This paper introduces a non-parametric estimation algorithm designed to effectively estimate the joint distribution of model parameters with application to population pharmacokinetics. Our research group has previously developed the non-parametric adaptive grid (NPAG) algorithm, which while accurate, explores parameter space using an ad-hoc method to suggest new support points. In contrast, the non-parametric optimal design (NPOD) algorithm uses a gradient approach to suggest new support points, which reduces the amount of time spent evaluating non-relevant points and by this the overall number of cycles required to reach convergence. In this paper, we demonstrate that the NPOD algorithm achieves similar solutions to NPAG across two datasets, while being significantly more efficient in both the number of cycles required and overall runtime. Given the importance of developing robust and efficient algorithms for determining drug doses quickly in pharmacokinetics, the NPOD algorithm represents a valuable advancement in non-parametric modeling. Further analysis is needed to determine which algorithm performs better under specific conditions.

This study introduces a specialized pipeline designed to classify the concentration state of an individual student during online learning sessions by training a custom-tailored machine learning model. Detailed protocols for acquiring and preprocessing EEG data are outlined, along with the extraction of fifty statistical features from five EEG signal bands: alpha, beta, theta, delta, and gamma. Following feature extraction, a thorough feature selection process was conducted to optimize the data inputs for a personalized analysis. The study also explores the benefits of hyperparameter fine-tuning to enhance the classification accuracy of the student's concentration state. EEG signals were captured from the student using a Muse headband (Gen 2), equipped with five electrodes (TP9, AF7, AF8, TP10, and a reference electrode NZ), during engagement with educational content on computer-based e-learning platforms. Employing a random forest model customized to the student's data, we achieved remarkable classification performance, with test accuracies of 97.6% in the computer-based learning setting and 98% in the virtual reality setting. These results underscore the effectiveness of our approach in delivering personalized insights into student concentration during online educational activities.

Autism spectrum disorder (ASD) remains a challenging condition to diagnose effectively and promptly, despite global efforts in public health, clinical screening, and scientific research (1). Traditional diagnostic methods, primarily reliant on supervised learning approaches, presuppose the availability of labeled data, which can be both time-consuming and resource-intensive to obtain (2). Unsupervised learning, in contrast, offers a means of gaining insights from unlabeled datasets in a manner that can expedite or support the diagnostic process (3). This paper explores the use of four distinct unsupervised clustering algorithms--K-Means, Gaussian Mixture Model (GMM), Agglomerative Clustering, and DBSCAN--to analyze a publicly available dataset of 704 adult individuals screened for ASD. After extensive hyperparameter tuning via cross-validation, the study documents how the Gaussian Mixture Model achieved the highest clustering-to-label accuracy (95.31%) when mapped to the original ASD/NO classification (4). Other key performance metrics included the Adjusted Rand Index (ARI) and silhouette scores, which further illustrated the internal coherence of each cluster. The dataset underwent preprocessing procedures including data cleaning, label encoding of categorical features, and standard scaling, followed by a thorough cross-validation approach to assess and compare the four clustering methods (5). These results highlight the significant potential of unsupervised methods in assisting ASD screening, especially in contexts where labeled data may be sparse, uncertain, or prohibitively expensive to obtain. With continued methodological refinements, unsupervised approaches hold promise for augmenting early detection initiatives and guiding resource allocation to individuals at high risk.

