Google Does it Again

🌈 Abstract

The article discusses the recent achievements of Google Deepmind's AI models, AlphaProof and AlphaGeometry 2, in solving challenging International Mathematical Olympiad problems. It provides insights into the current state of AI progress in mathematical reasoning and the potential implications for the future development of artificial general intelligence (AGI).

🙋 Q&A

[01] Depth vs Breadth

1. What is the key difference between "depth" and "breadth" in the context of AI systems?

• Depth refers to training AI models to perform one task as well as possible, while breadth refers to training models that can perform various tasks, albeit not as proficiently as depth-focused models.
• The article suggests that current AI systems, including ChatGPT, have sacrificed depth (per-task prowess) for better breadth (ability to perform many tasks, but with average performance).

2. What is the "ChatGPT Fallacy" mentioned in the article?

• The ChatGPT Fallacy refers to the tendency of people to test ChatGPT's capabilities by asking it questions they don't know the answers to, rather than testing it on tasks where they can evaluate the quality of the responses.
• This leads to an overestimation of ChatGPT's capabilities, as its responses may appear impressive even when they are actually average.

[02] From AlphaGo to ChatGPT... and Back

1. How do the AlphaGo and AlphaZero models work, and how do they differ from large language models like ChatGPT?

• AlphaGo and AlphaZero are based on Monte Carlo Tree Search, where the models explore thousands or millions of possible outcomes for each move and choose the one with the highest expected reward.
• These models are focused on depth, excelling at specific tasks like playing Go, but lack the breadth of large language models like ChatGPT.

2. What is the ultimate goal in merging the capabilities of depth-focused models like AlphaGo and the breadth of large language models?

• The article suggests that the ultimate goal is to create an AI system that combines the depth of models like AlphaGo with the breadth of large language models, resulting in a "deep generalizer" that can perform a variety of tasks at a high level.

[03] The Conquest of Maths Reasoning

1. How do the AlphaProof and AlphaGeometry 2 models work, and what are their key capabilities?

• AlphaProof uses an LLM to draft mathematical statements in a formal way, which are then used to train an AlphaZero-like model to prove the theorems.
• AlphaGeometry 2 is a neurosymbolic AI model that combines an LLM (Gemini) with symbolic engines. The LLM suggests "auxiliary constructions" to constrain the problem, and the symbolic engines then compute and verify the solution.
• Both models have achieved silver medalist-level performance on challenging International Mathematical Olympiad problems.

2. What is the significance of the Google Deepmind's research on AlphaProof and AlphaGeometry 2 in the context of AI progress?

• The article suggests that this research exemplifies the next frontier of AI, which is to combine LLM-powered search with reinforcement learning-trained models that excel in depth (task-specific prowess).
• Unlocking this paradigm at scale could lead to the creation of the first "deep generalizer" AI system that can perform a variety of tasks at a high level, akin to human intelligence.