This survey reviews the emerging field of Agentic Large Language Models (LLMs), defining them as models capable of reasoning, acting, and interacting. It organizes the literature into a taxonomy comprising three key pillars: reasoning enhancements like self-reflection and chain-of-thought; acting capabilities involving tool use, robotics, and specialized assistants; and social interaction within multi-agent environments. The paper explores applications in high-impact domains such as medicine and scientific research while outlining a future research agenda focused on safety, emergent behaviors, and the use of agent-generated data for training.

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This reference document contains a sample final examination for a MATH 102 course, accompanied by detailed handwritten solutions. The material covers a broad range of algebraic and pre-calculus concepts, including analyzing function properties, solving logarithmic and exponential equations, and graphing trigonometric functions. It also features applied word problems involving rates of change, compound interest, and piecewise tax functions. The first page presents eleven specific problems, while the subsequent pages demonstrate step-by-step methods for solving each equation and inequality, serving as a comprehensive study guide for exam preparation.

Maths papers

This reference presents PT-LiRPA, a novel neural network verification framework that combines Linear Relaxation-based Perturbation Analysis (LiRPA) with statistical sampling. By utilizing Extreme Value Theory to estimate tight intermediate reachable sets, the method significantly reduces the over-approximation errors typical of formal verification tools. PT-LiRPA provides probabilistic guarantees on verification soundness while maintaining low computational costs. Extensive experiments demonstrate that this approach tightens output bounds and outperforms state-of-the-art verifiers on complex benchmarks, offering robust certification in scenarios where traditional deterministic methods fail.

Probabilistically Tightened Linear Relaxation-based PerturbationAnalysis for Neural Network Verification

This survey explores Agentic Large Language Models (LLMs), defining them as systems capable of reasoning, acting, and interacting to achieve goals. The authors organize research into three core categories: reasoning techniques like self-reflection and Chain of Thought; acting through tool use and robotics; and interaction within multi-agent simulations. The paper highlights how these capabilities form a virtuous cycle that generates new training data and improves performance. Additionally, it outlines a research agenda addressing critical challenges in safety, ethics, and reliability as LLMs evolve into autonomous assistants for domains like science and medicine.

DOI: https://doi.org/10.1613/jair.1.18675

Agentic Large Language Models

This book provides a comprehensive introduction to the foundations of Large Language Models (LLMs). It outlines the core concepts and techniques driving modern NLP, starting with pre-training paradigms and architectures like BERT. It explores generative models, scaling laws, and long-sequence modeling. Key sections detail prompting strategies such as chain-of-thought, alongside alignment methods including instruction fine-tuning and Reinforcement Learning from Human Feedback (RLHF). The text also covers efficient inference techniques, decoding algorithms, and optimization strategies, serving as an educational resource for understanding the mechanisms behind intelligent language systems.

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