# LLM as an n-dimensional Object in n-dimensional Space

## ๐ Abstract

The article discusses the conceptualization of language models as n-dimensional objects in an n-dimensional space, and how understanding a prompt can be seen as an approximation of the surfaces of such an object. It also explores the role of the shape of the surface in ensuring predictive capability, and the generative abilities provided by the ability to move along the surface. The article raises the question of whether a language model alone is adequate for the emergence of cognition and reasoning.

## ๐ Q&A

### [01] Language Models as n-Dimensional Objects

**1. What is the key idea behind conceptualizing language models as n-dimensional objects?**

- Language models, regardless of their architecture (symbolic or neural network), can be conceptualized as n-dimensional objects in an n-dimensional space.
- These objects are initially constructed using training datasets (sequences).
- "Understanding" a prompt can be considered as an approximation of the surfaces of such an n-dimensional object.

**2. How are fine-tuning and retraining related to the language model's surface?**

- Fine-tuning and retraining are considered as modifications of the surface of the n-dimensional object.

**3. What is the role of the shape of the surface in a language model?**

- The shape of the surface of the n-dimensional object ensures the model's predictive capability.
- The generative abilities of the model are provided by the ability to move along the surface of the n-dimensional object from any point to other points in any permissible direction.

### [02] Adequacy of Language Models for Cognition and Reasoning

**1. What is the key question raised about the adequacy of language models for cognition and reasoning?**

- The article questions whether a language model alone is adequate for the emergence of cognition and reasoning. It suggests that mathematically, this may not be the case.

**2. What is the implication of the article's conclusion regarding language models and cognition/reasoning?**

- The article suggests that the selection of points on the surface of the n-dimensional object should not be determined solely by the language model itself, but rather by some generalization derived from it. This raises the question of whether a language model alone is sufficient for the emergence of cognition and reasoning.