trained stochastic gradient descent model achieved the highest overall performance trained on PCUSTe data with a sensitivity of 0.77 (95% CI 0.64‐0.89), specificity of 0.65 (95% CI 0.63‐0.67), AUC of 0.77 (95% CI 0.70‐0.84), and Matthews correlation coefficient of 0.12 (95% CI 0.08‐0.16). In contrast, logistic regression achieved balanced performance without resampling (sensitivity 0.70, 95% CI 0.57‐0.83; specificity 0.71, 95% CI 0.69‐0.72; AUC 0.75, 95% CI 0.68‐0.82). Our results showed that PCUSTe primarily enhanced sensitivity in more complex models at the expense of specificity.ConclusionsIntegrating epidemiological principles, including covariate frequency matching and threshold selection based on the observed cumulative incidence in the training data, improved minority class detection in GI cancer risk prediction. However, model performance varied by algorithm, and in some cases, decision threshold adjustment alone achieved comparable or superior results to data resampling. These findings highlight the importance of carefully selecting imbalance mitigation strategies based on modeling objectives. The resulting models achieved sensitivity levels that may be suitable for early risk identification in cohort settings and could contribute to personalized risk stratification and targeted prevention or screening strategies.

  • Research Article
  • 10.1007/s00330-025-12315-4
Multimodal deep learning for laryngeal squamous cell carcinoma staging using CT and laryngoscopy.
  • Jun 1, 2026
  • European radiology
  • Rui Liu + 12 more

To develop and validate a multimodal deep learning model integrating clinical data, contrast-enhanced CT, and laryngoscopic images for differentiating early-stage (I-II) from advanced-stage (III-IV) laryngeal squamous cell carcinoma (LSCC). This retrospective multicenter study included 450 patients with pathologically confirmed LSCC from two Chinese medical centers. All patients had contrast-enhanced CT, white-light laryngoscopy, and clinical records. They were divided into training (n = 235), internal validation (n = 101), and external validation (n = 114) cohorts. Three single-modality models (CT-based deep learning [CT-DL], laryngoscopy-based multiple instance learning [L-MIL], and a clinical logistic regression model [CL]) and their combinations were compared. A feature-level fusion strategy was applied, and the final integrated multimodal model (CL + CT + L) was built using a stochastic gradient descent (SGD) classifier. Performance was evaluated by AUC, accuracy, sensitivity, specificity, calibration, and decision curve analysis (DCA), with prognostic value assessed by Kaplan-Meier and concordance index (C-index). A total of 450 patients were included (median age, 62 years [range, 31-88]; 365 men). The integrated multimodal model achieved AUCs of 0.902 (0.833-0.954) in the internal cohort and 0.888 (0.826-0.944) in the external cohort, outperforming all single- and dual-modality models (p < 0.05). Calibration and DCA confirmed strong consistency and clinical utility. The model categorized patients into distinct risk groups, which exhibited notable differences in progression-free survival (C-index = 0.584, p = 0.036). The integrated multimodal model showed high accuracy and generalizability for preoperative LSCC staging and may aid individualized treatment planning. Question Can a multimodal deep learning model combining clinical, CT, and laryngoscopic data improve preoperative staging accuracy of LSCC? Findings The integrated multimodal model achieved higher diagnostic accuracy and provided reliable prognostic stratification compared with conventional approaches. Clinical relevance This multimodal model offers a non-invasive, accurate, and generalizable tool for LSCC staging, supporting individualized treatment planning and enhancing patient management.

  • Research Article
  • 10.1364/oe.595931
Transceiver impairment mitigation for digital subcarrier multiplexing signals by adaptive multi-layer filters with symmetric pairs.
  • Jun 1, 2026
  • Optics express
  • Masaki Sato + 3 more

