Vincent Martin

h-index39
2papers
5,465citations

2 Papers

6.1CLFeb 17, 2023
Complex QA and language models hybrid architectures, Survey

Xavier Daull, Patrice Bellot, Emmanuel Bruno et al.

This paper reviews the state-of-the-art of large language models (LLM) architectures and strategies for "complex" question-answering with a focus on hybrid architectures. LLM based chatbot services have allowed anyone to grasp the potential of LLM to solve many common problems, but soon discovered their limitations for complex questions. Addressing more specific, complex questions (e.g., "What is the best mix of power-generation methods to reduce climate change ?") often requires specialized architectures, domain knowledge, new skills, decomposition and multi-step resolution, deep reasoning, sensitive data protection, explainability, and human-in-the-loop processes. Therefore, we review: (1) necessary skills and tasks for handling complex questions and common LLM limits to overcome; (2) dataset, cost functions and evaluation metrics for measuring and improving (e.g. accuracy, explainability, fairness, robustness, groundedness, faithfulness, toxicity...); (3) family of solutions to overcome LLM limitations by (a) training and reinforcement (b) hybridization, (c) prompting, (d) agentic-architectures (agents, tools) and extended reasoning.

1.2LOOct 4, 2016
The Lax-Milgram Theorem. A detailed proof to be formalized in Coq

François Clément, Vincent Martin

To obtain the highest confidence on the correction of numerical simulation programs implementing the finite element method, one has to formalize the mathematical notions and results that allow to establish the soundness of the method. The Lax-Milgram theorem may be seen as one of those theoretical cornerstones: under some completeness and coercivity assumptions, it states existence and uniqueness of the solution to the weak formulation of some boundary value problems. The purpose of this document is to provide the formal proof community with a very detailed pen-and-paper proof of the Lax-Milgram theorem.