On the Origins of Linear Representations in Large Language Models
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909129762668544 |
|---|---|
| author | Jiang, Yibo Rajendran, Goutham Ravikumar, Pradeep Aragam, Bryon Veitch, Victor |
| author_facet | Jiang, Yibo Rajendran, Goutham Ravikumar, Pradeep Aragam, Bryon Veitch, Victor |
| contents | Recent works have argued that high-level semantic concepts are encoded "linearly" in the representation space of large language models. In this work, we study the origins of such linear representations. To that end, we introduce a simple latent variable model to abstract and formalize the concept dynamics of the next token prediction. We use this formalism to show that the next token prediction objective (softmax with cross-entropy) and the implicit bias of gradient descent together promote the linear representation of concepts. Experiments show that linear representations emerge when learning from data matching the latent variable model, confirming that this simple structure already suffices to yield linear representations. We additionally confirm some predictions of the theory using the LLaMA-2 large language model, giving evidence that the simplified model yields generalizable insights. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_03867 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Origins of Linear Representations in Large Language Models Jiang, Yibo Rajendran, Goutham Ravikumar, Pradeep Aragam, Bryon Veitch, Victor Computation and Language Machine Learning Recent works have argued that high-level semantic concepts are encoded "linearly" in the representation space of large language models. In this work, we study the origins of such linear representations. To that end, we introduce a simple latent variable model to abstract and formalize the concept dynamics of the next token prediction. We use this formalism to show that the next token prediction objective (softmax with cross-entropy) and the implicit bias of gradient descent together promote the linear representation of concepts. Experiments show that linear representations emerge when learning from data matching the latent variable model, confirming that this simple structure already suffices to yield linear representations. We additionally confirm some predictions of the theory using the LLaMA-2 large language model, giving evidence that the simplified model yields generalizable insights. |
| title | On the Origins of Linear Representations in Large Language Models |
| topic | Computation and Language Machine Learning |
| url | https://arxiv.org/abs/2403.03867 |