Summary of Geometric Analysis Of Reasoning Trajectories: a Phase Space Approach to Understanding Valid and Invalid Multi-hop Reasoning in Llms, by Javier Marin
Geometric Analysis of Reasoning Trajectories: A Phase Space Approach to Understanding Valid and Invalid Multi-Hop Reasoning in LLMs
by Javier Marin
First submitted to arxiv on: 6 Oct 2024
Categories
- Main: Artificial Intelligence (cs.AI)
- Secondary: Machine Learning (cs.LG)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The proposed approach uses Hamiltonian mechanics to analyze multi-hop reasoning in language models by mapping reasoning chains in embedding spaces to Hamiltonian systems. The function balances reasoning progression (kinetic energy) against question relevance (potential energy). The analysis reveals that valid reasoning shows lower Hamiltonian energy values, representing an optimal trade-off between information gathering and targeted answering. The framework offers complex visualization and quantification methods, but the claimed ability to “steer” or “improve” reasoning algorithms requires more rigorous empirical validation. Nevertheless, the analysis reveals consistent geometric patterns distinguishing valid reasoning, suggesting a promising diagnostic tool for large language models. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper uses special math to understand how language models think. It’s like studying how a car moves on a track. The model is trying to find the right answer by moving through different ideas. The math shows that when the model finds the right answer, it has used the “right” amount of energy. This could be useful for making better language models in the future. |
Keywords
» Artificial intelligence » Embedding
