Verifying textual claims against structured tabular data is a critical yet challenging task in Natural Language Processing with broad real-world impact. While recent advances in Large Language Models (LLMs) have enabled significant progress in table fact-checking, current solutions remain inaccessible to non-experts. We introduce T-REX (T-REX: Table -- Refute or Entail eXplainer), the first live, interactive tool for claim verification over multimodal, multilingual tables using state-of-the-art instruction-tuned reasoning LLMs. Designed for accuracy and transparency, T-REX empowers non-experts by providing access to advanced fact-checking technology. The system is openly available online.

Large language models (LLMs) have demonstrated impressive mathematical reasoning capabilities but remain susceptible to hallucinations--plausible yet incorrect statements--particularly in complex domains requiring rigorous logical deduction. Current approaches to improve reliability often neglect the logical consistency of intermediate reasoning steps, focusing primarily on final answer verification. We propose a structured self-consistency (SC) framework that systematically evaluates factual concordance across both intermediate reasoning steps and final outputs, thereby creating a hierarchical verification mechanism for mathematical reasoning. Our framework employs a probabilistic formulation that quantifies consistency through ensemble agreement, entropy minimization, and structural isomorphism detection in reasoning graphs. We evaluate our approach on three fundamental mathematical tasks: formal theorem proving, symbolic transformation, and numerical computation. Experimental results demonstrate that our method achieves significant improvements over baseline approaches: proof validity increases by 8.3% ( p < 0. 01), symbolic reasoning accuracy by 9.6%, and numerical stability by 42.8% while reducing computational overhead by 56.3%. Further analysis reveals that our structured SC framework exhibits strong correlation with human expert evaluation ( ρ = 0 .87),

This book provides a comprehensive introduction to the foundational concepts of machine learning (ML) and deep learning (DL). It bridges the gap between theoretical mathematics and practical application, focusing on Python as the primary programming language for implementing key algorithms and data structures. The book covers a wide range of topics, including basic and advanced Python programming, fundamental mathematical operations, matrix operations, linear algebra, and optimization techniques crucial for training ML and DL models. Advanced subjects like neural networks, optimization algorithms, and frequency domain methods are also explored, along with real-world applications of large language models (LLMs) and artificial intelligence (AI) in big data management. Designed for both beginners and advanced learners, the book emphasizes the critical role of mathematical principles in developing scalable AI solutions. Practical examples and Python code are provided throughout, ensuring readers gain hands-on experience in applying theoretical knowledge to solve complex problems in ML, DL, and big data analytics.

Based on the numerical manifold method principle, we developed a mathematical framework of a neural network manifold: Deep Manifold and discovered that neural networks: 1) is numerical computation combining forward and inverse; 2) have near infinite degrees of freedom; 3) exponential learning capacity with depth; 4) have self-progressing boundary conditions; 5) has training hidden bottleneck. We also define two concepts: neural network learning space and deep manifold space and introduce two concepts: neural network intrinsic pathway and fixed point. We raise three fundamental questions: 1). What is the training completion definition; 2). where is the deep learning convergence point (neural network fixed point); 3). How important is token timestamp in training data given negative time is critical in inverse problem.

Abstract: We investigate the general properties of the dimensional reduction of the Dirac theory, formulated in a Minkowski spacetime with an arbitrary number of spatial dimensions. This is done by applying Hadamard's method of descent, which consists in conceiving low-dimensional theories as a specialization of high-dimensional ones that are uniform along the additional space coordinate. We show that the Dirac equation reduces to either a single Dirac equation or two decoupled Dirac equations, depending on whether the higher-dimensional manifold has even or odd spatial dimensions, respectively. Abstract: Sparse reduced rank regression is an essential statistical learning method. In the contemporary literature, estimation is typically formulated as a nonconvex optimization that often yields to a local optimum in numerical computation. Yet, their theoretical analysis is always centered on the global optimum, resulting in a discrepancy between the statistical guarantee and the numerical computation.

Ankit currently works as a Senior Research Scientist at Uber AI Labs, the machine learning research arm of Uber. His work primarily involves the application of Deep Learning methods to a variety of Uber's problems ranging from forecasting, food delivery to self driving cars. Previously, he has worked in variety of data science roles at Bank of America, Facebook and other startups. Additionally, he has been a featured speaker in many of the top AI conferences and universities across US including UC Berkeley, OReilly AI conference etc. He completed his MS from UC Berkeley and BS from IIT Bombay (India).

TensorFlow is Google's brain child for machine learning and high performance numerical computation. Simply put, TensorFlow is an open source AI framework to perform complex numerical computations in large volumes using data-flow graphs and machine learning. TensorFlow operates on deep neural networks. We all have been using TensorFlow without even realizing its presence: from Google Photos to Google voice, these applications operate on large clusters of Google hardware.

TensorFlow is Google's brain child for machine learning and high performance numerical computation. Simply put, TensorFlow is an open source AI framework to perform complex numerical computations in large volumes using data-flow graphs and machine learning. TensorFlow operates on deep neural networks. We all have been using TensorFlow without even realizing its presence: from Google Photos to Google voice, these applications operate on large clusters of Google hardware.

How much faster does the application run when implemented with NumPy instead of pure Python? The purpose of this article is to begin to explore the improvements you can achieve by using these libraries. Python has a design philosophy that stresses allowing programmers to express concepts readably and in fewer lines of code. This philosophy makes the language suitable for a diverse set of use cases: simple scripts for web, large web applications (like YouTube), scripting language for other platforms (like Blender and Autodesk's Maya), and scientific applications in several areas, such as astronomy, meteorology, physics, and data science. It is technically possible to implement scalar and matrix calculations using Python lists.

One of the byproducts of our digitally transformed world is the accumulation of large quantities of data. Online transactions, medical records, social media posts, emails, instant messages, and connected sensors are just a few examples of the kinds of data being captured and stored on a daily basis. Scientists and research organizations have been exploring how to leverage big data for artificially intelligent applications since the 1970s. Nonetheless, until fairly recently, the big data issues for enterprises remained how to store it cost effectively, how to retrieve it efficiently when needed, and how to protect it from unauthorized access. The growth of the cloud opened up a whole new realm of cost-effective data storage and retrieval solutions, but big data was still largely perceived by enterprises as a passive asset that did not contribute significantly to their bottom lines.