We propose an adaptive multi-layer (ML) filter architecture to compensate for linear impairments of digital subcarrier (DSC) multiplexing signals that occur in transmitter (Tx) and receiver (Rx) components. In this architecture, DC-symmetric SC pairs of a DSC signal are individually processed by adaptive ML filters that consist of strictly linear (SL) and widely linear (WL) filter layers, and the coefficients of the ML filters are adaptively controlled through gradient calculation using back propagation and stochastic gradient descent. Static chromatic dispersion compensation is performed on the received DSC signal and its complex conjugate before SC demultiplexing. After SC demultiplexing, each DC-symmetric SC pair is fed into the first 2 × 1 SL filter layer of the ML filters for compensation of in-phase (I) and quadrature (Q) impairments on the Rx side, taking into account the conjugate-image component. Then each SC is fed into the 2 × 2 SL filter for polarization demultiplexing with carrier phase recovery. Finally, the 2 × 1 WL filter is operated on each DC-symmetric SC pair to compensate for Tx-side I and Q impairments. We experimentally evaluated the proposed adaptive ML filter for an 8-DSC signal and compared it with a single-carrier signal in an 11-channel wavelength-division multiplexed transmission using 128-Gbaud polarization-multiplexed 16-quadrature amplitude modulation signals over a 1,200-km single-mode fiber (SMF). The proposed adaptive ML filter architecture for DSC-multiplexed signals effectively mitigates various IQ impairments and achieves performance that is nearly equivalent to the single-carrier case. For the 8-DSC signal, it also achieves performance comparable to that of a 16 × 4 WL filter with a 23% reduction in DSP complexity in terms of required complex-valued multiplications. It also remains effective with up to 5 ps IQ skew, an IQ gain imbalance ratio of 1.5, and a 10° IQ phase imbalance on the Tx and Rx sides. Moreover, robust performance was confirmed under simultaneous Tx and Rx IQ impairments, and stable adaptation was maintained even under polarization scrambling rates up to 10 krad/s.

  • Research Article
  • 10.11591/ijai.v15.i3.pp2811-2825
Performance comparison of deep learning models for concrete crack detection on mobile devices
  • Jun 1, 2026
  • IAES International Journal of Artificial Intelligence (IJ-AI)
  • Sarapee Chunkaew + 3 more

Concrete crack detection is essential for structural maintenance, yet traditional manual inspection methods are time-consuming and require specialized expertise. While deep learning offers promising solutions, existing models often demand high computational resources unsuitable for mobile deployment. This research evaluates three convolutional neural network (CNN) architectures, namely mobile network (MobileNet), visual geometry group-16 (VGG-16), and residual network-50 (ResNet-50), to identify an optimal model for practical mobile-based crack detection. A dataset of 1,634 images was collected from online databases and field documentation, categorized into 10 classes across three severity levels: i) severe cracks requiring urgent repair (30%); ii) cracks requiring monitoring (40%); and iii) minor cracks (30%). The models were trained using standardized parameters with 224×224-pixel RGB input, rectified linear unit (ReLU) activation, and softmax classification. Systematic parameter optimization was conducted across epochs, learning rate, dropout rate, and optimizer selection, with stochastic gradient descent (SGD) identified as the optimal optimizer. Experimental results demonstrate that MobileNet achieves the best performance with 80% accuracy and a compact model size of 13.1 megabytes. This study concludes that MobileNet provides an optimal balance between detection accuracy and computational efficiency, enabling practical field deployment for automated concrete crack detection, with expert verification recommended for critical structural assessments.

  • Research Article
  • 10.1016/j.rineng.2026.110214
Integration of CFD and machine learning for vehicle cabin thermal management using innovative materials
  • Jun 1, 2026
  • Results in Engineering
  • Hasnaa Oubnaki + 4 more

Integration of CFD and machine learning for vehicle cabin thermal management using innovative materials

  • Research Article
  • 10.7717/peerj.21188
Clinical study of 18F-FDG PET/CT radiomics in differentiating pulmonary solitary solid adenocarcinoma nodules and inflammatory nodules
  • Jun 1, 2026
  • PeerJ
  • Yi Fan Liao + 6 more

ObjectiveThis study aimed to assess the diagnostic value of 18F-FDG PET/CT radiomics in distinguishing adenocarcinoma from inflammatory lesions in pulmonary solitary solid nodules (solid pulmonary nodules).MethodsA total of 222 patients with Solid pulmonary nodules were retrospectively analyzed and randomly divided into two groups: a training set (n = 155) and a validation set (n = 67). Radiomic features were extracted from positron emission tomography/computed tomography (PET/CT) images, and optimal features were selected from the training set. Three model groups were created (CT, PET, and PET+CT) using six machine learning classifiers: Support Vector Machine (SVM), Random Forest (RF), Stochastic Gradient Descent (SGD), K-Nearest Neighbors (KNN), Extreme Gradient Boosting (XGBoost), and Light Gradient Boosting Machine (LightGBM). The performance of the models was evaluated using the area under the receiver operating characteristic curve (ROC).ResultsA total of eleven, nine, and fourteen optimal features were identified for the CT, PET, and PET+CT groups, respectively. In the validation set, the Area Under the Curve (AUC) values for the CT models ranged from 0.731 to 0.831, for the PET models from 0.746 to 0.810, and for the PET+CT models from 0.800 to 0.847. Among these, the PET+CT model developed using the Random Forest (RF) classifier demonstrated the best diagnostic performance, with an AUC of 0.847, sensitivity of 0.804, and specificity of 0.821. Decision curve analysis (DCA) confirmed that the model has favorable clinical utility, while calibration curves showed a good agreement between predicted and observed outcomes.ConclusionThe PET+CT radiomics models outperformed the single-modality models in distinguishing Solid pulmonary nodules adenocarcinoma from inflammatory lesions. Overall, the RF-based PET+CT model achieved the highest diagnostic efficacy and indicates promising potential for clinical application.

