Trump Warned of a Tren de Aragua'Invasion.' Hundreds of records obtained by WIRED show thin intelligence on the Venezuelan gang in the United States, describing fragmented, low-level crime rather than a coordinated terrorist threat. Alleged members of Tren de Aragua sit handcuffed during a preliminary hearing on July 9, 2025, in Santiago, Chile, where they faced homicide charges. As the Trump administration publicly cast Venezuela's Tren de Aragua (TdA) as a unified terrorist force tied to President Nicolás Maduro and operating inside the United States, hundreds of internal US government records obtained by WIRED tell a far less certain story. Intelligence taskings, law-enforcement bulletins, and drug-task-force assessments show that agencies spent much of 2025 struggling to determine whether TdA even functioned as an organized entity in the US at all--let alone as a coordinated national security threat.

Modern business and economic datasets often exhibit nonlinear, multi-scale structures that traditional linear tools under-represent. Topological Data Analysis (TDA) offers a geometric lens for uncovering robust patterns, such as connected components, loops and voids, across scales. This paper provides an intuitive, figure-driven introduction to persistent homology and a practical, reproducible TDA pipeline for applied analysts. Through comparative case studies in consumer behavior, equity markets (SAX/eSAX vs.\ TDA) and foreign exchange dynamics, we demonstrate how topological features can reveal segmentation patterns and structural relationships beyond classical statistical methods. We discuss methodological choices regarding distance metrics, complex construction and interpretation, and we introduce the \textit{Topological Stability Index} (TSI), a simple yet interpretable indicator of structural variability derived from persistence lifetimes. We conclude with practical guidelines for TDA implementation, visualization and communication in business and economic analytics.

Now that disease-modifying therapies for Alzheimer disease have been approved by regulatory agencies, the early, objective, and accurate clinical diagnosis of AD based on the lowest-cost measurement modalities possible has become an increasingly urgent need. In this study, we propose a novel feature extraction method using persistent homology to analyze structural MRI of the brain. This approach converts topological features into powerful feature vectors through Betti functions. By integrating these feature vectors with a simple machine learning model like XGBoost, we achieve a computationally efficient machine learning model. Our model outperforms state-of-the-art deep learning models in both binary and three-class classification tasks for ADNI 3D MRI disease diagnosis. Using 10-fold cross-validation, our model achieved an average accuracy of 97.43 percent and sensitivity of 99.09 percent for binary classification. For three-class classification, it achieved an average accuracy of 95.47 percent and sensitivity of 94.98 percent. Unlike many deep learning models, our approach does not require data augmentation or extensive preprocessing, making it particularly suitable for smaller datasets. Topological features differ significantly from those commonly extracted using convolutional filters and other deep learning machinery. Because it provides an entirely different type of information from machine learning models, it has the potential to combine topological features with other models later on.

This study investigates whether Topological Data Analysis (TDA) can provide additional insights beyond traditional statistical methods in clustering currency behaviours. We focus on the foreign exchange (FX) market, which is a complex system often exhibiting non-linear and high-dimensional dynamics that classical techniques may not fully capture. We compare clustering results based on TDA-derived features versus classical statistical features using monthly logarithmic returns of 13 major currency exchange rates (all against the euro). Two widely-used clustering algorithms, \(k\)-means and Hierarchical clustering, are applied on both types of features, and cluster quality is evaluated via the Silhouette score and the Calinski-Harabasz index. Our findings show that TDA-based feature clustering produces more compact and well-separated clusters than clustering on traditional statistical features, particularly achieving substantially higher Calinski-Harabasz scores. However, all clustering approaches yield modest Silhouette scores, underscoring the inherent difficulty of grouping FX time series. The differing cluster compositions under TDA vs. classical features suggest that TDA captures structural patterns in currency co-movements that conventional methods might overlook. These results highlight TDA as a valuable complementary tool for analysing financial time series, with potential applications in risk management where understanding structural co-movements is crucial.

In the evolving domains of Machine Learning and Data Analytics, existing dataset characterization methods such as statistical, structural, and model-based analyses often fail to deliver the deep understanding and insights essential for innovation and explainability. This work surveys the current state-of-the-art conventional data analytic techniques and examines their limitations, and discusses a variety of tensor-based methods and how these may provide a more robust alternative to traditional statistical, structural, and model-based dataset characterization techniques. Through examples, we illustrate how tensor methods unveil nuanced data characteristics, offering enhanced interpretability and actionable intelligence. We advocate for the adoption of tensor-based characterization, promising a leap forward in understanding complex datasets and paving the way for intelligent, explainable data-driven discoveries.

