Lines of Thought in Large Language Models
Rapha\"el Sarfati, Toni J. B. Liu, Nicolas Boull\'e, and Christopher, J. Earls
TL;DR
This paper investigates the statistical properties of the trajectories in the embedding space of large language models, revealing that they cluster along a low-dimensional, non-Euclidean manifold and can be approximated by a simple stochastic model.
Contribution
It introduces a novel analysis of the 'lines of thought' in large language models, showing their low-dimensional structure and proposing a simplified stochastic approximation.
Findings
Trajectories cluster on a low-dimensional, non-Euclidean manifold.
A stochastic equation with few parameters effectively models the trajectories.
Complex model behavior can be reduced to simpler mathematical forms.
Abstract
Large Language Models achieve next-token prediction by transporting a vectorized piece of text (prompt) across an accompanying embedding space under the action of successive transformer layers. The resulting high-dimensional trajectories realize different contextualization, or 'thinking', steps, and fully determine the output probability distribution. We aim to characterize the statistical properties of ensembles of these 'lines of thought.' We observe that independent trajectories cluster along a low-dimensional, non-Euclidean manifold, and that their path can be well approximated by a stochastic equation with few parameters extracted from data. We find it remarkable that the vast complexity of such large models can be reduced to a much simpler form, and we reflect on implications.
Peer Reviews
Decision·ICLR 2025 Poster
- I find the question posed, and the consequent findings very interesting - I really appreciate the development of a linear approximation to the distribution of trajectories.
- One of my biggest gripes with the paper is, while I wanted to be excited about the findings, a recurring question that I had was "why should I care"? It is my opinion that the authors should invest in a motivation for why the reader should care about the presented findings. It's not clear to me what the takeaways are, or more concretely, how we can utilize the observation to develop better LLMs for instance. - A second gripe, which perhaps goes hand-in-hand with my first one, is that I often
- There has been a flurry of works trying to understand the inner workings of LLMs. Therefore, this direction is relevant and interesting. - This work studies this problem from a unique flow-based perspective by studying the dynamics of the embeddings as they evolve in the layers. The perspective is novel to the best of my knowledge and may potentially lead to a new perspective or algorithm to improve interpretability of LLMs.
- While potentially interesting, the paper feels too vague and very high-level without any concrete theoretical or experimental contributions. - No new theoretical contributions are made, other than standard langevin dynamics formulations of their ideas. The projection to lower dimensions and linear approximations are also somewhat too lossy, as the authors note, so it's not clear how well the observations here actually hold in real life. - Experiments seem limited to a few models and as the a
1.The idea of this paper is kind of interesting.
1. the Gaussian assumption seems to not hold in early layers. 2. It is unclear if the same type of paths would hold for larger and more complex model as we already see problems with newer model like LLaMA-3. I think it makes sense to model the intermediate layers with diffusion process but early and last layers might not work not well. 3. The theory here does not lead to any practical predictions. For example, can you use this model to predict next token?
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Taxonomy
TopicsTopic Modeling