Mental and cognitive representations are believed to reside on low-dimensional, non-linear manifolds embedded within high-dimensional brain activity. Uncovering these manifolds is key to understanding individual differences in brain function, yet most existing machine learning methods either rely on population-level spatial alignment or assume data that is temporally structured, either because data is aligned among subjects or because event timings are known. We introduce a manifold learning framework that can capture subject-specific spatial variations across both structured and temporally unstructured neuroimaging data. On simulated data and two naturalistic fMRI datasets (Sherlock and Forrest Gump), our framework outperforms group-based baselines by recovering more accurate and individualized representations. We further show that the framework scales efficiently to large datasets and generalizes well to new subjects. To test this, we apply the framework to temporally unstructured resting-state fMRI data from individuals with schizophrenia and healthy controls. We further apply our method to a large resting-state fMRI dataset comprising individuals with schizophrenia and controls. In this setting, we demonstrate that the framework scales efficiently to large populations and generalizes robustly to unseen subjects. The learned subject-specific spatial maps our model finds reveal clinically relevant patterns, including increased activation in the basal ganglia, visual, auditory, and somatosensory regions, and decreased activation in the insula, inferior frontal gyrus, and angular gyrus. These findings suggest that our framework can uncover clinically relevant subject-specific brain activity patterns. Our approach thus provides a scalable and individualized framework for modeling brain activity, with applications in computational neuroscience and clinical research.

Retrieval-Augmented Generation enhances language models by retrieving relevant information from external knowledge bases, relying on high-dimensional vector embeddings typically stored in float32 precision. However, storing these embeddings at scale presents significant memory challenges. To address this issue, we systematically investigate on MTEB benchmark two complementary optimization strategies: quantization, evaluating standard formats (float16, int8, binary) and low-bit floating-point types (float8), and dimensionality reduction, assessing methods like PCA, Kernel PCA, UMAP, Random Projections and Autoencoders. Our results show that float8 quantization achieves a 4x storage reduction with minimal performance degradation (<0.3%), significantly outperforming int8 quantization at the same compression level, being simpler to implement. PCA emerges as the most effective dimensionality reduction technique. Crucially, combining moderate PCA (e.g., retaining 50% dimensions) with float8 quantization offers an excellent trade-off, achieving 8x total compression with less performance impact than using int8 alone (which provides only 4x compression). To facilitate practical application, we propose a methodology based on visualizing the performance-storage trade-off space to identify the optimal configuration that maximizes performance within their specific memory constraints.

The unprecedented global COVID - 19 pandemic has prompted researchers to investigate both the biochemical changes associated with acute infection and the long - term effects of COVID - 19, with the goal of elucidating underlying mechanisms [ 1 4 ]. Among the diverse biochemical alterations observed in COVID - 19, change s in metabolomic and proteomic profiles have drawn particular attention due to their roles in fundamental biological processes, including protein expression and metabolic pathways [5, 6]. Early in the pandemic, several studies highlighted the significance of certain biomarkers for diagnosing COVID - 19 and assessing disease severity [7, 8]. These initial finding s reveal ed that specific biomarkers are involved in COVID - 19 pathogenesis and correlate with disease severity. S ubsequent research into post - acute sequelae of COVID - 19 (PASC, or long COVID) has further shown that variations in these biomarkers are associated with neurological and respiratory complications [9, 10]. Collectively, these studie s highlight the importance of identifying key biomarkers to support both acute COVID - 19 detection and the understanding of long COVID.

This paper presents a comprehensive computational framework for analyzing linguistic complexity and socio-cultural trends in hip-hop lyrics. Using a dataset of 3,814 songs from 146 influential artists spanning four decades (1980-2020), we employ natural language processing techniques to quantify multiple dimensions of lyrical complexity. Our analysis reveals a 23.7% increase in vocabulary diversity over the study period, with East Coast artists demonstrating 17.3% higher lexical variation than other regions. Rhyme density increased by 34.2% across all regions, with Midwest artists exhibiting the highest technical complexity (3.04 rhymes per line). Topic modeling identified significant shifts in thematic content, with social justice themes decreasing from 28.5% to 13.8% of content while introspective themes increased from 7.6% to 26.3%. Sentiment analysis demon- strated that lyrics became significantly more negative during sociopolitical crises, with polarity decreasing by 0.31 following major social unrest. Multi-dimensional analysis revealed four dis- tinct stylistic approaches that correlate strongly with geographic origin (r=0.68, p!0.001) and time period (r=0.59, p<0.001). These findings establish quantitative evidence for the evolution of hip- hop as both an art form and a reflection of societal dynamics, providing insights into the interplay between linguistic innovation and cultural context in popular music.

This paper proposed an approach to automatically discovering subject dimension, action dimension, object dimension and adverbial dimension from texts to efficiently operate texts and support query in natural language. The high quality of trees guarantees that all subjects, actions, objects and adverbials and their subclass relations within texts can be represented. The independency of trees ensures that there is no redundant representation between trees. The expressiveness of trees ensures that the majority of sentences can be accessed from each tree and the rest of sentences can be accessed from at least one tree so that the tree-based search mechanism can support querying in natural language. Experiments show that the average precision, recall and F1-score of the abstraction trees constructed by the subclass relations of subject, action, object and adverbial are all greater than 80%. The application of the proposed approach to supporting query in natural language demonstrates that different types of question patterns for querying subject or object have high coverage of texts, and searching multiple trees on subject, action, object and adverbial according to the question pattern can quickly reduce search space to locate target sentences, which can support precise operation on texts.

