Traditional filtering algorithms for state estimation -- such as classical Kalman filtering, unscented Kalman filtering, and particle filters - show performance degradation when applied to nonlinear systems whose uncertainty follows arbitrary non-Gaussian, and potentially multi-modal distributions. This study reviews recent approaches to state estimation via nonlinear filtering based on conditional normalizing flows, where the conditional embedding is generated by standard MLP architectures, transformers or selective state-space models (like Mamba-SSM). In addition, we test the effectiveness of an optimal-transport-inspired kinetic loss term in mitigating overparameterization in flows consisting of a large collection of transformations. We investigate the performance of these approaches on applications relevant to autonomous driving and patient population dynamics, paying special attention to how they handle time inversion and chained predictions. Finally, we assess the performance of various conditioning strategies for an application to real-world COVID-19 joint SIR system forecasting and parameter estimation.

The success of deep neural networks largely depends on the st atistical structure of the training data. While learning dynamics and generalization on iso tropic data are well-established, the impact of pronounced anisotropy on these crucial aspect s is not yet fully understood. We examine the impact of data anisotropy, represented by a sp iked covariance structure, a canonical yet tractable model, on the learning dynamics and generalization error of a two-layer linear network in a linear regression setting. Our ana lysis reveals that the learning dynamics proceed in two distinct phases, governed initiall y by the input-output correlation and subsequently by other principal directions of the data s tructure. Furthermore, we derive an analytical expression for the generalization error, quantifying how the alignment of the spike structure of the data with the learning task improv es performance. Our findings offer deep theoretical insights into how data anisotropy sha pes the learning trajectory and final performance, providing a foundation for understandin g complex interactions in more advanced network architectures.

Understanding the structure of complex, nonstationary, high-dimensional time-evolving signals is a central challenge in scientific data analysis. In many domains, such as speech and biomedical signal processing, the ability to learn disentangled and interpretable representations is critical for uncovering latent generative mechanisms. Traditional approaches to unsupervised representation learning, including variational autoencoders (VAEs), often struggle to capture the temporal and spectral diversity inherent in such data. Here we introduce variational decomposition autoencoding (VDA), a framework that extends VAEs by incorporating a strong structural bias toward signal decomposition. VDA is instantiated through variational decomposition autoencoders (DecVAEs), i.e., encoder-only neural networks that combine a signal decomposition model, a contrastive self-supervised task, and variational prior approximation to learn multiple latent subspaces aligned with time-frequency characteristics. We demonstrate the effectiveness of DecVAEs on simulated data and three publicly available scientific datasets, spanning speech recognition, dysarthria severity evaluation, and emotional speech classification. Our results demonstrate that DecVAEs surpass state-of-the-art VAE-based methods in terms of disentanglement quality, generalization across tasks, and the interpretability of latent encodings. These findings suggest that decomposition-aware architectures can serve as robust tools for extracting structured representations from dynamic signals, with potential applications in clinical diagnostics, human-computer interaction, and adaptive neurotechnologies.

Large language models (LLMs) such as GPT, Claude, Gemini, and Grok have been deeply integrated into our daily life. They now support a wide range of tasks -- from dialogue and email drafting to assisting with teaching and coding, serving as search engines, and much more. However, their ability to produce highly human-like text raises serious concerns, including the spread of fake news, the generation of misleading governmental reports, and academic misconduct. To address this practical problem, we train a classifier to determine whether a piece of text is authored by an LLM or a human. Our detector is deployed on an online CPU-based platform https://huggingface.co/spaces/stats-powered-ai/StatDetectLLM, and contains three novelties over existing detectors: (i) it does not rely on auxiliary information, such as watermarks or knowledge of the specific LLM used to generate the text; (ii) it more effectively distinguishes between human- and LLM-authored text; and (iii) it enables statistical inference, which is largely absent in the current literature. Empirically, our classifier achieves higher classification accuracy compared to existing detectors, while maintaining type-I error control, high statistical power, and computational efficiency.