Modern deep neural networks are powerful predictive tools yet often lack valid inference for causal parameters, such as treatment effects or entire survival curves. While frameworks like Double Machine Learning (DML) and Targeted Maximum Likelihood Estimation (TMLE) can debias machine-learning fits, existing neural implementations either rely on "targeted losses" that do not guarantee solving the efficient influence function equation or computationally expensive post-hoc "fluctuations" for multi-parameter settings. We propose Targeted Deep Architectures (TDA), a new framework that embeds TMLE directly into the network's parameter space with no restrictions on the backbone architecture. Specifically, TDA partitions model parameters - freezing all but a small "targeting" subset - and iteratively updates them along a targeting gradient, derived from projecting the influence functions onto the span of the gradients of the loss with respect to weights. This procedure yields plug-in estimates that remove first-order bias and produce asymptotically valid confidence intervals. Crucially, TDA easily extends to multi-dimensional causal estimands (e.g., entire survival curves) by merging separate targeting gradients into a single universal targeting update. Theoretically, TDA inherits classical TMLE properties, including double robustness and semiparametric efficiency. Empirically, on the benchmark IHDP dataset (average treatment effects) and simulated survival data with informative censoring, TDA reduces bias and improves coverage relative to both standard neural-network estimators and prior post-hoc approaches. In doing so, TDA establishes a direct, scalable pathway toward rigorous causal inference within modern deep architectures for complex multi-parameter targets.

We present the first comparative study of two fundamentally distinct feature extraction techniques: Histogram of Oriented Gradients (HOG) and Topological Data Analysis (TDA), for medical image classification using retinal fundus images. HOG captures local texture and edge patterns through gradient orientation histograms, while TDA, using cubical persistent homology, extracts high-level topological signatures that reflect the global structure of pixel intensities. We evaluate both methods on the large APTOS dataset for two classification tasks: binary detection (normal versus diabetic retinopathy) and five-class diabetic retinopathy severity grading. From each image, we extract 26244 HOG features and 800 TDA features, using them independently to train seven classical machine learning models with 10-fold cross-validation. XGBoost achieved the best performance in both cases: 94.29 percent accuracy (HOG) and 94.18 percent (TDA) on the binary task; 74.41 percent (HOG) and 74.69 percent (TDA) on the multi-class task. Our results show that both methods offer competitive performance but encode different structural aspects of the images. This is the first work to benchmark gradient-based and topological features on retinal imagery. The techniques are interpretable, applicable to other medical imaging domains, and suitable for integration into deep learning pipelines.

Understanding temporal patterns in online search behavior is crucial for real-time marketing and trend forecasting. Google Trends offers a rich proxy for public interest, yet the high dimensionality and noise of its time-series data present challenges for effective clustering. This study evaluates three unsupervised clustering approaches, Symbolic Aggregate approXimation (SAX), enhanced SAX (eSAX), and Topological Data Analysis (TDA), applied to 20 Google Trends keywords representing major consumer categories. Our results show that while SAX and eSAX offer fast and interpretable clustering for stable time series, they struggle with volatility and complexity, often producing ambiguous ``catch-all'' clusters. TDA, by contrast, captures global structural features through persistent homology and achieves more balanced and meaningful groupings. We conclude with practical guidance for using symbolic and topological methods in consumer analytics and suggest that hybrid approaches combining both perspectives hold strong potential for future applications.

Dynamic activation (DA) techniques, such as DejaVu and MoEfication, have demonstrated their potential to significantly enhance the inference efficiency of large language models (LLMs). However, these techniques often rely on ReLU activation functions or require additional parameters and training to maintain performance. This paper introduces a training-free Threshold-based Dynamic Activation(TDA) method that leverage sequence information to exploit the inherent sparsity of models across various architectures. This method is designed to accelerate generation speed by 18-25\% without significantly compromising task performance, thereby addressing the limitations of existing DA techniques. Moreover, we delve into the root causes of LLM sparsity and theoretically analyze two of its critical features: history-related activation uncertainty and semantic-irrelevant activation inertia. Our comprehensive analyses not only provide a robust theoretical foundation for DA methods but also offer valuable insights to guide future research in optimizing LLMs for greater efficiency and effectiveness.

Machine learning (ML) on tabular data is ubiquitous, yet obtaining abundant high-quality tabular data for model training remains a significant obstacle. Numerous works have focused on tabular data augmentation (TDA) to enhance the original table with additional data, thereby improving downstream ML tasks. Recently, there has been a growing interest in leveraging the capabilities of generative AI for TDA. Therefore, we believe it is time to provide a comprehensive review of the progress and future prospects of TDA, with a particular emphasis on the trending generative AI. Specifically, we present an architectural view of the TDA pipeline, comprising three main procedures: pre-augmentation, augmentation, and post-augmentation. Pre-augmentation encompasses preparation tasks that facilitate subsequent TDA, including error handling, table annotation, table simplification, table representation, table indexing, table navigation, schema matching, and entity matching. Augmentation systematically analyzes current TDA methods, categorized into retrieval-based methods, which retrieve external data, and generation-based methods, which generate synthetic data. We further subdivide these methods based on the granularity of the augmentation process at the row, column, cell, and table levels. Post-augmentation focuses on the datasets, evaluation and optimization aspects of TDA. We also summarize current trends and future directions for TDA, highlighting promising opportunities in the era of generative AI. In addition, the accompanying papers and related resources are continuously updated and maintained in the GitHub repository at https://github.com/SuDIS-ZJU/awesome-tabular-data-augmentation to reflect ongoing advancements in the field.