Pursuing Top Growth with Novel Loss Function Ruoyu Guo 1,, Haochen Qiu 1 1 Department of Mathematics, Brandeis University, 415 South Street, Waltham, 02453, MA, USAAbstract Making consistently profitable financial decisions in a continuously evolving and volatile stock market has always been a difficult task. Professionals from different disciplines have developed foundational theories to anticipate price movement and evaluate securities such as the famed Capital Asset Pricing Model (CAPM). In recent years, the role of artificial intelligence (AI) in asset pricing has been growing. Although the black-box nature of deep learning models lacks interpretability, they have continued to solidify their position in the financial industry. We aim to further enhance AI's potential and utility by introducing a return-weighted loss function that will drive top growth while providing the ML models a limited amount of information. Using only publicly accessible stock data (open/close/high/low, trading volume, sector information) and several technical indicators constructed from them, we propose an efficient daily trading system that detects top growth opportunities. Our best models achieve 61.73% annual return on daily rebalancing with an annualized Sharpe Ratio of 1.18 over 1340 testing days from 2019 to 2024, and 37.61% annual return with an annualized Sharpe Ratio of 0.97 over 1360 testing days from 2005 to 2010. The main drivers for success, especially independent of any domain knowledge, are the novel return-weighted loss function, the integration of categorical and continuous data, and the ML model architecture. We also demonstrate the superiority of our novel loss function over traditional loss functions via several performance metrics and statistical evidence. Introduction Stock price and movement prediction have always been extraordinarily challenging yet heavily sought-after tasks. Before the popularity of artificial intelligence and availability of unforeseen computing power present today, initial stages of our financial understanding consist of the Capital Asset Pricing Model (CAPM) (Sharpe, 1964), the Efficient Market Hypothesis (EMH) (Fama, 1970), and more. Decades of research following them have witnessed a vast number of articles that build upon these very fundamental concepts, including the 3, 4, and 5-factor models (Fama and French, 1993; Carhart, 1997; Fama and French, 2015).

Western music is an innately hierarchical system of interacting levels of structure, from fine-grained melody to high-level form. In order to analyze music compositions holistically and at multiple granularities, we propose a unified, hierarchical meta-representation of musical structure called the structural temporal graph (STG). For a single piece, the STG is a data structure that defines a hierarchy of progressively finer structural musical features and the temporal relationships between them. We use the STG to enable a novel approach for deriving a representative structural summary of a music corpus, which we formalize as a dually NP-hard combinatorial optimization problem extending the Generalized Median Graph problem. Our approach first applies simulated annealing to develop a measure of structural distance between two music pieces rooted in graph isomorphism. Our approach then combines the formal guarantees of SMT solvers with nested simulated annealing over structural distances to produce a structurally sound, representative centroid STG for an entire corpus of STGs from individual pieces. To evaluate our approach, we conduct experiments verifying that structural distance accurately differentiates between music pieces, and that derived centroids accurately structurally characterize their corpora.

The Web of Things (WoT) enhances interoperability across web-based and ubiquitous computing platforms while complementing existing IoT standards. The multimodal Federated Learning (FL) paradigm has been introduced to enhance WoT by enabling the fusion of multi-source mobile sensing data while preserving privacy. However, a key challenge in mobile sensing systems using multimodal FL is modality incompleteness, where some modalities may be unavailable or only partially captured, potentially degrading the system's performance and reliability. Current multimodal FL frameworks typically train multiple unimodal FL subsystems or apply interpolation techniques on the node side to approximate missing modalities. However, these approaches overlook the shared latent feature space among incomplete modalities across different nodes and fail to discriminate against low-quality nodes. To address this gap, we present FedMobile, a new knowledge contribution-aware multimodal FL framework designed for robust learning despite missing modalities. FedMobile prioritizes local-to-global knowledge transfer, leveraging cross-node multimodal feature information to reconstruct missing features. It also enhances system performance and resilience to modality heterogeneity through rigorous node contribution assessments and knowledge contribution-aware aggregation rules. Empirical evaluations on five widely recognized multimodal benchmark datasets demonstrate that FedMobile maintains robust learning even when up to 90% of modality information is missing or when data from two modalities are randomly missing, outperforming state-of-the-art baselines.