Foundation models pre-trained on large-scale source datasets are reshaping the traditional training paradigm for time series classification. However, existing time series foundation models primarily focus on forecasting tasks and often overlook classification-specific challenges, such as modeling interpretable shapelets that capture class-discriminative temporal features. To bridge this gap, we propose UniShape, a unified shape-aware foundation model designed for time series classification. UniShape incorporates a shape-aware adapter that adaptively aggregates multiscale discriminative subsequences (shapes) into class tokens, effectively selecting the most relevant subsequence scales to enhance model interpretability. Meanwhile, a prototype-based pretraining module is introduced to jointly learn instance- and shape-level representations, enabling the capture of transferable shape patterns. Pre-trained on a large-scale multi-domain time series dataset comprising 1.89 million samples, UniShape exhibits superior generalization across diverse target domains. Experiments on 128 UCR datasets and 30 additional time series datasets demonstrate that UniShape achieves state-of-the-art classification performance, with interpretability and ablation analyses further validating its effectiveness.

Supporting Go/No-Go decisions prior to launch requires assessing real-time telemetry data against redline limits established during the design qualification phase. Family data from ground testing or previous flights is commonly used to detect initiating failure modes and their timing; however, this approach relies heavily on engineering judgment and is more error-prone for new launch vehicles. To address these limitations, we utilize Long-Term Short-Term Memory (LSTM) networks for supervised classification of time-series anomalies. Although, initial training labels derived from simulated anomaly data may be suboptimal due to variations in anomaly strength, anomaly settling times, and other factors. In this work, we propose a novel statistical detector based on the Mahalanobis distance and forward-backward detection fractions to adjust the supervised training labels. We demonstrate our method on digital twin simulations of a ground-stage propulsion system with 20.8 minutes of operation per trial and O(10^8) training timesteps. The statistical data relabeling improved precision and recall of the LSTM classifier by 7% and 22% respectively.

Cardiovascular disease (CVD) continues to be the major cause of death globally, calling for predictive models that not only handle diverse and high-dimensional biomedical signals but also maintain interpretability and privacy. We create a single multimodal learning framework that integrates cross modal transformers with graph neural networks and causal representation learning to measure personalized CVD risk. The model combines genomic variation, cardiac MRI, ECG waveforms, wearable streams, and structured EHR data to predict risk while also implementing causal invariance constraints across different clinical subpopulations. To maintain transparency, we employ SHAP based feature attribution, counterfactual explanations and causal latent alignment for understandable risk factors. Besides, we position the design in a federated, privacy, preserving optimization protocol and establish rules for convergence, calibration and uncertainty quantification under distributional shift. Experimental studies based on large-scale biobank and multi institutional datasets reveal state discrimination and robustness, exhibiting fair performance across demographic strata and clinically distinct cohorts. This study paves the way for a principled approach to clinically trustworthy, interpretable and privacy respecting CVD prediction at the population level.

Google's parent company hit a major financial milestone on Monday, reaching a $4tn valuation for the first time and surpassing Apple to become the second-most valuable company in the world. Alphabet is the fourth company to hit the $4tn milestone after Nvidia, which later hit $5tn, Microsoft and Apple . The spike in share price comes after Apple announced it had chosen Google's Gemini AI model to power a major overhaul of the iPhone maker's digital assistant Siri, which comes installed in every iPhone. Neither company disclosed how much the deal was worth. "After careful evaluation, we determined that Google's technology provides the most capable foundation for Apple Foundation Models," Apple said in a statement to CNBC . As tech stocks continue a years-long meteoric rise, fears of a bubble in the stock market persist; however, Wall Street's excitement for new avenues of investment in AI does as well.

Apple's Siri AI will be powered by Gemini Google's technology provides the most capable foundation for Apple Foundation Models, Apple said in a statement obtained by CNBC. Apple has confirmed reports that it will use Google Gemini's models to help it power the new version of Siri and other generative AI features. "After careful evaluation, we determined that Google's technology provides the most capable foundation for Apple Foundation Models and we're excited about the innovative new experiences it will unlock for our users," Apple said in a statement obtained by . In March 2025, the company said it was delaying a major Siri update until this year, but it appears that Apple is not quite ready to publicly release a more capable version of the voice assistant. In June, it was reported that Apple was considering partnerships with OpenAI and Anthropic for Siri (the voice assistant can currently tap ChatGPT for certain queries as part of Apple Intelligence).

PCWorld reports that Microsoft's Copilot AI holds only 1.1% of the web AI market share, declining from 1.5% over the past year. ChatGPT dominates with 64.5% market share while Google's Gemini has grown to 21.5%, leaving Copilot far behind major competitors.