In this paper we provide evidence that a virtual model of U.S. congresspersons based on a collection of language models satisfies the definition of a digital twin. In particular, we introduce and provide high-level descriptions of a daily-updated dataset that contains every Tweet from every U.S. congressperson during their respective terms. We demonstrate that a modern language model equipped with congressperson-specific subsets of this data are capable of producing Tweets that are largely indistinguishable from actual Tweets posted by their physical counterparts. We illustrate how generated Tweets can be used to predict roll-call vote behaviors and to quantify the likelihood of congresspersons crossing party lines, thereby assisting stakeholders in allocating resources and potentially impacting real-world legislative dynamics. We conclude with a discussion of the limitations and important extensions of our analysis.

Contrastive methods, dimensionality reduction algorithms like t-SNE, and clustering objectives such as k-Means all implicitly or explicitly define distributions over neighborhoods and minimize some divergence between them. The Information Contrastive Learning (I-Con) framework recently unified many such approaches by expressing them as the minimization of KL divergence between a fixed supervisory distribution p (j | i) and a learned distribution q ( j |i) over data neighborhoods [1]. However, I-Con treats this KL alignment statically, as if each point-wise loss were independent. In this paper, we propose a deeper view: that representation learning is fundamentally a process of recursive divergence minimization across a structured field of conditional distributions. Each neighborhood distribution depends on prior learned representations, forming a dynamic system that we call Recursive KL Divergence Optimization (RKDO). While the exponential moving average (EMA) recursion we employ has been used in several well-known self-supervised and semi-supervised methods such as Temporal Ensembling [2], Mean Teacher [3], and momentum-based frameworks like MoCo [4], BYOL [5], and DINO [6], our novel contribution lies in applying this recursive structure to the entire response field (the joint conditional distribution over representation pairs), rather than to individual weights or per-sample predictions. RKDO captures the temporal dynamics of representation learning that are absent in static frameworks, with significant implications for optimization efficiency. Our contributions include: A new theoretical framework that generalizes representation learning as recursive alignment of conditional distributions across the entire response field Mathematical formulations showing how RKDO captures temporal dynamics absent in static frameworks, with a formal proof of linear-rate convergence under this recursion Empirical evidence that RKDO's recursive approach results in significantly lower loss values (approximately 30% reduction across all tested datasets) Demonstration that RKDO requires 60-80% fewer computational resources (training epochs) to achieve results comparable to longer I-Con training Analysis of the trade-offs between optimization efficiency and generalization in recursive versus static approaches Our experiments suggest that while I-Con effectively represents a unified view of many typical representation learning approaches, RKDO can provide substantial efficiency improvements: achieving comparable optimization objectives with approximately 30% lower loss values, while potentially reducing computational requirements by 60-80% in the specific scenarios we studied. 2 Background and Related Work The KL divergence [7] is a foundational object in representation learning.

Satellite-based estimates of greenhouse gas (GHG) properties from observations of reflected solar spectra are integral for understanding and monitoring complex terrestrial systems and their impact on the carbon cycle due to their near global coverage. Known as retrieval, making GHG concentration estimations from these observations is a non-linear Bayesian inverse problem, which is operationally solved using a computationally expensive algorithm called Optimal Estimation (OE), providing a Gaussian approximation to a non-Gaussian posterior. This leads to issues in solver algorithm convergence, and to unrealistically confident uncertainty estimates for the retrieved quantities. Upcoming satellite missions will provide orders of magnitude more data than the current constellation of GHG observers. Development of fast and accurate retrieval algorithms with robust uncertainty quantification is critical. Doing so stands to provide substantial climate impact of moving towards the goal of near continuous real-time global monitoring of carbon sources and sinks which is essential for policy making. To achieve this goal, we propose a diffusion-based approach to flexibly retrieve a Gaussian or non-Gaussian posterior, for NASA's Orbiting Carbon Observatory-2 spectrometer, while providing a substantial computational speed-up over the current operational state-of-the-art.

However, most human dynamic-behavior models focus only on the sequence of users' actions, abstracting the intervals between actions (i.e., inter-temporal information). Statistical time-series models, for instance, study the variation of values in the data over time; however, such models do not explicitly capture the interdependence between actions and their intervals. While some point-process models incorporate intervals, they use them to predict only a single or a few event types rather than to characterize diverse human actions enriched with temporal information from massive data (Zhao et al., 2015; Mei and Eisner, 2017). Therefore, in contrast with the sophisticated advancement of statistical behavior models, understanding human behavior from the perspective of inter-temporal context remains a difficult and often elusive goal. W e perform actions in many different contexts--from using smartphones to walking across campus. Studying these situations can help us understand what human actions are like. Even the same action can differ depending on when and where it happens. Time intervals between actions provide crucial contextual information, and much literature shows that they can reveal human cognitive states (Stanovich and W est, 2000; 1 arXiv:2206.09535v2

This paper develops a novel hybrid approach for estimating the mixture model of $t$-factor analyzers (MtFA) that employs multivariate $t$-distribution and factor model to cluster and characterize grouped data. The traditional estimation method for MtFA faces computational challenges, particularly in high-dimensional settings, where the eigendecomposition of large covariance matrices and the iterative nature of Expectation-Maximization (EM) algorithms lead to scalability issues. We propose a computational scheme that integrates a profile likelihood method into the EM framework to efficiently obtain the model parameter estimates. The effectiveness of our approach is demonstrated through simulations showcasing its superior computational efficiency compared to the existing method, while preserving clustering accuracy and resilience against outliers. Our method is applied to cluster the Gamma-ray bursts, reinforcing several claims in the literature that Gamma-ray bursts have heterogeneous subpopulations and providing characterizations of the estimated groups.