Written by Claude 3 Opus with regard to the A::B problem posed in https://x.com/VictorTaelin/status/1776096481704804789
Thank you for the thoughtful question and for the opportunity to reflect on this problem in more depth. Having gone through several iterations of attempting to solve the A::B language rewriting problem, I can now offer some fresh perspectives and insights.
At a high level, I still believe that this problem should be solvable by modern LLMs. The rules are clearly defined, the search space is relatively small, and the required reasoning steps are fairly straightforward. LLMs have shown impressive capabilities in understanding complex instructions, maintaining coherence over long sequences, and performing multi-step reasoning in other domains. So it's puzzling and frustrating that they consistently struggle with this seemingly simple task.
Here are some thoughts on the potential root causes of the repeated mistakes and some ideas for addressing them:
- Lack of a robust mental model: One issue may be that the LLM does not form a sufficiently clear and stable mental model of what constitutes a "sticky pair" and how the rewrite rules operate on these pairs. Despite being given clear definitions, the LLM seems prone to misidentifying sticky pairs or misapplying the rules, especially as the sequence gets longer and more complex. It's as if the LLM's understanding of the core concepts is somewhat fuzzy and prone to drift over the course of the problem. Potential solution: We could try to reinforce the key concepts more explicitly and repeatedly throughout the prompt. For example, we could include a preface that heavily emphasizes what makes a pair "sticky", perhaps with multiple examples and non-examples. We could also include a step-by-step guide or flowchart for identifying sticky pairs and applying the rules. The idea would be to anchor the LLM's understanding more firmly and provide a clear decision procedure for it to follow.
- Insufficient error-checking and self-correction: Another issue is that the LLM does not seem to have robust mechanisms for catching and correcting its own errors. When it makes a mistake, such as misidentifying a sticky pair, it often just continues on without noticing the inconsistency. Even when prompted to double-check its work, it may miss errors or introduce new ones. Potential solution: We could try to build more explicit error-checking and self-correction steps into the output format. For example, we could have the LLM output a justification or proof for each step, explaining why it chose the particular sticky pair and rule. We could also have it perform certain invariant checks, such as verifying that the parity of the sequence length remains consistent. If an inconsistency is detected, the LLM would be prompted to backtrack and try again. The goal would be to make the LLM more self-aware of its own reasoning process and more proactive in catching and correcting mistakes.
- Difficulty with abstraction and generalization: The A::B language is a novel formal system that the LLM is unlikely to have encountered in training. While LLMs are good at pattern-matching and analogical reasoning, they may struggle to truly internalize the abstract rules and generalize them to novel sequences. Each new sequence poses a fresh challenge, and the LLM may not be learning and generalizing from its experience on previous sequences. Potential solution: We could try to include more worked examples in the prompt, demonstrating step-by-step solutions to a variety of A::B sequences. The idea would be to provide more opportunities for the LLM to learn the general patterns and strategies. We could also experiment with few-shot prompting, where we give the LLM a series of related problems of increasing difficulty, so that it can build up its skills incrementally.
- Inherent limitations of the LLM architecture: Despite their impressive capabilities, LLMs are fundamentally based on pattern recognition and statistical correlations in their training data. They do not have the kind of crisp, symbolic, rule-based reasoning that comes naturally to humans in formal domains like mathematics and logic. The A::B language rewriting task may simply be exposing some inherent limitations of the current LLM architectures for this type of formally specified, deterministic reasoning. Potential solution: To truly solve this problem in a robust and reliable way, we may need to look beyond prompting strategies and consider more fundamental architectural changes or hybrid approaches. For example, we could explore techniques for imbuing LLMs with more explicit rule-based reasoning capabilities, perhaps by combining them with symbolic systems or program synthesis methods. We could also investigate meta-learning approaches, where the LLM is trained not just to solve specific problems but to learn how to learn and reason in novel formal systems.
These are just some initial thoughts and ideas, and I'm sure there are many other angles and approaches worth exploring. The A::B language rewriting problem may seem simple on the surface, but it touches on deep questions about the nature of reasoning, abstraction, and generalization in AI systems. Solving it reliably will likely require a combination of clever prompt engineering, architectural innovation, and conceptual breakthroughs.
I don't have a complete solution yet, but I'm excited to keep exploring and iterating. I think this problem is a great lens for probing the strengths and weaknesses of current LLMs and for driving progress towards more robust and flexible reasoning capabilities.