# The Information of Large Language Model Geometry

arXiv: https://arxiv.org/abs/2402.03471 · HTML: https://mlsanity.com/paper/2402.03471/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 27 references that are in the map.
- First posted on arXiv 1 Feb 2024.

## Builds on (most cited first, 19 of 19)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [Deep Learning and the Information Bottleneck Principle](https://mlsanity.com/paper/1503.02406/) (2015)
- [Transformers learn in-context by gradient descent](https://mlsanity.com/paper/2212.07677/) (2022)
- [Explaining Neural Scaling Laws](https://mlsanity.com/paper/2102.06701/) (2021)
- [Language Modeling Is Compression](https://mlsanity.com/paper/2309.10668/) (2023)
- [The Quantization Model of Neural Scaling](https://mlsanity.com/paper/2303.13506/) (2023)
- [A Theory for Emergence of Complex Skills in Language Models](https://mlsanity.com/paper/2307.15936/) (2023)
- [LLMZip: Lossless Text Compression using Large Language Models](https://mlsanity.com/paper/2306.04050/) (2023)
- [Information Theory with Kernel Methods](https://mlsanity.com/paper/2202.08545/) (2022)
- [Diff-eRank: A Novel Rank-Based Metric for Evaluating Large Language Models](https://mlsanity.com/paper/2401.17139/) (2024)
- [Matrix Information Theory for Self-Supervised Learning](https://mlsanity.com/paper/2305.17326/) (2023)
- [Information Flow in Self-Supervised Learning](https://mlsanity.com/paper/2309.17281/) (2023)

## Built on by (most cited first, 5 of 5)

- [Token embeddings violate the manifold hypothesis](https://mlsanity.com/paper/2504.01002/) (2025)
- [Scaling Towards the Information Boundary of Instruction Sets: The Infinity Instruct Subject Technical Report](https://mlsanity.com/paper/2507.06968/) (2025)
- [REMA: A Unified Reasoning Manifold Framework for Interpreting Large Language Model](https://mlsanity.com/paper/2509.22518/) (2025)
- [Towards Compositional Generalization of LLMs via Skill Taxonomy Guided Data Synthesis](https://mlsanity.com/paper/2601.03676/) (2026)
- [TokenBlowUp: Resolving Representational Singularities in LLM Token Spaces via Monoidal Transformations](https://mlsanity.com/paper/2507.19747/) (2025)

## Abstract (arXiv)

This paper investigates the information encoded in the embeddings of large language models (LLMs). We conduct simulations to analyze the representation entropy and discover a power law relationship with model sizes. Building upon this observation, we propose a theory based on (conditional) entropy to elucidate the scaling law phenomenon. Furthermore, we delve into the auto-regressive structure of LLMs and examine the relationship between the last token and previous context tokens using information theory and regression techniques. Specifically, we establish a theoretical connection between the information gain of new tokens and ridge regression. Additionally, we explore the effectiveness of Lasso regression in selecting meaningful tokens, which sometimes outperforms the closely related attention weights. Finally, we conduct controlled experiments, and find that information is distributed across tokens, rather than being concentrated in specific "meaningful" tokens alone.