# Layerwise Recall and the Geometry of Interwoven Knowledge in LLMs

arXiv: https://arxiv.org/abs/2502.10871 · HTML: https://mlsanity.com/paper/2502.10871/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 32 references that are in the map.
- First posted on arXiv 15 Feb 2025.

## Builds on (most cited first, 29 of 29)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Understanding intermediate layers using linear classifier probes](https://mlsanity.com/paper/1610.01644/) (2016)
- [A Survey on Evaluation of Large Language Models](https://mlsanity.com/paper/2307.03109/) (2023)
- [Progress measures for grokking via mechanistic interpretability](https://mlsanity.com/paper/2301.05217/) (2023)
- [A Comprehensive Overview of Large Language Models](https://mlsanity.com/paper/2307.06435/) (2023)
- [Eliciting Latent Predictions from Transformers with the Tuned Lens](https://mlsanity.com/paper/2303.08112/) (2023)
- [Dissecting Recall of Factual Associations in Auto-Regressive Language Models](https://mlsanity.com/paper/2304.14767/) (2023)
- [Mechanistic Interpretability for AI Safety -- A Review](https://mlsanity.com/paper/2404.14082/) (2024)
- [Language Models Represent Space and Time](https://mlsanity.com/paper/2310.02207/) (2023)
- [In-Context Learning Creates Task Vectors](https://mlsanity.com/paper/2310.15916/) (2023)
- [Layer by Layer: Uncovering Hidden Representations in Language Models](https://mlsanity.com/paper/2502.02013/) (2025)
- [AI Alignment: A Comprehensive Survey](https://mlsanity.com/paper/2310.19852/) (2023)
- [Challenges and Applications of Large Language Models](https://mlsanity.com/paper/2307.10169/) (2023)
- [Linearity of Relation Decoding in Transformer Language Models](https://mlsanity.com/paper/2308.09124/) (2023)
- [Linear Representations of Sentiment in Large Language Models](https://mlsanity.com/paper/2310.15154/) (2023)
- [The Clock and the Pizza: Two Stories in Mechanistic Explanation of Neural Networks](https://mlsanity.com/paper/2306.17844/) (2023)
- [Analyzing Transformers in Embedding Space](https://mlsanity.com/paper/2209.02535/) (2022)
- [Rethinking Interpretability in the Era of Large Language Models](https://mlsanity.com/paper/2402.01761/) (2024)
- [Language Models Use Trigonometry to Do Addition](https://mlsanity.com/paper/2502.00873/) (2025)
- [How Large Language Models Encode Context Knowledge? A Layer-Wise Probing Study](https://mlsanity.com/paper/2402.16061/) (2024)
- [Fantastic Semantics and Where to Find Them: Investigating Which Layers of Generative LLMs Reflect Lexical Semantics](https://mlsanity.com/paper/2403.01509/) (2024)
- [Entropy Law: The Story Behind Data Compression and LLM Performance](https://mlsanity.com/paper/2407.06645/) (2024)
- [Investigating Layer Importance in Large Language Models](https://mlsanity.com/paper/2409.14381/) (2024)
- [Transformer Circuit Faithfulness Metrics are not Robust](https://mlsanity.com/paper/2407.08734/) (2024)
- [The representation landscape of few-shot learning and fine-tuning in large language models](https://mlsanity.com/paper/2409.03662/) (2024)
- [Sorted LLaMA: Unlocking the Potential of Intermediate Layers of Large Language Models for Dynamic Inference](https://mlsanity.com/paper/2309.08968/) (2023)

## Built on by (most cited first, 6 of 6)

- [A Survey on Latent Reasoning](https://mlsanity.com/paper/2507.06203/) (2025)
- [Large Language Models Show Signs of Alignment with Human Neurocognition During Abstract Reasoning](https://mlsanity.com/paper/2508.10057/) (2025)
- [Geometry of Human Perceptual Domains Emerges Transiently in LLM Representations](https://mlsanity.com/paper/2605.27970/) (2026)
- [From Fact Overwriting to Knowledge Evolution: Causal Editing via On-Policy Self-Distillation](https://mlsanity.com/paper/2605.28303/) (2026)
- [Shared Doubt: Zero-Shot Cross-Lingual Confidence Estimation for Language Models](https://mlsanity.com/paper/2605.31220/) (2026)
- [Manifold Bandits: Bayesian Curriculum Learning over the Latent Geometry of Large Language Models](https://mlsanity.com/paper/2606.19750/) (2026)

## Abstract (arXiv)

This study explores how large language models (LLMs) encode interwoven scientific knowledge, using chemical elements and LLaMA-series models as a case study. We identify a 3D spiral structure in the hidden states that aligns with the conceptual structure of the periodic table, suggesting that LLMs can reflect the geometric organization of scientific concepts learned from text. Linear probing reveals that middle layers encode continuous, overlapping attributes that enable indirect recall, while deeper layers sharpen categorical distinctions and incorporate linguistic context. These findings suggest that LLMs represent symbolic knowledge not as isolated facts, but as structured geometric manifolds that intertwine semantic information across layers. We hope this work inspires further exploration of how LLMs represent and reason about scientific knowledge, particularly in domains such as materials science.