  • Research Article
  • 10.1109/tvcg.2026.3694437
Graph Drawing Stress Model with Resistance Distances.
  • Jun 1, 2026
  • IEEE transactions on visualization and computer graphics
  • Yosuke Onoue

This paper challenges the convention of using graph-theoretic shortest distance in stress-based graph drawing. We propose a new paradigm based on resistance distance, derived from the graph Laplacian's spectrum, which better captures global graph structure. This approach overcomes theoretical and computational limitations of traditional methods, as resistance distance admits a natural isometric embedding in Euclidean space. Our experiments demonstrate improved neighborhood preservation and cluster faithfulness. We introduce Omega, a linear-time graph drawing algorithm that integrates a fast resistance distance embedding with random node-pair sampling for Stochastic Gradient Descent (SGD). This comprehensive random sampling strategy, enabled by efficient pre-computation of resistance distance embeddings, is more effective and robust than pivot-based sampling used in prior algorithms, consistently achieving lower and more stable stress values. The algorithm maintains $O(\vert E\vert)$ complexity for both weighted and unweighted graphs. Our work establishes a connection between spectral graph theory and stress-based layouts, providing a practical and scalable solution for network visualization.

  • Research Article
  • 10.1002/sim.70609
Interpretable Deep Regression Models With Interval-Censored Failure Time Data.
  • Jun 1, 2026
  • Statistics in medicine
  • Changhui Yuan + 5 more

Deep neural networks (DNNs) have become powerful tools for modeling complex data structures through sequentially integrating simple functions in each hidden layer. In survival analysis, recent advances of DNNs primarily focus on enhancing model capabilities, especially in exploring nonlinear covariate effects under right censoring. However, deep learning methods for interval-censored data, where the unobservable failure time is only known to lie in an interval, remain underexplored and limited to specific data types or models. This work proposes a general regression framework for interval-censored data with a broad class of partially linear transformation models, where key covariate effects are modeled parametrically while nonlinear effects of nuisance covariates are approximated via DNNs, balancing interpretability and flexibility. We employ sieve maximum likelihood estimation by leveraging monotone splines to approximate the cumulative baseline hazard function. To ensure reliable and tractable estimation, we develop an EM algorithm incorporating stochastic gradient descent. We establish the asymptotic properties of parameter estimators and show that the DNN estimator achieves minimax-optimal convergence. Extensive simulations demonstrate superior estimation and prediction accuracy over state-of-the-art methods. Applying our method to the Alzheimer's Disease Neuroimaging Initiative dataset yields novel insights and improved predictive performance compared to traditional approaches.

  • Research Article
  • 10.1016/j.neucom.2026.133413
Convergence analysis of the last iterate in distributed stochastic gradient descent with momentum
  • Jun 1, 2026
  • Neurocomputing
  • Difei Cheng + 2 more

Convergence analysis of the last iterate in distributed stochastic gradient descent with momentum

  • Research Article
  • 10.1080/01621459.2026.2641199
Adaptive Debiased Lasso in High-Dimensional Generalized Linear Models with Streaming Data
  • May 27, 2026
  • Journal of the American Statistical Association
  • Ruijian Han + 4 more

