- Claude Artifacts Showcase | Share Your AI Creations
The LOR for Claude artifacts . . . - Vertices and Edges – D3 Graph Theory
- DeepSeek – Into the Unknown
- DeepSeek | DeepSeek-V2 | Kaggle
“DeepSeek Prover is an improved open-source language model
for theorem proving in Lean 4. It offers optimized training and
inference processes with state-of-the-art results across multiple
benchmarks.” - [2404.12534] Towards Large Language Models as Copilots for Theorem Proving in Lean
Theorem proving is an important challenge for large language models (LLMs), as formal proofs can be checked rigorously by proof assistants such as Lean, leaving no room for hallucination. Existing LLM-based provers try to prove theorems in a fully autonomous mode without human intervention. In this mode, they struggle with novel and challenging theorems, for which human insights may be critical. In this paper, we explore LLMs as copilots that assist humans in proving theorems. We introduce Lean Copilot, a framework for running LLM inference in Lean. It enables programmers to build various LLM-based proof automation tools that integrate seamlessly into the workflow of Lean users. Using Lean Copilot, we build tools for suggesting proof steps (tactic suggestion), completing intermediate proof goals (proof search), and selecting relevant premises (premise selection) using LLMs. Users can use our pretrained models or bring their own ones that run either locally (with or without GPUs) or on the cloud. Experimental results demonstrate the effectiveness of our method in assisting humans and automating theorem proving process compared to existing rule-based proof automation in Lean. We open source all codes under a permissive MIT license to facilitate further research.
- Mathematicians’ Newest Assistants Are Artificially Intelligent | Scientific American
If you are writing a proof with the help of the Caltech co-pilot, you can click on a button to request new lines of Lean’s programming language to represent the mathematics you are working with. Several options, which Anandkumar calls “tactic suggestions,” will appear on the right-hand side of the screen; you then simply choose whichever option looks most appropriate. If your proof is headed in a direction that has obvious or well-known intermediate conclusions, the co-pilot can also suggest how to complete that trajectory.“There’s no trust issue” with Lean because the software checks the work, says Martin Hairer, a professor of pure mathematics at the Swiss Federal Institute of Technology in Lausanne and at Imperial College London. Still, many academics haven’t adopted it yet. “It’s hard to use because you have to enter all the mathematics as code,” Hairer says. Coding in Lean requires entering details that would be omitted when writing up a paper, he notes, so it might take multiple pages of code to show what’s self-evidently true or obvious.