The expansion of artificial intelligence (AI) has raised concerns about transparency, accountability, and interpretability, with counterfactual reasoning emerging as a key approach to addressing these issues. However, current mathematical, technological, and causal methodologies rely on externalization techniques that normalize feature relationships within a single coordinate space, often distorting intrinsic interactions. This study proposes the Convergent Fusion Paradigm (CFP) theory, a framework integrating mathematical, technological, and causal perspectives to provide a more precise and comprehensive analysis of feature relationships. CFP theory introduces Hilbert space and backward causation to reinterpret the feature relationships as emergent structures, offering a potential solution to the common cause problem -- a fundamental challenge in causal modeling. From a mathematical -- technical perspective, it utilizes a Riemannian manifold-based framework, thereby improving the structural representation of high- and low-dimensional data interactions. From a causal inference perspective, CFP theory adopts abduction as a methodological foundation, employing Hilbert space for a dynamic causal reasoning approach, where causal relationships are inferred abductively, and feature relationships evolve as emergent properties. Ultimately, CFP theory introduces a novel AI modeling methodology that integrates Hilbert space, backward causation, and Riemannian geometry, strengthening AI governance and transparency in counterfactual reasoning.

In the domain of machine learning, the assumption that training and test data share the same distribution is often violated in real-world scenarios, requiring effective out-of-distribution (OOD) detection. This paper presents a novel OOD detection method that leverages the unique local neuroplasticity property of Kolmogorov-Arnold Networks (KANs). Unlike traditional multilayer perceptrons, KANs exhibit local plasticity, allowing them to preserve learned information while adapting to new tasks. Our method compares the activation patterns of a trained KAN against its untrained counterpart to detect OOD samples. We validate our approach on benchmarks from image and medical domains, demonstrating superior performance and robustness compared to state-of-the-art techniques. These results underscore the potential of KANs in enhancing the reliability of machine learning systems in diverse environments.

In order to streamline the fine-tuning of foundation models, Low-Rank Adapters (LoRAs) have been substantially adopted across various fields, including instruction tuning and domain adaptation. The underlying concept of LoRA involves decomposing a full-rank matrix into the product of two lower-rank matrices, which reduces storage consumption and accelerates the training process. Furthermore, to address the limited expressive capacity of LoRA, the Mixture-of-Expert (MoE) has been introduced for incorporating multiple LoRA adapters. The integration of LoRA experts leads to a visible improvement across several downstream scenes. However, the mixture of LoRAs (MoE-LoRA) still exhibits its low robustness during tuning and inferring. Inspired by the Riemannian Preconditioners which train LoRA as a sub-space projector, we propose a new training strategy for MoE-LoRA, to stabilize and boost its feature learning procedure by multi-space projections. Examinations on SGD and AdamW optimizers demonstrate the effectiveness of our methodology. Source code is available at https://github.com/THUDM/MoELoRA_Riemannian.

Graph-language models (GLMs) have demonstrated great potential in graph-based semi-supervised learning. A typical GLM consists of two key stages: graph generation and text embedding, which are usually implemented by inferring a latent graph and finetuning a language model (LM), respectively. However, the former often relies on artificial assumptions about the underlying edge distribution, while the latter requires extensive data annotations. To tackle these challenges, this paper introduces a novel GLM that integrates graph generation and text embedding within a unified framework. We unexpectedly find that this natural property can be effectively approximated by a simple k -nearest neighbor (KNN) graph. For text embedding, we develop a graph-based pseudo-labeler that utilizes scale-free graphs to provide complementary supervision for improved LM finetuning. Extensive experiments on representative datasets validate our findings on the scale-free structural approximation of KNN graphs and demonstrate the effectiveness of integrating graph generation and text embedding with a real structural prior. Recently, graph-language models (GLMs) have been widely explored in graph-based semi-supervised classification on documents, especially for citation networks (Qin et al., 2023; Y u et al., 2025; Lu et al., 2023; He et al., 2024). When designing a GLM for classification, two key challenges arise: graph generation --how to generate a reasonable graph structure for the given documents, and text embedding --how to encode the textual sequences into meaningful semantic features. To address these problems, various GLMs have been proposed, which can be broadly categorized into latent graph inference (LGI) models and language-assisted graph (LAG) models. LGI models focus on graph generation and typically rely on feature engineering approaches, such as bag-of-words (Harris, 1954), TF-IDF (Aizawa, 2003), and skip-gram (Mikolov et al., 2013), to encode textual sequences into shallow representations.