Online statistical inference facilitates real-time analysis of sequentially collected data, making it different from traditional methods that rely on static datasets. This article introduces a novel approach to online inference in high-dimensional generalized linear models, where we update regression coefficient estimates and their standard errors upon each new data arrival. In contrast to existing methods that either require full dataset access or large-dimensional summary statistics storage, our method operates in a single-pass mode, significantly reducing both time and space complexity. The core of our methodological innovation lies in an adaptive stochastic gradient descent algorithm tailored for dynamic objective functions, coupled with a novel online debiasing procedure. This allows us to maintain low-dimensional summary statistics while effectively controlling the optimization error introduced by the dynamically changing loss functions. We establish the asymptotic normality of our proposed Adaptive Debiased Lasso (ADL) estimator. We conduct extensive simulation experiments to show the statistical validity and computational efficiency of our ADL estimator across various settings. Its computational efficiency is further demonstrated via a real data application to the spam email classification. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

  • Research Article
  • 10.1038/s41598-026-52610-8
A deep learning approach for solving a fractional order Monkeypox transmission model using a harmonic neural network optimized with SGDM.
  • May 26, 2026
  • Scientific reports
  • Nimra Shoket + 4 more

This study investigates the transmission dynamics of Monkeypox disease using a Harmonic neural network (HNN) framework optimized through stochastic gradient descent with momentum (SGDM). The proposed HNN-SGDM approach is applied to a nonlinear Monkeypox model consisting of nine coupled differential equations describing the interactions between human and rodent populations. HNN are employed because traditional non-oscillatory activation functions often struggle to capture the periodic and complex dynamics of disease transmission, whereas harmonic activation functions efficiently approximate such oscillatory patterns. SGDM is chosen to improve convergence and optimization stability in high-dimensional, non-convex search spaces. The proposed solver achieves high precision, with absolute errors ranging from [Formula: see text] to [Formula: see text], confirming its numerical stability and convergence. The robustness and reliability of HNN-SGDM framework are further validated through statistical performance measures, including mean absolute error, root mean square error, and Theil's inequality coefficient. Graphical analyses, including weight distributions, box plots, histograms, and loss curves, further validate the model's performance. This approach highlights the effectiveness of deep learning in epidemiological modeling and provides a methodology extendable to other infectious disease frameworks.

  • Research Article
  • 10.1080/03610918.2026.2678508
Flexible Tree-Informed Mixed Model regression
  • May 26, 2026
  • Communications in Statistics - Simulation and Computation
  • Jeremiah Allis + 2 more

The standard regression tree method applied to observations within clusters poses both methodological and implementation challenges. Effectively leveraging these data requires methods that account for both individual-level and sample-level effects. We propose the Flexible Tree-Informed Mixed Model, which replaces the linear fixed effect in a generalized linear mixed model with the output of a regression tree. Traditional parameter estimation and prediction techniques, such as the expectation-maximization algorithm, scale poorly in high-dimensional settings, creating a computational bottleneck. To address this, we employ a quasi-likelihood framework with stochastic gradient descent for optimized parameter estimation. Additionally, we establish a theoretical bound for the mean squared prediction error. The predictive performance of our method is evaluated through simulations and compared with existing approaches. Finally, we apply our model to predict country-level gross domestic product based on trade, foreign direct investment, unemployment, inflation, and geographic region.

  • Research Article
  • 10.1093/pnasnexus/pgag182
A statistical physics framework for optimal learning
  • May 26, 2026
  • PNAS Nexus
  • Francesca Mignacco + 1 more

Learning is a complex dynamical process shaped by a range of interconnected decisions. Careful design of hyperparameter schedules for artificial neural networks or efficient allocation of cognitive resources by biological learners can dramatically affect performance. Yet, theoretical understanding of optimal learning strategies remains sparse, especially due to the intricate interplay between evolving metaparameters and nonlinear learning dynamics. The search for optimal protocols is further hindered by the high dimensionality of the learning space, often resulting in predominantly heuristic, difficult to interpret, and computationally demanding solutions. Here, we combine statistical physics with control theory in a unified theoretical framework to identify optimal learning protocols in prototypical neural network models. In the high-dimensional limit, we derive closed-form ordinary differential equations that track online stochastic gradient descent through low-dimensional order parameters. We formulate the design of learning protocols as an optimal control problem directly on the dynamics of the order parameters with the goal of minimizing the generalization error. This formulation encompasses a variety of learning scenarios, optimization constraints, and control budgets. We apply it to representative cases, including optimal curricula, adaptive dropout regularization and noise schedules in denoising autoencoders. We find nontrivial yet interpretable strategies highlighting how optimal protocols mediate learning trade-offs. Our results establish a principled foundation for understanding and designing optimal protocols and suggest a path toward a theory of meta-learning grounded in statistical physics.

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